[abstract] [pdf] [Movie: relaminarization] [Movie: transitional]

A weakly nonlinear approach is described to identify the couple of oblique waves capable to optimally excite transition to turbulence in a plane shear flow. Optimal oblique wave pairs are found to exist in a very narrow wavenumber range – demonstrating the strong selectivity of the identified mechanism – and lead to rapid breakdown past a well defined threshold value of the disturbance amplitude. Direct numerical simulations of the Navier-Stokes equations corroborate the weakly nonlinear results.

[abstract] [pdf]

Background: Aim of the work is to achieve a chemico-physical characterisation of the interfacial properties between Silicone oils (SOs) and aqueous solutions, in the presence of surfactant biomolecules, possibly responsible for emulsion formation after vitrectomy. Methods: The interfacial tension (IT) and the interfacial dilational viscoelasticity (DV) were measured for the interface between SO (Siluron1000) and serum proteins (albumin and γ-globulins) at various concentrations in a Dulbecco alkaline buffer. Similar measurements were conducted on whole human blood serum (WHBS) solutions. The equilibrium IT value is relevant for the onset of emulsification and the DV influences the stability of an emulsion, once formed. The study is complemented by preliminary emulsification tests. Results: When proteins are dissolved in the aqueous solution, the rheological properties of the interface change. The IT decreases significantly for physiologically protein concentrations and the DV modulus achieves high values, even for small proteins concentrations. The emulsification tests confirm that, in the presence of proteins, emulsions are stable on the time scale of months. Conclusions: The measured values of IT in the presence of serum proteins are compatible with the promotion of droplets formation, which, in addition, are expected to be stable against coalescence, owing to the large values of the DV modulus. This is confirmed by the emulsification tests. Adsorption of biomolecules at the interface with the SO is, therefore, likely to play an important role in the generation of an emulsion. These findings are relevant to identify strategies to avoid or control the formation of emulsions in eyes.

[abstract]

The aerodynamic efficiency of turbomachinery blades is pro- foundly affected by the occurrence of laminar-turbulent transi- tion in the boundary layer since skin friction and losses rise for the turbulent state. Depending on the free-stream turbulence level, we can identify different paths towards a turbulent state. The present study uses direct numerical simulation as the pri- mary tool to investigate the flow behaviour of the low-pressure turbine blade. The computational set-up was designed to follow the experiments by Lengani & Simoni [1]. In the simulations, the flow past only one blade is computed, with periodic boundary conditions in the cross-flow directions to account for the cascade. Isotropic homogeneous free-stream turbulence is prescribed at the inlet. The free-stream turbulence is prescribed as a superpo- sition of Fourier modes with a random phase shift. Two levels of the free-stream turbulence intensity were simulated (Tu = 0.19% and 5.2%), with the integral length scale being 0.167c, at the leading edge. We observed that in case of low free-stream turbu- lence on the suction side, the Kelvin–Helmholz instability dom- inated the transition process and full-span vortices were shed from the separation bubble. Transition on the suction side pro- ceeded more rapidly in the high-turbulence case, where streaks broke down into turbulent spots and caused bypass transition. On the pressure side, we have identified the appearance of longi- tudinal vortical structures, where increasing the turbulence level gives rise to more longitudinal structures. We note that these vortical structures are not produced by Görtler instability.

[link]

[abstract] [pdf] [link]

*Purpose:* Optimal surgical use of gas in Descemets membrane endothelial keratoplasty (DMEK) is currently unknown. We investigate how positioning, gas fill and anterior chamber size influence bubble configuration and graft coverage.

*Methods:* We use a mathematical model to study the bubble shape and graft coverage in eyes of varying anterior chamber depths (ACD). The governing equations are solved numerically using the open source software OpenFOAM. Numerical results are validated clinically so that clinical gas fill measures can be correlated to numerical results providing gas-graft coverage information otherwise clinically inaccessible.

*Results:* In a phakic eye (ACD = 2.65 mm) with a gas fill of 35%, graft contact ranges 35%-38% depending on positioning and increases to 85%-92% with a 70% fill. In con- trast, positioning of a pseudophakic eye (ACD = 4.35) with a gas fill of 35% results in graft contact ranges 8%-52%, increasing to 63%-94% with a 70% fill. We present cover- age of grafts as a function of parameters that are available to aid clinicians with effective gas use. The differences between air and SF6 results are negligible. Interestingly, a very thin central patch of aqueous humour within the gas bubble is found in some cases.

*Conclusions:* Graft coverage in phakic eyes (ACD ≤ 3 mm) is dominated by the gas fill and less sensitive to patient positioning. In pseudophakic eyes with larger values of ACD, the graft coverage depends both on gas fill and patient positioning with positioning even more important as ACD increases.

[link]

[abstract] [pdf]

*Purpose:* Corneal endothelial cell loss is one of the possible complications associated with the phakic iris-fixated intraocular lenses (PIOL) implantation. We postulate that this might be connected to the alteration of corneal metabolism secondary to the lens implantation.

*Methods:* A mathematical model of transport and consumption/production of metabolic species in the cornea is proposed, coupled with a model of aqueous flow and transport of metabolic species in the anterior chamber.

*Results:* Results are presented both for open and closed eyelids. We show that in the presence of a PIOL glucose availability at the corneal endothelium decreases significantly during sleeping.

*Conclusions:* Implantation of a PIOL significantly affects nutrient transport processes to the corneal endothelium especially during sleeping. It must still be verified whether this finding has a clinical relevance.

[abstract] [pdf]

Shape optimization is a very time-consuming and expensive task, especially if experimental tests need to be performed. To overcome the challenges of geometry optimization, the industry is increasingly relying on numerical simulations. This kind of problems typically involves the interaction of three main applications: a solid modeler or shape morpher, a multi-physics solver, and an optimizer. In this manuscript, we present a shape optimization framework entirely based on open-source tools, where we take an initial geometry, and we manipulate it using the MiMMO library, the multi-physics simulations are performed using OpenFOAM, and the optimization loop is controlled with Dakota. To demonstrate the usability and flexibility of the proposed framework, we test it in a practical case related to the naval industry, where we aim at optimizing the shape of a bulbous bow in order to minimize the hydrodynamic resistance. To tackle this problem, we first validate the solver and calibrate the numerical model using a reference geometry for which experimental data are available. After having found the ideal mesh and solver parameters, we setup the optimization loop. As design variables, we consider the protrusion and immersion of the bulbous bow, and we use Surrogate- Based Optimization to minimize the hydrodynamic resistance. Additionally, we highlight the logic behind the choices made, we give a few guidelines on how to deal with some problematic issues encountered during the optimization loop (e.g., sampling, interpolation techniques, infilling, the effect of numerical noise), and we compare the output of the meta-model with the outcome of high-fidelity simulations.

