A novel laminar flow control based on generation of spanwise mean velocity gradients (SVG) in a flat plate boundary layer is investigated where disturbances of different types are introduced in the wall-bounded shear layer. The experimental investigations are aimed at; (i) generating stable and steady streamwise streaks in the boundary layer which set up spanwise gradients in the mean flow, and (ii) attenuating disturbance energy growth in the streaky boundary layers and hence delaying the onset of turbulence transition. The streamwise streaks generated by four different methods are investigated, which are spanwise arrays of triangular/rectangular miniature vortex generators (MVGs) and roughness elements, non-linear pair of oblique waves, and spanwise-periodic finite discrete suction. For all the investigated methods the boundary layer is modulated into regions of high- and low speed streaks through formation of pairs of counter-rotating streamwise vortices. For the streaky boundary layers generated by the MVGs a parameter study on a wide range of MVG configurations is performed in order to investigate the transient growth of the streaks. A general scaling of the streak amplitudes is found based on empiricism where an integral amplitude definition is proposed for the streaks. The disturbances are introduced as single- and broad band frequency twodimensional Tollmien–Schlichting (TS) waves, and three-dimensional single and a pair of oblique waves. In an attempt to obtain a more realistic configuration compared to previous investigations the disturbances are introduced upstream of the location were streaks are generated. It is shown that the SVG method is efficient in attenuating the growth of disturbance amplitudes in the linear regime for a wide range of frequencies although the disturbances have an initial amplitude response to the generation of the streaks. The attenuation rate of the disturbance amplitude is found to be optimized for an integral streak amplitude of 30% of the free-stream velocity which takes into account the periodic wavelength of the streaky base flow. The stabilizing effect of the streamwise streaks can be extended to the nonlinear regime of disturbances which in turn results in transition to turbulence delay. This results in significant drag reduction when comparing the skin friction coefficient of a laminar- to a turbulent boundary layer. It is also shown that consecutive turbulence transition delay can be obtained by reinforcing the streaky boundary layer in the streamwise direction. For the streaky boundary layer generated by pair of oblique waves their forcing frequency sets the upper limit for the frequency of disturbances beyond which the control fails. / <p>QC 20160208</p>

<p>Magnetized planets, such as Earth, are strongly influenced by the solar wind. The Sun is very dynamic, releasing varying amounts of energy, resulting in a fluctuating energy and momentum exchange between the solar wind and planetary magnetospheres. The efficiency of this coupling is thought to be controlled by magnetic reconnection occurring at the boundary between solar wind and planetary magnetic fields. One of the main tasks in space physics research is to increase the understanding of this coupling between the Sun and other solar system bodies. Perhaps the most important aspect regards the transfer of energy from the solar wind to the terrestrial magnetosphere as this is the main source for driving plasma processes in the magnetosphere-ionosphere system. This may also have a direct practical influence on our life here on Earth as it is responsible for Space Weather effects. In this thesis I investigate both the global scale of the varying solar-terrestrial coupling and local phenomena in more detail. I use mainly the European Space Agency Cluster mission which provide unprecedented three-dimensional observations via its formation of four identical spacecraft. The Cluster data are complimented with observations from a broad range of instruments both onboard spacecraft and from groundbased magnetometers and radars.</p><p>A period of very strong solar driving in late October 2003 is investigated. We show that some of the strongest substorms in the history of magnetic recordings were triggered by pressure pulses impacting a quasi-stable magnetosphere. We make for the first time direct estimates of the local energy flow into the magnetotail using Cluster measurements. Observational estimates suggest a good energy balance between the magnetosphere-ionosphere system while empirical proxies seem to suffer from over/under estimations during such extreme conditions.</p><p>Another period of extreme interplanetary conditions give rise to accelerated flows along the magnetopause which could account for an enhanced energy coupling between the solar wind and the magnetosphere. We discuss whether such conditions could explain the simultaneous observation of a large auroral spiral across the polar cap.</p><p>Contrary to extreme conditions the energy conversion across the dayside magnetopause has been estimated during an extended period of steady interplanetary conditions. A new method to determine the rate at which reconnection occurs is described that utilizes the magnitude of the local energy conversion from Cluster. The observations show a varying reconnection rate which support the previous interpretation that reconnection is continuous but its rate is modulated.</p><p>Finally, we compare local energy estimates from Cluster with a global magnetohydrodynamic simulation. The results show that the observations are reliably reproduced by the model and may be used to validate and scale global magnetohydrodynamic models.</p>