[abstract] [pdf] Natali, Repetto, Tweedy, Williamson & Pralits

The conditions under which rhegmatogenous retinal detachment occurs are poorly understood, which hampers the success rates of surgery. Fluid dy- namical effects play a major role, and in this paper we analyse the tendency for the retina to detach further in both the case of a free flap giant reti- nal tear (GRT) and in the case of a retinal hole (RH). For this purpose we use a mathematical model to investigate the interaction between the fluid flow and the detached retina during saccadic eye movements. The governing equations are solved numerically using a code developed ad hoc. An idealised two-dimensional geometry is used and realistic values of almost all governing parameters used are taken from the literature. For the cases of both GRT and a RH we investigate the tendency for the detachment to progress, analysing different lengths of the detached retina, different attachment angles and, in the case of a RH, different hole diameters. We find that in both cases in- creasing the length of the detached retina increases the tendency for further detachment, while in the case of a hole, changing its diameter has little or no effect. We also find the existence of an attachment angle that maximises the tendency to detach, and the model indicates that RHs are more prone to de- tach further than GRTs. In spite of the fact that the model is highly idealised the results agree qualitatively well with the available clinical evidence.

doi:10.1115/1.4040588

[abstract] [pdf]

Iris–fixated aphakic intraocular lenses (IFIOL) are used in cataract surgery, when more common intraocular lenses cannot be adopted because of the absence of capsular bag support. These lenses can be implanted either on the posterior or the anterior surface of the iris. In this work we study whether one of these options is preferable over the other from the mechanical point of view. In particular, we focus on the forces that the IFIOL transmits to the iris, which are associated with the risk of lens dislocation. We study the problem numerically and consider aqueous flow induced by saccadic rotations in the cases of an IFIOL in the anterior and posterior side of the iris. The IFIOL considered is the Artisan Aphakia +30.0 D lens (IFIOL) produced by Ophtec BV. We perform the simulations in OpenFOAM. We find that the forces transmitted by the aphakic IFIOL to the iris are significantly higher in the case of posterior implantation. This suggests that lens implantation on the posterior surface of the iris might be associated with a higher risk of lens dislocation, when an inadequate amount of iris tissue is enclavated during implantation.

[abstract] [pdf]

One of the possible risks associated with the implant of iris-fixated phakic intraocular lenses (pIOL) is loss of corneal endothelial cells. We hypothesize that this might be due to alterations in corneal metabolism secondary to the lens implantation. To verify the feasibility of this assumption, we propose a mathematical model of the transport and di usion of metabolic species in the anterior chamber and the cornea, coupled to a model of aqueous flow. Results are obtained both with and without the pIOL in the case of closed eyelids. The results suggest that glucose availability may be significantly reduced at the corneal endothelium. However, it must still be verified whether this finding has clinical relevance.

[abstract] [pdf]

The formation and stability of emulsions in vitrectomized eyes is linked to the properties of the silicone oil-aqueous humor interface, in particular the surface tension. In the presence of natural surfactants, such as serum and plasma, the value of the surface tension is likely to change, but little quantitative information is presently available. To this end, we perform accurate experiments measuring the interfacial properties of the Siluron 1000 (Fluoron GmbH, Ulm, Germany) silicone oil with an aqueous solution in the presence of endogenous-like proteins. It is found that the surface tension is significantly reduced when physiologically realistic concentrations are used. Moreover, the values obtained for the dilational viscoelastic modulus are compatible with the formation of stable emulsions.

doi.org/10.1007/s00162-018-0454-4

[abstract] [pdf]

Flow control has been the subject of numerous experimental and theoretical works. In this numerical study, we analyse full-order, optimal controllers for large dynamical systems in presence of multiple actuators and sen- sors. We start from the original technique proposed by Bewley, Luchini & Pralits, Meccanica, 2016, the adjoint of the direct-adjoint (ADA) algorithm. The algorithm is iterative and allows bypassing the solution of the algebraic Riccati equation associated with the optimal control problems, typically unfeasible for large systems. We extend ADA into a more generalized framework that includes the design of multi-input, coupled controllers and robust controllers based on the H∞ framework. The full-order controllers do not require any preliminary step of model reduction or low-order approximation: this feature allows to pre-assess the optimal performances of an actuated flow without relying on any estimation process or further hypothesis. We show that the algorithm outperforms analogous technique, in terms of convergence performances considering two numerical cases: a distributed system and the linearized Kuramoto-Sivashinsky equation, mimicking a full three-dimensional control setup. For the ADA algorithm we find excellent scalability with the number of inputs (actuators) in terms of convergence to the solution, making the method a viable way for full-order controller design in complex settings.

[abstract]

It has come to the attention of the authors that the aforementioned paper contains a typing error in Equation 3. Instead of reading(Formula Presented.)Equation 3 should read:(Formula Presented.).

[abstract] [pdf] [abstract]

Flow in the anterior chamber of the eye oc- curs in response to the production and drainage of aque- ous humor and also due to buoyancy effects produced y thermal gradients. Phakic intraocular lenses (pIOLs) are inserted in the eyes of patients to correct refractive errors. Their presence has a dramatic effect on the cir- culation of the aqueous humor, resulting a very different flow in the anterior chamber, the effects of which have not been extensively investigated. In this article we use a simplified mathematical model to analyse the flow, in order to assess the effect of the implanted lens on the pressure drop required to drive the flow and also the wall shear stress experienced by the corneal endothelial cells and the cells of the iris. A high pressure drop could result in an increased risk of glaucoma, whilst raised shear stress on the cornea could result in a reduction in the density of endothelial cells there and on the iris it could result in the detachment of pigment cells, which block the outflow of the eye, also leading to glaucoma. Our results show that, although the presence of the lens causes significant differences in the flow topology and direction, the typical magnitudes of the shear stress are not significantly changed from the natural case.

[abstract] [pdf]

This article investigates the structural stability and sensitivity properties of the confined turbulent wake behind an elongated D-shaped cylinder of aspect-ratio 10 at Re = 32000. The stability analysis is performed by linearising the incompressible Navier-Stokes equations around the numerically computed and the experimentally measured mean flows. We found that the vortex-shedding frequency is very well captured by the leading unstable global mode, espe- cially when the additional turbulent diffusion is modelled in the stability equations by means of a frozen eddy-viscosity approach. The sensitivity maps derived from the computed and the measured mean flows are then compared, showing a good qualitative agreement. The careful inspection of their spatial structure highlights that the highest sensitivity is attained not only across the recirculation bubble but also at the body blunt-edge, where tiny pockets of maximum re- ceptivity are found. The impact of the turbulent diffusion on the obtained results is investigated. Finally, we show how the knowledge of the unstable adjoint global mode of the linearised mean-flow dynamics can be exploited to design an active feedback control of the unsteady turbulent wake, which leads, under the adopted numerical framework, to completely suppress its low-frequency oscillation.

[abstract] [pdf]

The modal and nonmodal linear stability of the flow in a microchannel with either one or both walls coated with a superhydrophobic material is studied. The topography of the bounding wall(s) has the shape of elongated micro-ridges with arbitrary alignment with respect to the direction of the mean pressure gradient. The superhydrophobic walls are modelled using the Navier slip condition through a slip-tensor, and the results depend parametrically on the slip-length and orientation angle of the ridges. The stability analysis is carried out in the temporal framework; the modal analysis is performed by solving a generalized eigenvalue problem, and the nonmodal, optimal perturbation analysis is done with an adjoint optimisation approach. We show theoretically and verify numerically that Squire’s theorem does not apply in the present settings, despite the fact that Squire modes are found to be always damped. The most notable result is the appearance of a streamwise wall-vortex mode at very low Reynolds numbers when the ridges are sufficiently inclined with respect to the mean pressure gradient, in the case of a single superhydrophobic wall. When two walls are rendered water repellent, the exponential growth of the instability results from either a two-dimensional or a three-dimensional Orr-Sommerfeld mode, depending on the ridges orientation and amplitude. Nonmodal results for either one or two superhydrophobic wall(s) display but a mild modification of the no-slip case.

[abstract] [pdf]

**Purpose**: To predict the shape of the interface between aqueous humor and a tamponade, gas or silicone oil (SO), in vitrectomized eyes. To quantify the tamponated retinal surface for various eye shapes, from emmetropic to highly myopic eyes.

**Methods**: We use a mathematical model to determine the equilibrium shape of the interface between the two fluids. The model is based on the VOF (volume of fluids) method. The governing equations are solved numerically using the free software OpenFOAM. We apply the model both to the case of idealized, yet realistic, geometries of emmetropic and myopic eyes and to a real geometry reconstructed from MRI images of the vitreous chamber.

**Results**: The numerical model allows us to compute the equilibrium shape of the inter face between the aqueous humor and the tamponade fluid. From this we can compute the portion of the retinal surface which is effectively tamponated by the fluid. We compare the tamponating ability of gases and SOs. We also compare the tamponating effect in emmetropic and myopic eyes by computing both tamponated area and angular coverage.

**Conclusions**: The numerical results show that gases have better tamponating properties than SOs. We also show that, for a given filling ratio the percentage of tamponated retinal surface area is smaller in myopic eyes. The method is valuable for clinical purposes,
30 especially in patients with pathological eye shapes, to predict the area of the retina that
31 will be tamponated for a given amount of injected tamponade fluid.

[abstract]

The aim of this study is to investigate the characteristics of the aqueous humor flow in the anterior chamber of the eye in the presence of a perforated, phakic, iris-fixated intraocular lens (pIOL). Such pIOLs are implanted in the anterior chamber, in front of the iris and they therefore interfere with aqueous motion. The aim of this work is to investigate whether a perforation in the body of the pIOL can improve its fluid dynamics performance. Numerical simulations are conducted using the free computational fluid dynamics program OpenFOAM. The aqueous humor is modeled as a Newtonian incompressible fluid and, when temperature effects are considered, the Navier-Stokes equations are coupled to the energy equation, using Boussinesq’s approach to account for fluid density changes associated temperature variations. The pressure drop across the anterior chamber is calculated considering perforations in the pIOL of various sizes and also studying the extreme case in which the passage between the iris and the pIOL gets plugged, thus leaving the hole in the pIOL as the only possible pathway for aqueous flow. The study shows that the presence of a hole in the pIOL can only have a significant role on the pressure in the eye if the normal aqueous flow in the region between the pIOL and the iris gets blocked.

[abstract] [pdf] [springer pdf]

Three algorithms for efficient solution of op- timal control problems for high-dimensional systems are presented. Each bypasses the intermediate (and, unnecessary) step of open-loop model reduction. Each also bypasses the solution of the full Riccati equation corresponding to the LQR problem, which is numeri- cally intractable for large n. Motivation for this effort comes from the field of model-based flow control, where open-loop model reduction often fails to capture the dynamics of interest (governed by the Navier-Stokes equation). Our Minimum Control Energy method is a simplified expression for the well-known minimum- energy stabilizing control feedback that depends only on the left eigenvectors corresponding to the unstable eigenvalues of the system matrix A. Our Adjoint of the Direct-Adjoint method is based on the repeated itera- tive computation of the adjoint of a forward problem, itself defined to be the direct-adjoint vector pair asso- ciated with the LQR problem. Our Oppositely-Shifted Subspace Iteration method is based on our new sub- space iteration method for computing the Schur vectors corresponding, notably, to the m ≪ n central eigenval- ues (near the imaginary axis) of the Hamiltonian ma- trix related to the Riccati equation of interest. These three approaches are compared to the classical Chan- drasekhar’s method for approximate solution of large Riccati equations on a representative control problem.

[abstract] [pdf]

A new way of handling, simultaneously, porosity and bending resistance of a massive filament is proposed. Our strategy extends the previous methods where porosity was taken into account in the absence of bending resistance of the structure and overcomes related numerical issues. The new strategy has been exploited to investigate how porosity affects the stability of slender elastic objects exposed to a uniform stream. To understand under which conditions porosity becomes important, we propose a simple resonance mechanism between a properly defined characteristic porous time-scale and the standard characteristic hydrodynamic time-scale. The resonance condition results in a critical value for the porosity above which porosity is important for the resulting filament flapping regime, otherwise its role can be considered of little importance. Our estimation for the critical value of the porosity is in fairly good agreement with our DNS results. The computations also allow us to quantitatively establish the stabilizing role of porosity in the flapping regimes.

[abstract] [pdf]

A simple approach is described for computing spatially extended, weakly nonlinear optimal disturbances, suitable for maintaining a disturbance-regeneration cycle in a simple shear flow. Weakly nonlinear optimals, computed over a short time interval for the expansion used to remain tenable, are oblique waves which display a shorter streamwise and a longer spanwise wavelength than their linear counterparts. Threshold values of the initial excitation energy, separating the region of damped waves from that where disturbances grow without bounds, are found. Weakly nonlinear optimal solutions of varying initial amplitudes are then fed as initial conditions into direct numerical simulations of the Navier–Stokes equations and it is shown that the weakly nonlinear model permits the identification of flow states which cause rapid breakdown to turbulence.

[abstract] [pdf]

**Abstract.**
The preliminary design of a biologically inspired flapping UAV is presented. Starting from a set of initial design specifications, namely: weight, maximum flapping frequency and minimum hand-launch velocity of the model, a parametric numerical study of the proposed avian model is conducted in terms of the aerodynamic performance and longitudinal static stability in gliding and flapping conditions. The model shape, size and flight conditions are chosen to approximate those of a gull. The wing kinematics is selected after conducting an extensive parametric study, starting from the simplest flapping pattern and progressively adding more degrees of freedom and control parameters until reaching a functional and realistic wing kinematics. The results give us an initial insight of the aerodynamic performance and longitudinal static stability of a biomimetic flapping UAV, designed at minimum flight velocity and maximum flapping frequency.

[abstract]

**Purpose**: In this study we investigated how implantation of iris-fixated intraocular lenses (IOLs) affects aqueous humor flow characteristics and mass transport processes in the anterior chamber. Specifically, we studied changes in the wall shear stress distribution and oxygen/nutrient availability on the cornea, after lens implantation.

**Methods**: We adopted a mathematical model to study aqueous flow and oxygen/nutrient concentration distribution in the anterior chamber in the presence of an iris-fixated IOL. Numerical solutions on idealized but realistic geometries were obtained employing the open source software OpenFOAM. The validity of the numerical results were confirmed by analytical solutions obtained through a simplified model based on the lubrication theory. We considered various mechanisms that generate aqueous flow in the anterior chamber and focused, in particular, on the production/drainage flow and the thermal flow generated by a temperature gradient across the anterior chamber.