Ce manuscrit porte sur les transitions compressible-incompressible dans les équations aux dérivées partielles de la mécanique des fluides. On s'intéresse à deux problèmes : les structures flottantes et les fluides en rotation. Dans le premier problème, l'introduction d'un objet flottant dans les vagues induit une contrainte sur le fluide et les équations gouvernant le mouvement acquièrent une structure compressible-incompressible. Dans le deuxième problème, le mouvement de fluides géophysiques compressibles est influencé par la rotation de la Terre. L'étude de la limite à rotation rapide montre que le champ vectoriel de vitesse tend vers une configuration horizontale et incompressible.Les structures flottantes constituent un exemple particulier d'interaction fluide-structure, où un solide partiellement immergé flotte à la surface du fluide. Ce problème mathématique modélise le mouvement de convertisseurs d'énergie marine. En particulier, on s'intéresse aux bouées pilonnantes, installées proche de la côte où les modèles asymptotiques en eaux peu profondes sont valables. On étudie les équations de Saint-Venant axisymétriques en dimension deux avec un objet flottant à murs verticaux se déplaçant seulement verticalement. Les hypothèses sur le solide permettent de supprimer le problème à bord libre associé avec la ligne de contact entre l'air, le fluide et le solide. Les équations pour le fluide dans le domaine extérieur au solide sont donc écrites comme un problème au bord quasi-linéaire hyperbolique. Celui-ci est couplé avec une EDO non-linéaire du second ordre qui est dérivée de l'équation de Newton pour le mouvement libre du solide. On montre le caractère bien posé localement en temps du système couplé lorsque que les données initiales satisfont des conditions de compatibilité afin de générer des solutions régulières.Ensuite on considère une configuration particulière: le retour à l'équilibre. Il s'agit de considérer un solide partiellement immergé dans un fluide initialement au repos et de le laisser retourner à sa position d'équilibre. Pour cela, on utilise un modèle hydrodynamique différent, où les équations sont linearisées dans le domaine extérieur, tandis que les effets non-linéaires sont considérés en dessous du solide. Le mouvement du solide est décrit par une équation intégro-différentielle non-linéaire du second ordre qui justifie rigoureusement l'équation de Cummins, utilisée par les ingénieurs pour les mouvements des objets flottants. L'équation que l'on dérive améliore l'approche linéaire de Cummins en tenant compte des effets non-linéaires. On montre l'existence et l'unicité globale de la solution pour des données petites en utilisant la conservation de l'énergie du système fluide-structure.Dans la deuxième partie du manuscrit, on étudie les fluides en rotation rapide. Ce problème mathématique modélise le mouvement des flots géophysiques à grandes échelles influencés par la rotation de la Terre. Le mouvement est aussi affecté par la gravité, ce qui donne lieu à une stratification de la densité dans les fluides compressibles. La rotation génère de l'anisotropie dans les flots visqueux et la viscosité turbulente verticale tend vers zéro dans la limite à rotation rapide. Notre interêt porte sur ce problème de limite singulière en tenant compte des effets gravitationnels et compressibles. On étudie les équations de Navier-Stokes-Coriolis anisotropes compressibles avec force gravitationnelle dans la bande infinie horizontale avec une condition au bord de non glissement. Celle-ci et la force de Coriolis donnent lieu à l'apparition des couches d'Ekman proche du bord. Dans ce travail on considère des données initiales bien préparées. On montre un résultat de stabilité des solutions faibles globales pour des lois de pression particulières. La dynamique limite est décrite par une équation quasi-géostrophique visqueuse en dimension deux avec un terme d'amortissement qui tient compte des couches limites. / This manuscript deals with compressible-incompressible transitions arising in partial differential equations of fluid mechanics. We investigate two problems: floating structures and rotating fluids. In the first problem, the introduction of a floating object into water waves enforces a constraint on the fluid and the governing equations turn out to have a compressible-incompressible structure. In the second problem, the motion