**Results**: The model provides a detailed description of the velocity, pressure and concentration distribution in the anterior chamber, both in the presence and absence of the IOL. Results show that changes in fluid pressure after implantation of the IOL are negligible. Wall shear stress distribution and mass transport processes in the anterior chamber are significantly modified by the presence of the IOL. However, the maximum wall shear stress on the cornea does not grow after IOL implantation.

**Conclusions**: The study sheds some light on the changes induced by implantation of an iris-fixated IOL on fluid flow and mass transport in the anterior chamber, an information that would be difficult to obtain without making use of a mathematical model. Results suggest that changes in the wall shear stress, albeit significant, are unlikely to be the cause of the complications associated with the use of iris-fixated IOLs.

[abstract]

**Purpose**: Phakic intraocular lenses (pIOLs) are used for correcting vision; in this study we investigate some of the possible effects of an iris-fixated pIOL. We assess whether fluid dynamical changes associated with pIOL placement could give rise to clinical problems. In particular, we focus on modifications of the wall shear stress (WSS) on the cornea and iris, which could be responsible for endothelial and pigment cell loss, respectively, and also on the possible increase of the intraocular pressure (IOP), which is known to correlate with the incidence of secondary glaucoma.

**Methods**: We use a mathematical model to study fluid flow in the anterior chamber in the presence of a pIOL. The governing equations are solved numerically using the open source software OpenFOAM. We use an idealized standard geometry for the anterior chamber and a realistic geometrical description of the pIOL.

**Results**: We consider separately the main mechanisms that produce fluid flow in the anterior chamber. The numerical simulations allow us to obtain a detailed description of the velocity and pressure distribution in the anterior chamber in the presence of a pIOL. Results show that implantation of the pIOL significantly modifies the fluid dynamics of the anterior chamber. However, lens implantation has negligible influence on the intraocular pressure, does not produce a significant increase of the shear stress on the cornea, while the stress on the iris, although increased, is not large enough to cause detachment of cells from this tissue.

**Conclusions**: We conclude that alterations in the fluid dynamics in the anterior chamber as a result of lens implantation are unlikely to be the cause of medical complications associated with their use.

[abstract] [pdf]

**Abstract.**
Il testo si propone di presentare le equazioni e i principi fondamentali della meccanica dei fluidi, e mostrare esempi di molte e diverse applicazioni a problemi pratici di ingegneria per fornire agli studenti esempi di come la meccanica dei fluidi venga usata nella pratica ingegneristica. Tra gli obiettivi c'è anche la comprensione intuitiva della meccanica dei fluidi enfatizzandone la fisica, attraverso l'uso di immagini che aiutino a comprenderla. Novità della terza edizione sono il capitolo 14 Introduzione alla fluidodinamica computazionale e l'introduzione di alcuni box applicativi scritti da guest author.

[abstract] [pdf]

**Abstract.**
Il testo si propone di presentare le equazioni e i principi fondamentali della meccanica dei fluidi, e mostrare esempi di molte e diverse applicazioni a problemi pratici di ingegneria per fornire agli studenti esempi di come la meccanica dei fluidi venga usata nella pratica ingegneristica. Tra gli obiettivi c'è anche la comprensione intuitiva della meccanica dei fluidi enfatizzandone la fisica, attraverso l'uso di immagini che aiutino a comprenderla. Novità della terza edizione sono il capitolo 14 Introduzione alla fluidodinamica computazionale e l'introduzione di alcuni box applicativi scritti da guest author.

[abstract] [pdf]

**Abstract.**
We investigate the stability properties of flows over an open square cavity for fluids with shear-dependent viscosity. The analysis is carried out in the context of linear theory using a normal-mode decomposition. The incompressible Cauchy equations, with a Carreau viscosity model, are discretized with a finite-element method. The characteristics of direct and adjoint eigenmodes are analyzed and discussed in order to understand the receptivity features of the flow. Furthermore, we identify the regions of the flow more sensitive to a spatially localized feedbacks by building a spatial map obtained from the product between the direct and the adjoint eigenfunctions. The analysis shows that the first global linear instability of the steady flow is a steady or unsteady three-dimensional bifurcation depending on the value of the power-law index n. The instability mechanism is always located inside the cavity and the linear stability results suggest a strong connection with the classical lid-driven cavity problem.

[abstract] [pdf]

**Abstract.**
In the present study a linear feedback control strategy is derived and used to suppress the cylinder vortex shed- ding at low Reynolds numbers. The classical small-gain solution of the optimal control and estimation problems is exploited in order to design a full-dimensional stabilizing compensator of the linearized Navier-Stokes equations, thus bypassing the open-loop model reduction of the fluid plant. Both feedback and observer gains are efficiently computed based solely on the knowledge of the unstable adjoint and direct global modes, respectively. In our control setup, the actuation is realized by means of unsteady angular rotations of the cylinder surface while a single velocity sensor located along the symmetry line is employed for the state estimation. For Re = 50 the derived compensator is shown to be able to drive the flow from the natural limit cycle to the unstable steady state which is finally restored. Then the sensitivity of the control performance to sensor placement and Reynolds number is investigated. For selected locations of the sensor the derived compensator is able to delay the onset of vortex shedding up to Re = 59 which compares well with the threshold found by other authors both in numerical (Re ≈ 60) and experimental investigations (Re ≈ 58) using linear feedback control strategies.

[abstract] [pdf]

Featured as

**Abstract.**
We consider the motion of two immiscible viscous fluids induced by periodic oscilla- tions of a flat solid surface along its plane. The interface between the two fluids is parallel to the solid wall; one fluid occupies the region between the wall and the in- terface and the other extends from the interface to infinity. We study numerically the linear stability of the interface with respect to two-dimensional perturbations using the normal mode analysis and assuming quasi-steady flow conditions. The analysis is motivated by the need of understanding the behavior of vitreous substitutes inserted in the vitreous chamber of the eye after vitrectomy. This is a common surgical pro- cedure adopted to treat retinal detachments, whereby the vitreous humor is removed from the eye and replaced by fluids immiscible with water. Owing to their hydropho- bic nature vitreous substitutes coexist in the vitreous chamber with a certain amount of aqueous humor (the fluid produced in the anterior part of the eye) and, typically, a thin layer of aqueous separates the tamponade fluid from the retina. A common problem with this treatment is that, in some cases, the interface between the two fluids breaks down and this might eventually lead to the generation of an emulsion. It is believed that mechanics plays an important role in this process but the problem remains very poorly understood. We find that instability of the interface is possible in a range of parameters that is relevant for the problem that motivated the present analysis. This suggests that shear instability is likely a possible mechanism triggering the onset of vitreous substitutes–aqueous interface instability.