of geophysical compressible fluids is affected by the Earth's rotation and the study of the high rotation limit shows that the velocity vector field tends to be horizontal and with an incompressibility constraint.Floating structures are a particular example of fluid-structure interaction, in which a partially immersed solid is floating at the fluid surface. This mathematical problem models the motion of wave energy converters in sea water. In particular, we focus on heaving buoys, usually implemented in the near-shore zone, where the shallow water asymptotic models describe accurately the motion of waves. We study the two-dimensional nonlinear shallow water equations in the axisymmetric configuration in the presence of a floating object with vertical side-walls moving only vertically. The assumptions on the solid permit to avoid the free boundary problem associated with the moving contact line between the air, the water and the solid. Hence, in the domain exterior to the solid the fluid equations can be written as an hyperbolic quasilinear initial boundary value problem. This couples with a nonlinear second order ODE derived from Newton's law for the free solid motion. Local in time well-posedness of the coupled system is shown provided some compatibility conditions are satisfied by the initial data in order to generate smooth solutions.Afterwards, we address a particular configuration of this fluid-structure interaction: the return to equilibrium. It consists in releasing a partially immersed solid body into a fluid initially at rest and letting it evolve towards its equilibrium position. A different hydrodynamical model is used. In the exterior domain the equations are linearized but the nonlinear effects are taken into account under the solid. The equation for the solid motion becomes a nonlinear second order integro-differential equation which rigorously justifies the Cummins equation, assumed by engineers to govern the motion of floating objects. Moreover, the equation derived improves the linear approach of Cummins by taking into account the nonlinear effects. The global existence and uniqueness of the solution is shown for small data using the conservation of the energy of the fluid-structure system.In the second part of the manuscript, highly rotating fluids are studied. This mathematical problem models the motion of geophysical flows at large scales affected by the Earth's rotation, such as massive oceanic and atmospheric currents. The motion is also influenced by the gravity, which causes a stratification of the density in compressible fluids. The rotation generates anisotropy in viscous flows and the vertical turbulent viscosity tends to zero in the high rotation limit. Our interest lies in this singular limit problem taking into account gravitational and compressible effects. We study the compressible anisotropic Navier-Stokes-Coriolis equations with gravitational force in the horizontal infinite slab with no-slip boundary condition. Both this condition and the Coriolis force cause the apparition of Ekman layers near the boundary. They are taken into account in the analysis by adding corrector terms which decay in the interior of the domain. In this work well-prepared initial data are considered. A stability result of global weak solutions is shown for power-type pressure laws. The limit dynamics is described by a two-dimensional viscous quasi-geostrophic equation with a damping term that accounts for the boundary layers.

<p>Magnetic reconnection is a universal process occurring at boundaries between magnetized plasmas, where changes in the topology of the magnetic field lead to the transport of charged particles across the boundaries and to the conversion of electromagnetic energy into kinetic and thermal energy of the particles. Reconnection occurs in laboratory plasmas, in solar system plasmas and it is considered to play a key role in many other space environments such as magnetized stars and accretion disks around stars and planets under formation. Magnetic reconnection is a multi-scale plasma process where the small spatial and temporal scales are strongly coupled to the large scales. Reconnection is initiated rapidly in small regions by microphysical processes but it affects very large volumes of space for long times. The best laboratory to experimentally study magnetic reconnection at different scales is the near-Earth space, the so-called Geospace, where Cluster spacecraft <i>in situ</i> measurements are available. The European Space Agency Cluster mission is composed of four-spacecraft flying in a formation and this allows, for the first time, simultaneous four-point measurements at different scales, thanks to the changeable spacecraft separation. In this thesis Cluster observations of magnetic reconnection in Geospace are presented both at large and at small scales. </p><p>At large temporal (a few hours) and spatial (several thousands km) scales, both fluid and kinetic evidence of reconnection is provided. The evidence consist of ions accelerated and transmitted across the Earth’s magnetopause. The observations show that component reconnection occurs at the magnetopause and that reconnection is continuous in time. </p><p>The microphysics of reconnection is investigated at smaller temporal (a few ion gyroperiods) and spatial (a few ion gyroradii) scales. Two regions are important for the microphysics: the X-region, around the X-line, where reconnection is initiated and the separatrix region, away from the X-line, where most of the energy conversion occurs. Observations of a separatrix region at the magnetopause are shown and the microphysics is described in detail. The separatrix region is shown to be highly structured and dynamic even away from the X-line.