[abstract] [pdf]

**Abstract.**
In the present paper we discuss some aspects of the fluid dynamics of vitreous substitutes in the vitreous chamber, focussing on the flow induced by rotations of the eye bulb. We use simple, yet not trivial, theoretical models to highlight mechanical concepts which are of great relevance to understand the behaviour of vitreous substitutes in the vitreous chamber and also to identify ideal properties for vitreous replacement fluids. We first consider the dependency of the maximum shear stress on the retina on the viscosity of the fluid, and also discuss the differences between the motion of purely viscous and viscoelastic fluids. We then investigate how the wall shear stress changes if a thin layer of aqueous is present in the vitreous chamber, separating the retina from the vitreous replacement fluid. In relation to this, we also discuss results from a theoretical model that predicts the stability conditions of the interface between aqueous and a vitreous substitute. We discuss the implications of this model results to understand the mechanisms leading to the formation of an emulsion in the vitreous chamber.

[abstract] [pdf]

**Abstract.**
Mixing control in microchannels is a problem of paramount importance in a variety of situations ranging from applications in chemistry and biochemistry to fundamental research in fluid mechanics and transport. The main problem to solve is related to the fact that purely hydrodynamic fluid instabilities are inhibited due to negligible inertia of microchannel flow. Since mixing times or distances con be very long, strategies are required to enhance mixing in microdevices. Two different approaches are commonly used to induce mixing, according to their active or passive character. Active micromixers use the disturbance generated by an external time-dependent field for the mixing process, eg., pressure gradient, electric fields and sound. Those methods are often difficult because of the tiny scales involved and they also pose several problems from a manufacturing point of view. Passive micromixer do not require external energy, the mixing process relies entirely on diffusion or chaotic advection. In the first approach, the molecular diffusion is enhanced by increasing the contact surface and decreasing the mixing path. In the second, the geometrical structure of the microchannel is projected to trigger Lagrangian chaos (and thus mixing via eddy-diffusivity mechanisms). Suitable non-Newtonian fluid solutions often provide an alternative valid answer to trigger mixing exploiting elastic instabilities in the limit of very small Reynolds numbers or, eventually, turbulence.
Our aim here is to show how, exploiting state-of-the-art control/optimization techniques, the mixing efficiency of a passive scalar quantity emitted in a microchannel can be easily enhanced by a time-dependent injection in punctual and multi-source configuration. The technique is active but does not require any time-dependent variation of the emission source position. The system is especially suitable for noncontinuous mixing and, at the same time, for dosing with a minimal emitted substance.

[abstract] [pdf]

**Abstract.**
The emergence of fluid instabilities in the relevant limit of zero fluid inertia (i.e. zero Reynolds numbers) has been investigated for the well-known Kolmogorov flow. The finite-time shear-induced order-disorder transition of the non-Newtonian micro-structure and the corresponding viscosity change from lower to higher values, are the crucial ingredients for the instabilities to emerge. The finite-time low-to-high viscosity change for increasing shear characterizes the rheopectic fluids. The instability does not emerge in shear-thinning/thickening fluids where viscosity adjustment to lo- cal shear occurs almost instantaneously. The lack of instabilities at zero Reynolds number is also observed for thixotropic fluids, in spite of the fact that the viscosity adjustment time to shear is finite as in rheopectic fluids. Renormalized perturbative expansions (multiple-scale expansions), energy-based arguments (on the linearized equations of motion) and numerical results (of suitable eigenvalue problems from the linear stability analysis) are the main tools leading to our conclusions. Our findings may have important consequences in all situations where purely hydrodynamic fluid instabilities/mixing are inhibited due to negligible inertia, as in microfluidic applications. To trig- ger mixing in these situations, suitable (not necessarily viscoelastic) non-Newtonian fluid solutions appear as a valid answer. Our results open interesting questions and challenges in the field of smart (fluid) material.

[abstract] [pdf]

**Abstract.**
The two-dimensional stationary flow past a rotating cylinder is analyzed for both two and three-dimensional perturbations. The instability mechanisms for the high and low- frequency modes are analyzed and the complete neutral curve presented. It is shown that the first bifurcation in the case of the rotating cylinder occurs for stationary three- dimensional perturbations, confirming recent experiments. Interestingly, the critical Reynolds number at high rotation rates is lower than the one for the stationary circular cylinder. The spatial characteristics of the disturbance and a qualitative comparison with the re- sults obtained for linear flows suggest that the stationary unstable three-dimensional mode could be of a hyperbolic nature.

[abstract] [pdf]

**Abstract.**
The control of Tollmien-Schlichting (TS) in a 2D boundary layer is analysed by using
numerical simulation. Full-dimensional optimal controllers are used in combination with
a set-up of spatially localised inputs (actuators and disturbance) and outputs (sensors).
The Adjoint of the Direct-Adjoint (ADA) algorithm, recently proposed by Pralits &
Luchini (2010), is used to efficiently compute the Linear Quadratic Regulator (LQR) controller;
the method is iterative and allows to by-pass the solution of the corresponding
Riccati equation, unfeasible for high-dimensional systems. We show that an analogous iteration
can be cast for the estimation problem; the dual algorithm is referred to as Adjoint
of the Adjoint-Direct (AAD). By combining the solutions of the estimation and control
problem, a full dimensional, model-free, Linear Gaussian Quadratic (LQG) controllers
are obtained and used for the attenuation of the disturbances arising in the boundary
layer flow.
Model-free, full dimensional controllers turn out to be an excellent benchmark for
evaluating the performance of the optimal control/estimation design based on open-loop
model reduction. We show the conditions under which the two strategies are in perfect
agreement by focusing on the issues arising when feedback configurations are considered.
An analysis of the finite amplitude cases is also carried out addressing the limitations of
the optimal controllers, the role of the estimation and the robustness to the nonlinearities
arising in the flow of the control design.

[abstract] [pdf]

**Abstract.**
A linear stability analysis of the laminar flow in the boundary layer at the bottom
of a solitary wave is made to determine the conditions leading to transition and the
appearance of turbulence. The Reynolds number of the phenomenon is assumed to
be large and a ‘momentary’ criterion of instability is used. The results show that the
laminar regime becomes unstable during the decelerating phase, when the height of
the solitary wave exceeds a threshold value which depends on the ratio between the
boundary layer thickness and the local water depth. A comparison of the theoretical
results with the experimental measurements of Sumer et al. (*J. Fluid Mech.*, vol. 646,
2010, pp. 207–231) supports the analysis.

[abstract] [pdf]

**Abstract.**
The first bifurcation and the instability mechanisms of shear-thinning and shearthickening
fluids flowing past a circular cylinder are studied using linear theory
and numerical simulations. Structural sensitivity analysis based on the idea of a
‘wavemaker’ is performed to identify the core of the instability. The shear-dependent
viscosity is modelled by the Carreau model where the rheological parameters,
i.e. the power-index and the material time constant, are chosen in the range
*0.4 < n < 1.75* and *0.1<λ<100*. We show how shear-thinning/shear-thickening
effects destabilize/stabilize the flow dramatically when scaling the problem with the
reference zero-shear-rate viscosity. These variations are explained by modifications of
the steady base flow due to the shear-dependent viscosity; the instability mechanisms
are only slightly changed. The characteristics of the base flow, drag coefficient
and size of recirculation bubble are presented to assess shear-thinning effects. We
demonstrate that at critical conditions the local Reynolds number in the core of the
instability is around 50 as for Newtonian fluids. The perturbation kinetic energy budget
is also considered to examine the physical mechanism of the instability.