</p><p>Finally the discovery of magnetic reconnection in turbulent plasma is presented by showing, for the first time, <i>in situ</i> evidence of reconnection in a thin current sheet found in the turbulent plasma downstream of the quasi-parallel Earth’s bow shock. It is shown that turbulent reconnection is fast and that electromagnetic energy is converted into heating and acceleration of particles in turbulent plasma. It is also shown that reconnecting current sheets are abundant in turbulent plasma and that reconnection can be an efficient energy dissipation mechanism.</p>

A series of laboratory experiments were conducted at three fetches of 4.8, 8.8 and 12.4 m, and at six wind speeds ranging from 4.1 to 9.6 m/s at each fetch in a wind-wave-current research facility. In addition, five surfactant-influenced experiments were conducted at concentrations ranging from 0.1 to 5.0 ppm at a wind speed of 7.9 m/s and a fetch of 4.8 m. The goals were to examine the momentum transfer and to characterize the turbulent flow structure beneath wind waves, and to investigate the relationship between wind waves and the gas transfer rate at the air-water interface. Digital particle image velocimetry (DPIV) was used to measure two-dimensional instantaneous velocity fields beneath the wind waves. The friction velocities and roughness lengths of the coupled boundary layers were used to characterize the flow regime and momentum transfer. The air-side flows were found to be aerodynamically rough and the water-side flows were found to be in transition and then become hydrodynamically smooth as wind speed increased. Airflow separation from the crests of breaking waves may be responsible for making the air-side boundary layer rougher and water-side boundary layer smoother. Momentum transfer was studied by examining the partitioning of the wind stress into the viscous tangential stress and wave-induced stress. It was found that the wave steepness was the most important wind-wave property that controls the momentum transfer in the coupled boundary layers. Two distinct layers were observed in the near-surface turbulence in the presence of a surfactant and three layers in clean water. In the surfactant-influenced experiments, the energy dissipation rate decayed as zeta^(-0.3) in the upper layer and in the lower layer energy dissipation rate decayed as zeta^(-1.0) similar to a wall-layer. For clean experiments, the energy dissipation rate could be scaled using the depth, friction velocity, wave height and phase speed as proposed by Terray et al. (1996) provided that layer based friction velocities were used. In the upper layer, the near-surface turbulence was dominated by wave-induced motions and the dissipation rates decayed as zeta^(-0.2) at all fetches. Below this in the transition layer turbulence was generated by both wave-induced motions and shear currents and the dissipation rate decayed as zeta^(-2.0) at a fetch of 4.8 m. However, at fetches of 8.8 and 12.4 m, the dissipation rate decayed at two different rates; as zeta^(-2.0) in the upper region and as zeta^(-4.0) in the lower region. In the third layer, the dissipation rate decayed as zeta^(-1.0) similar to a wall-layer at a fetch of 4.8 m. Four empirical relationships commonly used to predict the gas transfer rate were evaluated using laboratory measurements. The gas transfer rate was found to correlate most closely with the total mean square wave slope and varied linearly with this parameter. The three other parameterizations using wind speed, wind friction velocity and energy dissipation did not correlate as well. / Water Resources Engineering

Magnetic reconnection is a universal process occurring at boundaries between magnetized plasmas, where changes in the topology of the magnetic field lead to the transport of charged particles across the boundaries and to the conversion of electromagnetic energy into kinetic and thermal energy of the particles. Reconnection occurs in laboratory plasmas, in solar system plasmas and it is considered to play a key role in many other space environments such as magnetized stars and accretion disks around stars and planets under formation. Magnetic reconnection is a multi-scale plasma process where the small spatial and temporal scales are strongly coupled to the large scales. Reconnection is initiated rapidly in small regions by microphysical processes but it affects very large volumes of space for long times. The best laboratory to experimentally study magnetic reconnection at different scales is the near-Earth space, the so-called Geospace, where Cluster spacecraft in situ measurements are available. The European Space Agency Cluster mission is composed of four-spacecraft flying in a formation and this allows, for the first time, simultaneous four-point measurements at different scales, thanks to the changeable spacecraft separation. In this thesis Cluster observations of magnetic reconnection in Geospace are presented both at large and at small scales. At large temporal (a few hours) and spatial (several thousands km) scales, both fluid and kinetic evidence of reconnection is provided. The evidence consist of ions accelerated and transmitted across the Earth’s magnetopause. The observations show that component reconnection occurs at the magnetopause and that reconnection is continuous in time. The microphysics of reconnection is investigated at smaller temporal (a few ion gyroperiods) and spatial (a few ion gyroradii) scales. Two regions are important for the microphysics: the X-region, around the X-line, where reconnection is initiated and the separatrix region, away from the X-line, where most of the energy conversion occurs. Observations of a separatrix region at the magnetopause are shown and the microphysics is described in detail. The separatrix region is shown to be highly structured and dynamic even away from the X-line. Finally the discovery of magnetic reconnection in turbulent plasma is presented by showing, for the first time, in situ evidence of reconnection in a thin current sheet found in the turbulent plasma downstream of the quasi-parallel Earth’s bow shock. It is shown that turbulent reconnection is fast and that electromagnetic energy is converted into heating and acceleration of particles in turbulent plasma. It is also shown that reconnecting current sheets are abundant in turbulent plasma and that reconnection can be an efficient energy dissipation mechanism.

Magnetized planets, such as Earth, are strongly influenced by the solar wind. The Sun is very dynamic, releasing varying amounts of energy, resulting in a fluctuating energy and momentum exchange between the solar wind and planetary magnetospheres. The efficiency of this coupling is thought to be controlled by magnetic reconnection occurring at the boundary between solar wind and planetary magnetic fields. One of the main tasks in space physics research is to increase the understanding of this coupling between the Sun and other solar system bodies. Perhaps the most important aspect regards the transfer of energy from the solar wind to the terrestrial magnetosphere as this is the main source for driving plasma processes in the magnetosphere-ionosphere system. This may also have a direct practical influence on our life here on Earth as it is responsible for Space Weather effects. In this thesis I investigate both the global scale of the varying solar-terrestrial coupling and local phenomena in more detail. I use mainly the European Space Agency Cluster mission which provide unprecedented three-dimensional observations via its formation of four identical spacecraft. The Cluster data are complimented with observations from a broad range of instruments both onboard spacecraft and from groundbased magnetometers and radars. A period of very strong solar driving in late October 2003 is investigated. We show that some of the strongest substorms in the history of magnetic recordings were triggered by pressure pulses impacting a quasi-stable magnetosphere. We make for the first time direct estimates of the local energy flow into the magnetotail using Cluster measurements. Observational estimates suggest a good energy balance between the magnetosphere-ionosphere system while empirical proxies seem to suffer from over/under estimations during such extreme conditions. Another period of extreme interplanetary conditions give rise to accelerated flows along the magnetopause which could account for an enhanced energy coupling between the solar wind and the magnetosphere. We discuss whether such conditions could explain the simultaneous observation of a large auroral spiral across the polar cap. Contrary to extreme conditions the energy conversion across the dayside magnetopause has been estimated during an extended period of steady interplanetary conditions. A new method to determine the rate at which reconnection occurs is described that utilizes the magnitude of the local energy conversion from Cluster. The observations show a varying reconnection rate which support the previous interpretation that reconnection is continuous but its rate is modulated. Finally, we compare local energy estimates from Cluster with a global magnetohydrodynamic simulation. The results show that the observations are reliably reproduced by the model and may be used to validate and scale global magnetohydrodynamic models.