[abstract] [pdf]

**Abstract.**
Non-modal analysis determines the potential for energy amplification in stable flows.
The latter is quantified in the frequency domain by the singular values of the resolvent
operator. The present work extends previous analysis on the effect of base-flow
modifications on flow stability by considering the sensitivity of the flow non-modal
behaviour. Using a variational technique, we derive an analytical expression for
the gradient of a singular value with respect to base-flow modifications and show
how it depends on the singular vectors of the resolvent operator, also denoted the
optimal forcing and optimal response of the flow. As an application, we examine
zero-pressure-gradient boundary layers where the different instability mechanisms of
wall-bounded shear flows are all at work. The effect of the component-type nonnormality
of the linearized Navier–Stokes operator, which concentrates the optimal
forcing and response on different components, is first studied in the case of a parallel
boundary layer. The effect of the convective-type non-normality of the linearized
Navier–Stokes operator, which separates the spatial support of the structures of the
optimal forcing and response, is studied in the case of a spatially evolving boundary
layer. The results clearly indicate that base-flow modifications have a strong impact
on the Tollmien–Schlichting (TS) instability mechanism whereas the amplification of
streamwise streaks is a very robust process. This is explained by simply examining the
expression for the gradient of the resolvent norm. It is shown that the sensitive region
of the lift-up (LU) instability spreads out all over the flat plate and even upstream of it,
whereas it is reduced to the region between branch I and branch II for the TS waves.

[abstract] [pdf]

**Abstract.**
The two-dimensional flow around a rotating circular cylinder is studied at Re = 100.
The instability mechanisms for the first and second shedding modes are analysed. The
region in the flow with a role of ‘wavemaker’ in the excitation of the global instability is
identified by considering the structural sensitivity of the unstable mode. This approach
is compared with the analysis of the perturbation kinetic energy production, a classic
approach in linear stability analysis. Multiple steady-state solutions are found at high
rotation rates, explaining the quenching of the second shedding mode. Turning points
in phase space are associated with the movement of the flow stagnation point. In
addition, a method to examine which structural variation of the base flow has the
largest impact on the instability features is proposed. This has relevant implications
for the passive control of instabilities. Finally, numerical simulations of the flow are
performed to verify that the structural sensitivity analysis is able to provide correct
indications on where to position passive control devices, e.g. small obstacles, in order
to suppress the shedding modes.

[abstract] [pdf]

**Abstract.**
A method using gradient-based optimization is introduced for the design of wing profiles with the aim of natural
laminar flow, as well as minimum wave drag. The Euler equations of gasdynamics, the laminar boundary-layer
equations for compressible flows on infinite swept wings, and the linear parabolized stability equations (PSE) are
solved to analyze the evolution of convectively unstable disturbances. Laminar–turbulent transition is assumed to
be delayed by minimizing a measure of the disturbance kinetic energy of a chosen disturbance, which is computed
using the PSE. The shape gradients of the disturbance kinetic energy are computed based on the solutions of the
adjoints of the state equations just named. Numerical tests are carried out to optimize the RAE 2822 airfoil with
the aim to delay simultaneously the transition, reduce the pressure drag coefficient, and maintain the coefficients
of lift and pitch moments. Constraints are also applied on the geometry. Results show a reduction of the total
amplification of a large number of disturbances, which is assumed to represent a delay of the transition in the
boundary layer. Because delay of the transition implies reduction of the viscous drag, the present method enables
shape optimization to perform viscous drag reduction.

[abstract] [pdf]

**Abstract.**
We present a theory for computing the optimal steady suction distribution to suppress convectively unstable disturbances in growing boundary layers on infinite swept wings. This work includes
optimization based on minimizing the disturbance kinetic energy and the integral of the shape factor.
Further, a suction distribution in a continuous control domain is compared to an approach using a
number of discrete pressure chambers. In the latter case, the internal static pressures of these
chambers are optimized. Optimality systems are derived using Lagrange multipliers. The
corresponding optimality conditions are evaluated using the adjoint of the parabolized stability
equations and the adjoint of the boundary layer equations. Results are presented for an airfoil
designed for medium range commercial aircraft. We show that an optimal suction distribution based
on a minimization of the integral of the shape factor is not always successful in the sense of delaying
laminar-turbulent transition. It is also demonstrated that including different types of disturbances,
e.g., Tollmien–Schlichting and cross-flow types, in the analysis may be crucial.

[abstract] [pdf]

**Abstract.**
The optimal distribution of steady suction needed to control the growth of single or
multiple disturbances in quasi-three-dimensional incompressible boundary layers on
a flat plate is investigated. The evolution of disturbances is analysed in the framework
of the parabolized stability equations (PSE). A gradient-based optimization procedure
is used and the gradients are evaluated using the adjoint of the parabolized stability
equations (APSE) and the adjoint of the boundary layer equations (ABLE). The
accuracy of the gradient is increased by introducing a stabilization procedure for the
PSE. Results show that a suction peak appears in the upstream part of the suction
region for optimal control of Tollmien{Schlichting (T{S) waves, steady streamwise
streaks in a two-dimensional boundary layer and oblique waves in a quasi-threedimensional
boundary layer subject to an adverse pressure gradient. The mean flow
modications due to suction are shown to have a stabilizing eect similar to that of
a favourable pressure gradient. It is also shown that the optimal suction distribution
for the disturbance of interest reduces the growth rate of other perturbations. Results
for control of a steady cross-flow mode in a three-dimensional boundary layer subject
to a favourable pressure gradient show that not even large amounts of suction can
completely stabilize the disturbance.

[pdf]

[abstract] [pdf]

**Abstract.**
An input/output framework is used to analyze the sensitivity of two- and three-dimensional disturbances in a compressible boundary layer for changes in wall and momentum forcing. The sensitivity is defined as the gradient of the kinetic disturbance energy at a given downstream position with respect to the forcing. The gradients are derived using the parabolized stability equations (PSE) and their adjoint (APSE). The adjoint equations are derived in a consistent way for a quasi-two-dimensional compressible flow in an orthogonal curvilinear coordinate system. The input/output framework provides a basis for optimal control studies. Analysis of two-dimensional boundary layers for Mach numbers between 0 and 1.2 show that wall and momentum forcing close to branch I of the neutral stability curve give the maximum magnitude of the gradient. Forcing at the wall gives the largest magnitude using the wall normal velocity component. In case of incompressible flow, the two-dimensional disturbances are the most sensitive ones to wall inhomogeneity. For compressible flow, the three-dimensional disturbances are the most sensitive ones. Further, it is shown that momentum forcing is most effectively done in the vicinity of the critical layer.

[abstract] [pdf]

**Abstract.**
In the present paper, two different approaches to compute the optimal disturbances in the quasi threedimensional flows are presented. One of the approaches is based on the Multiple Scales method and the other one utilises the Parabolised Stability Equations.