This is an experimental and theoretical study of a laminar separation bubble and the associated transition dynamics in its early stages. The separation of a laminar boundary layer from a solid surface is prevalent in very many flow situations such as over gas turbine blades (especially in the low-pressure turbine stage) and the wings of micro-aero-vehicles (MAVs) that operate at fairly low Reynolds numbers. Flow separation occurs in such cases due to the presence of an adverse pressure gradient. The separated shear layer becomes unstable due to the presence of an inflection point and presumably transitions to turbulence rapidly. Eventually, there is reattachment back to the solid surface further downstream, if conditions are right. The region enclosed by the shear layer is called a laminar separation bubble and has been a subject of many studies in the past. The present experiments have been conducted in a closed-circuit wind tunnel. A separation bubble was obtained on the upper surface of a flat plate by appropriately contouring the top wall of the tunnel. Four different techniques were used for qualitative and quantitative study viz. surface flow visualisation, smoke flow visualisation, surface pressure measurements and hotwire anemometry. Response of the bubble to both natural as well as artificial (impulsive excitation) disturbance environment has been studied. Linear stability analyses (both Orr-Sommerfeld and Rayleigh calculations), in the spatial framework, have been performed for the mean velocity profiles starting from an attached adverse pressure gradient boundary layer all the way up to the front portion of the separation bubble region (i.e. up to the end of the dead-air region where linear evolution of disturbances could be expected). The measured velocity profiles (both attached and separated) were fitted with analytical model profiles for doing stability calculations. A separation bubble consists of aspects of both wall-bounded and wall-free shear layers and therefore both viscous and inviscid mechanisms are expected to be at play. Most of the studies in the literature point to the inviscid instability associated with the shear layer to be the main mechanism. The main aim of the present work is to understand the exact origin of the primary instability mechanism responsible for the amplification of disturbances. We argue that at least up to the front portion of the bubble, the instability mechanism is due to the inflectional mode associated with the mean velocity profile. However, the seeds of this inviscid inflectional instability could be traced back to the attached boundary layer upstream of separation. In other words, the inviscid inflectional instability of the separated shear layer should be logically seen as an extension of the instability of the upstream attached adverse-pressure-gradient boundary layer. This modifies the traditional view that pegs the origin of the instability in a separation bubble to the free shear layer outside the bubble with its associated Kelvin-Helmholtz mechanism. Our contention is that only when the separated shear layer has moved considerably away from the wall (and this happens near the maximum height of the mean bubble) that a description by Kelvin-Helmholtz instability paradigm with its associated scaling principles could become relevant. We also propose a new scaling for the most amplified frequency for a wall-bounded shear layer in terms of the inflection point height and the vorticity thickness, and show its universality. Next, we theoretically investigate the role played by the re-circulating region of the separation bubble in the linear instability regime. In the re-circulating region near the wall, associated with the so-called wall mode, the production of disturbance kinetic energy is found to be negative. This is a very interesting observation which has been cursorily noted in earlier studies. Here we show that the near-wall negative production region exerts a stabilising influence on the downstream travelling disturbances. A theoretical support for such a mechanism to exist close to the wall is presented. It is shown that the stabilising wall-proximity effect is not a peripheral aspect but has a significant effect on the overall stability especially for the waves close to the upper neutral branch. We demonstrate the appropriateness of inviscid analysis for the stability of the separated flow velocity profile away from the wall, by comparing the numerical solutions of Rayleigh and Orr-Sommerfeld equations. Following this, the analytical consequences of the Rayleigh equation such as the inflection point criterion and the Fjortoft criterion are derived for the wall-bounded inflectional velocity profiles. Furthermore, we also discuss the relevance of the negative production region towards flow control and management for the wall-bounded flows. It appears fruitful to divide the separation bubble region into two parts with respect to the nature of disturbance dynamics: one outside the mean dividing streamline (which behaves as an amplifier) and the other inside the bubble corresponding to the re-circulating region (having oscillator type characteristics). To explore the oscillator-like behaviour of the bubble further, we have carried out spatio-temporal stability analysis of the reversed flow velocity profiles and determined the conditions for the onset of absolute instability. We contend that the presence of the negative production region for the upstream travelling waves has a restraining effect arresting the tendency of the flow (both wall-free and wall-bounded) to become absolutely unstable and thereby requiring a particular threshold of the backflow velocity to be crossed for its realisation. Moreover, the delay in the onset of absolute instability for a wall-bounded profile as compared to a free shear layer is attributed to a certain ‘negative-drag’ effect of the wall on the overall flow which increases the group velocities for the