[abstract] [pdf]

**Abstract.**
Gradient-based shape optimization of an airfoil is performed with respect to the location of the laminar-turbulent transition in the boundary layer. The shape gradients are efficiently computed based on the solutions of the adjoint equations of the Euler, boundary-layer and stability equations. Results show a reduction of the total amplification of a large number of disturbances, which is assumed to represent a delay of the transition in the boundary layer. As delay of the transition implies reduction of the viscous drag, the present method enables shape optimization to perform viscous drag reduction.

[abstract] [pdf]

**Abstract.**
Methods for optimal design of different means of control are developed in this thesis. The main purpose is to maintain the laminar flow on wings at a chord Reynolds number beyond what is usually transitional or turbulent. Linear sta- bility analysis is used to compute the exponential amplification of infinitesimal disturbances, which can be used to predict the location of laminar-turbulent transition. The controls are computed using gradient-based optimization tech- niques where the aim is to minimize an objective function based upon, or re- lated to, the disturbance growth. The gradients of the objective functions with respect to the controls are evaluated from the solutions of adjoint equations.
Sensitivity analysis using the gradients of the disturbance kinetic energy with respect to different periodic forcing show where and by what means control is most efficiently made. The results are presented for flat plate boundary layer flows with different free stream Mach numbers.
A method to compute optimal steady suction distributions to minimize the disturbance kinetic energy is presented for both incompressible and compress- ible boundary layer flows. It is shown how to formulate an objective function in order to minimize simultaneously different types of disturbances which might exist in two, and three-dimensional boundary layer flows. The problem for- mulation also includes control by means of realistic pressure chambers, and results are presented where the method is applied on a swept wing designed for commercial aircraft.
Optimal temperature distributions for disturbance control are presented for flat plate boundary layer flows. It is shown that the efficiency of the control depends both on the free stream Mach number, and whether the wall down- stream of the control domain is insulated, or heat transfer occurs.
Shape optimization is presented with the aim of reducing the aerodynamic drag, while maintaining operational properties. Results of optimized airfoils are presented for cases where both the disturbance kinetic energy, and wave drag are reduced simultaneously while lift, and pitch-moment coefficients as well as the volume are kept at desired values.

[abstract] [poster]

**Abstract.**

[abstract] [poster]

**Abstract.**
Purpose: To investigate the effects of implantation of a phakic iris-fixated intraocular lens (IOL) on aqueous flow in the anterior chamber. Methods: We use a mathematical model to study fluid flow in the anterior chamber in the presence of a IOL. The governing equations are solved numerically using the free software OpenFoam. Results: IOL implantation has very little influence on the pressure in the anterior chamber, unless the IOL is placed very close to the iris. The presence of the IOL significantly modifies the thermal flow induced by temperature differences between the cornea and the posterior region of the chamber. The maximum corneal WSS does not increase for normal IOL placement. Relatively large values of the WSS can be attained on the iris. Conclusions: The numerical simulations suggest that cell detachment from the iris and cornea, which is a known possible complication of IOL implantation, is not induced by large values of the WSS. In the case of correct IOL placement the intraocular pressure (IOP) is almost unaffected.

[abstract]

**Abstract.**

[abstract] [talk]

**Abstract.**
Il controllo del mixing nei micro-canali, di dimensioni nell’ordine del micron, è un problema di estrema importanza in molte applicazioni scientifiche ed industriali, che vanno dalla biochimica fino alle tecnologie per l’informazione. Se da un lato le tecnologie miniaturizzate hanno l’indubbio vantaggio di utilizzare una ridotta quantità di fluido, dall’altro hanno dimensioni tali da inibire le instabilità idrodinamiche, rendendo estremamente lento il processo di mixing. Due differenti approcci sono tipicamente utilizzati per indurre mixing: sistemi attivi, in cui il disturbo è generato da una forza esterna tempo-dipendente, e sistemi passivi, in cui ci si affida interamente alla diffusione molecolare e/o caotica. Il presente lavoro dimostra come, controllando l’iniezione, sia possibile incrementare efficacia ed efficienza del mixing di un tracciante in un micro-canale.

[abstract] [pdf] [talk]

**Abstract.**
We consider a flat solid surface located at y = 0, performing sinusoidal oscillations along the x–direction, with (x, y) being a Cartesian system of coordinates. We assume that two immiscible fluids occupy the region of space y>= 0. The interface between the two fluids is at y = d; fluid 1 occupies the region 0 <=y<=d, and fluid 2 extends from d to infinity. We study the linear stability of the interface using the normal mode analysis and assuming quasi-steady flow conditions, e.g. assuming that perturbations evolve on a time scale significantly smaller than the period of oscillations of the basic flow. The stability problem leads to two Orr-Sommerfeld equations for the streamfunctions in fluids 1 and 2, coupled with suitable boundary conditions. The resulting eigenvalue problem is solved numerically employing a second order finite-difference scheme and using an inverse iteration approach. The results show that instability of the interface is possible for long enough waves. We study how stability conditions depend on the dimensionless controlling parameters, showing, in particular, the relevant role played by the surface tension between the two fluids.
The work represents a first attempt to understand the instability of the aqueous humour–vitreous substitute instability in vitrectomised eyes. The simple geometrical configuration considered in this work well represents the real case when the thickness of the aqueous layer in contact with the retina is much smaller than the radius of the eye, which is often the case. Our results suggest that shear instability at the aqueous humour–vitreous substitute interface is a plausible mechanism responsible for the onset of emulsification in the vitreous chamber.

[abstract] [pdf]

**Abstract.**
In this work, we present the preliminary design of a biologically inspired flapping UAV. Starting from a set of initial design specifications, namely: weight, maximum flapping frequency and the minimum hand-launch velocity of the model; we conduct a wide numerical study of the proposed avian model in terms of the aerodynamic performance and flight stability in flapping and gliding conditions. The model shape, size and flight conditions are chosen to approximate those of a seagull. Additionally, an extensive study is conducted in order to dissect the kinematics of the wings, where starting from the simplest wing kinematics we keep on adding more degrees of freedom and control parameters until reaching a functional and realistic wing kinematics. The results give us an initial insight of the aerodynamic performance and flight stability of a biomimetic flapping UAV designed at minimum flight velocity and maximum flapping frequency.

[abstract] [talk]

**Abstract.**

[abstract]

**Abstract.**
Mixing control in fluid environments having very low Reynolds numbers is a crucial need for many practical purposes ranging from biochemistry analysis in microfluidic devices, where mixing has to be rapid and efficient, to lab-on-a-chip applications, where mixing has to be reduced to avoid spurious effects as in microfluidic rheometer applications. The ability to control fluid mixing properties is clearly subjected to a deep understanding of physical mechanisms able to originate such a mixing for very small Reynolds numbers. In this respect, a simple model to capture mesoscopic effects of order-disorder transitions of an underlying non-Newtonian fluid microstructure subjected to shear is proposed and its behaviors investigated (numerically and by means of asymptotic perturbative methods) in relation to the possible emergence of fluid elatic-like instabilities occurring for arbitrarily small flow inertia (i.e. zero Reynolds numbers). A crucial ingredient for instabilities to emerge has been identified in the finite-time response of the network structure to strain where the order-disorder transition corresponds to a change from low-to-high fluid viscosity (and not viceversa). Our results generalizes the concept of ``elastic instabilities'' in viscoelastic fluids to a more general and larger class of non-Newtonian fluids.