wall-bounded flows. A related theme in the literature regarding the dynamics of laminar separation bubbles is the so-called ‘bursting’ of the bubble wherein there is a sudden increase in the length and height of the bubble as some critical conditions are reached. Bubbles before bursting are termed as ‘short’ bubbles and those after bursting as ‘long’ bubbles. In this work, we provide a criterion to predict bursting which is a refinement over the existing criteria. The proposed criterion takes into account not just the length of the bubble but also the maximum height and it is shown to be more universal in differentiating short bubbles from the long ones, as compared to the other criteria. We also present a hypothesis regarding the sequence of events leading to bubble bursting by relating its onset to the instability of the re-circulating region. For this we observe that as the amount of backflow velocity is increased for a reversed flow velocity profile, the inflection point moves inside the mean dividing streamline and this happens before the onset of absolute instability. This causes a vorticity maximum to develop inside the re-circulating region which could lead to the instability of the closed streamlines with respect to two-dimensional cylindrical disturbances. The actual bursting process may be expected to involve non-linear interactions of the disturbances and the long bubble could be a nonlinearly saturated state of the instability of the re-circulating region. In order to explore the three-dimensionality associated with the bubble, extensive surface flow visualisation experiments have been performed. The surface streamline pattern is obtained for the entire span of the plate for three different freestream velocities. The patterns have been interpreted using topological ideas and various critical points have been identified. It is shown that the arrangement of critical points satisfies the ‘index theorem’ which is a topological necessity and the streamline patterns are ‘structurally stable’. An interesting observation from these patterns is the presence of three-dimensionality upstream of the separation line close to the wall even though the oncoming flow is nominally two-dimensional. Using the critical point theory, we propose a hypothesis which could be used to construct a semi-empirical model wherein the critical points are assigned with a quantity called ‘strength’ for determining the extent of upstream influence of a given separation line. Finally, we derive a necessary condition for the existence of inviscid spatial instability in plane parallel flows. It states that for spatial instability the curvature of the velocity profile should be positive in some region of the profile. This includes Rayleigh’s inflection point theorem (which was proposed and proved by Rayleigh for temporal instability) as a special case. It thus provides a rigorous basis for applying the inflection point criterion to the flows in the framework of spatial stability theory (which we have used extensively in the present thesis). Moreover, the condition derived here is more general as it also includes velocity profiles with the curvature positive everywhere which are excluded by Rayleigh’s theorem in the temporal framework. An example of such a profile is presented (Couette-Poiseuille flow with adverse pressure gradient) and it is shown that this flow is an exceptional case which is temporally stable but spatially unstable. Eigenvalue calculations as well as energy considerations suggest that the mechanism governing instability of this flow is inviscid and non-inflectional in character. This is a new result which could have important implications in understanding the instability dynamics of parallel flows.

No description available.

Shock Boundary Layer Interactions (SBLIs) and shock-shock interactions are some of the most fundamental problems in high speed aerodynamics. These interactions are of particular importance in scramjet intakes at hypersonic speeds. In hypersonic own with strong SBLI accompanied by own separation, large separation bubbles can form due to high impinging shock strengths. While experiments involving large separation lengths for the impinging shock boundary layer interactions near sharp leading edge are well documented in the literature, only few investigations on the effect of leading edge bluntness on the interactions are studied. In the present study, experiments were carried out to study the role of leading edge bluntness on the impinging shock boundary layer interactions. An oblique shock generated by a wedge (wedge angle 31 degrees) is made to impinge on a at plate (length 200 mm) over which a boundary layer develops. Different leading edge inserts were used on a at plate to get either a sharp or a blunt (radii from 2 to 8 mm) leading edge. The position of the at plate was moved horizontally with respect to the wedge to vary the shock impingement location relative to the leading edge. Experiments were carried out at two freestream conditions - Mach 5.88 (total enthalpy of 1.26 MJ/kg and freestream Reynolds number of 3.85 million per meter) and Mach 8.54 (total enthalpy of 1.85 MJ/kg and freestream Reynolds number of 1.41 million per meter). The various features of the interaction along with different parameters were obtained from schlieren visualizations and surface pressure measurements. The schlieren visualization was used to obtain the separation length, while the reattachment pressure was obtained from the surface pressure distribution. From the present experimental study, a reduction in separation length was observed with an increase in leading edge bluntness. It was also seen that the sharp leading edge had the maximum separation length. Correlations for the separation length and the reattachment pressure have been proposed for these experimental conditions. Numerical simulations were also carried out using commercial software and they had a qualitative agreement with the experiments.