[abstract] [pdf]

**Abstract.**
We study the stability of the interface between to immiscible fluids, the motion of which is induced by oscillations of a solid flat wall. The work represents a first step towards a mechanical understanding of the conditions leading to emulsification of vitreous substitute in the vitreous chamber.

[abstract] [pdf]

**Abstract.**
In the present work a linear feedback control strategy is used to control and suppress the cylinder vortex- shedding at low Reynolds numbers. The classical minimal control energy or small gain solution of the optimal control and estimation problems is exploited in order to design a full-dimensional stabilizing com- pensator of the linearized Navier–Stokes equations. Both feedback and observer gains are efficiently com- puted based solely on the knowledge of the unstable adjoint and direct global modes, respectively. In our control setup, actuation is realized by means of angular oscillations of the cylinder surface while a single velocity sensor is employed for the state estimate. The derived compensator is shown to be able to drive the flow from the natural limit cycle to the unstable steady state which is finally restored. Then the sensitivity of the control performance to sensor placement and Reynolds number is investigated.

[abstract] [pdf]

**Abstract.**
The conditions leading to transition and turbulence appearance at the bottom of a solitary waveare determined by means of a linear stability analysis of the laminar flow in the bottom boundary layer. The ratio between the wave amplitude and the thickness of the viscous bottom boundary layer is assumed to be large and a ’momentary’ criterion of instability is used. The results obtained show that the laminar regime becomes unstable, during the decelerating phase, if the height of the wave is larger than a threshold value which depends on the ratio between the boundary layer thickness and the local water depth. A comparison of the theoretical results with the experimental measurements of Sumer et al. (2010) seems to support the stability analysis.

[abstract] [pdf]

**Abstract.**
A gradient-based optimization method for minimization of the total drag of an airfoil is presented. The viscous drag is minimized by delaying the laminar- turbulent transition. The gradients are obtained solving the adojoint of the Eu- ler, boundary-layer and stability equations. The optimization is subjected to con- straints such as restrictions on geometry, lift and pitch moment. The geometry is parametrised using radial basis functions.

[abstract] [pdf]

**Abstract.**
In this paper we propose a new method to solve the optimal control prob- lem in which the feedback matrix K is computed in an efficient way for com- plex flows, with large number of degrees of freedom, using an approach similar to adjoint-based control optimization. The idea is to consider the direct-adjoint sys- tem as an input-output problem where the input is given by the current state and the output is the control. Since the control has much smaller dimension than the state, the feedback matrix K can be efficiently obtained from the solution of the adjoint of the direct-adjoint system. It can further be shown using the symplectic product that the direct-adjoint system is self adjoint. As a consequence the new adjoint system is equivalent to the direct-adjoint system with suitable initial and terminal condi- tions. With this method the optimal control problem can be solved efficiently for any value of the control penalty l2. Results are presented of this novel technique as applied to suppressing the vortex shedding behind a circular cylinder, and compared to the minimal-energy feedback control presented in Pralits et al. (2008).

[abstract] [pdf]

**Abstract.**
In this paper we study the structural sensitivity of the nonlinear periodic oscillation arising in the wake of a circular cylinder for Re47. The sensibility of the periodic state to a spatially localised feedback from velocity to force is anal- ysed by performing a structural stability analysis of the problem. The sensitivity of the vortex shedding frequency is analysed by evaluating the adjoint eigenvectors of the Floquet transition operator. The product of the resulting neutral mode with the nonlinear periodic state is then used to localise the instability core. The results ob- tained with this new approach are then compared with those derived by Giannetti & Luchini (2007). An excellent agreement is found comparing the present results with the experimental data of Strykowski & Sreenivasan (1990).

[abstract] [pdf]

**Abstract.**
In this paper we review the problem of the wake-flow stability for a thin airfoil by using both a locally plane-wave analysis, based on a WKBJ approximation, and a global numerical stability analysis. The core of the instability is further localized by performing a structural sensitivity analysis of the linearized Navier-Stokes operator as outlined in Giannetti & Luchini (2007). In particular the sensitivity of the eigenvalue to a spatially-localized feedback from velocity to force is evaluated by using the product of the direct and adjoint global mode. It is shown, using a plane wave analysis, that the flow at the trailing edge is absolutely unstable for any Reynolds number for values of the parameter m corresponding to separation of the base flow. The analysis further shows that the base flow at the trailing edge is not absolutely unstable as the value of m tends to zero. The global eigenvalue analysis shows that the frequency and growth rate are very similar to what is found with the local plane wave analysis at the trailing edge. Finally, the structural sensitivity analysis indicates that the wavemaker is situated just downstream of the trailing edge.

[abstract] [pdf]

**Abstract.**
The concept of ``structural sensitivity'' of a global mode is introduced and used to study the formation of the classical Karman vortex street in the wake of a circular cylinder. By evaluating the functional derivative of the global mode frequency with respect to an external local feedback from velocity to force, we show how to locate the ``wavemaker'' of the asymptotic theory, ie the point in space where the instability originates and from which propagates as a wave in all direction. This can be done by exploiting the properties of the numerically computed direct and adjoint global eigenfunctions, without any assumptions on the quasi-parallelism of the flow. This new approach is presented both in the context of linear as well nonlinear oscillations. Finally, recent results obtained by the application of the structural sensitivity concept to the study of the secondary instability of the cylinder wake are shown and discussed.

[abstract] [pdf]

**Abstract.**
We present a theory for computing the optimal steady suction distribution in order to minimize the growth of convectively unstable disturbances, and thus delay laminar-turbulent transition on swept wings. Here, we use the optimal control theory and minimize an objective function based on a sum of the kinetic energy of an arbitrary number of disturbances. The optimization procedure is gradient-based where the gradients are obtained using the adjoint of the parabo- lized stability equations and the adjoint of the boundary layer equations. Results are presented for an air foil designed for medium range commercial air crafts.

[abstract] [pdf]

**Abstract.**
Linear stability analysis of flat plate boundary layers implies, for wave like perturbations, to solve the so called Orr-Sommerfeld equations which solution can be expressed in terms of a continuous, and discrete spectrum. As the number of discrete modes change with the Reynolds number, and further seem to disappear behind the continuous spectrum at certain Reynolds numbers, it is of interest to investigate if an all-discrete representation of the solution is possible. This can be done solving the response of the flat plate boundary forced instantaneously in space. Since the solution of the forced and homogeneous Laplace transformed problem both depend on the free stream boundary conditions, it is shown here that an opportune change of variables can remove the branch cut in the complex eigen value plane. As a result integration of the inversed Laplace transform along the new path corresponding to the continuous spectrum, which is now given by a straight line, equals the summation of residues of additional discrete eigen values appearing to the left of it. It is further shown that these additional modes are computed accounting for solution which grow in the wall normal direction. A similar problem is found in the theory of optical waveguides, such as optical fibers, where so called leaky waves are attenuated in the direction of the wave-guide, while it grows unbounded in a direction perpendicular to it. The theory is here applied to the case of two-dimensional flat plate boundary layers, of incompressible flows, subject to a pressure gradient.