The study presented in this thesis investigates the passive exchange of enclosed water with seawater in an offshore wind turbine foundation. This thesis was undertaken in collaboration with Vattenfall R&D, Älvkarleby, Sweden. The water exchange is studied by utilizing Computational Fluid Dynamics (CFD) simulations. A standard monopile foundation, which is installed in Horns Rev 3 wind farm, is considered for the study. The considered geometry consists of two replenishment holes.  The study aims to develop a methodology to utilize CFD simulations to quantify the exchange rate of water. CFD enables studying the effects of different wave parameters and sea states on the economic exchange rate. However, the secondary aim to develop the methodology for the CFD simulations is also to utilize the available computational resources efficiently.  The CFD methodology incorporates the learning from experiments and utilizes a semi-circular domain to enclose the control volume. The results from a mesh sensitivity study establish that a coarser mesh in the domain and a finer mesh within the monopile, coupled with Implicit LES is appropriate to study the overall effect of wave motion on the exchange rate. Also, the additional term scalar transport, incorporated to study the change in concentration within the monopile, provided an appropriate and computationally efficient tool to visualize the variation in water concentration.

This thesis is devoted to the study of the dynamics of spiral and scroll waves in a mathematical model for cardiac tissue. We study the effects of the presence of heterogeneities on electrical-wave dynamics. The heterogeneities in the medium occur because of the variation in the electrophysiological properties of the constituent myocytes in the tissue, or because of the presence of cells like fibroblasts and pathological myocytes that can trigger early afterdepolarizations (EADs). We study how these heterogeneities can lead to the formation of spiral and scroll waves and how they can affect the stability of the spiral and scroll waves in cardiac tissue. We also investigate the role of abnormal cells, which can trigger pathological excitations like EADs, on the formation of spiral and scroll waves, and how such cells can trigger premature electrical pulses like premature-ventricular-complexes (PVCs) in cardiac tissue. Earlier studies have examined the role of ionic heterogeneities on spiral-wave initiation and their effects on spiral-wave stability. However, none of these studies has calculated, in a controlled way, the effects of individual ion-channel conductances on spiral- and scroll-wave properties, such as the frequency of these waves, and the effects of the spatial gradients, in each ion-channel conductance, on their stability; we present these results in Chapter 2. Although many studies in the past have studied the effects of fibroblast coupling on wave-dynamics in cardiac tissue, a detailed study of spiral-wave dynamics in a medium with a well-defined, heterogeneous distribution of fibroblasts (e.g., with a gradient in the fibroblast density (GFD)) has not been performed; therefore, in Chapter 3 we present the effects of such GFD on spiral- and scroll-wave dynamics. Then, in Chapter 4, we present a systematic study of how a clump of fibroblasts can lead to spiral waves via high-frequency pacing. Some studies in the past have studied the role of early afterdepolarizations (EADs) in the formation of arrhythmias in cardiac tissue; we build on such studies and present a detailed study of the effects of EADs on the formation of spiral waves and their dynamics, in Chapter 5. Finally, in Chapter 6 we provide the results of our detailed investigation of the factors that assist the triggering of abnormal electrical pulses like premature ventricular complexes by a cluster of EAD-capable cells. A brief summary of the chapters is provided below: Chapter 2: In this chapter we investigate the effects of spatial gradients in the ion-channel conductances of various ionic currents on spiral-and scroll-wave dynamics. Ionic heterogeneities in cardiac tissue arise from spatial variations in the electrophysiological properties of cells in the tissue. Such variations, which are known to be arrhythmogenic, can be induced by diseases like ischemia. It is important, therefore, to understand the effects of such ionic heterogeneities on electrical-wave dynamics in cardiac tissue. To investigate such effects systematically, of changing the ion-channel properties by modifying the conductances of each ionic currents, on the action-potential duration (APD) of a myocyte cell. We then study how these changes in the APD affect the spiral-wave frequency ω in two-dimensional tissue. We also show that changing the ion-channel conductance not only changes ω but also the meandering pattern of the spiral wave. We then study how spatial gradients in the ion-channel conductances affect the spiral-wave stability. We find that the presence of this ionic gradient induces a spatial variation of the local ω, which leads to an anisotropic reduction of the spiral wavelength in the low-ω region and, thereby, leads to a breakup of the spiral wave. We find that the degree of the spiral-wave stability depends on the magnitude of the spatial variation in ω, induced by the gradient in the ion-channel conductances. We observe that ω varies most drastically with the ion-channel conductance of rapid delayed rectifier K+ current GKr, and, hence, a spiral wave is most unstable in the presence of a gradient in GKr (as compared to other ion-channel conductances). By contrast, we find that ω varies least prominently with the conductances of the transient outward K+ current Gto and the fast inward Na+ current (GNa); hence, gradients in these conduc-tances are least likely to lead to spiral-wave breaks. We also investigate scroll-wave instability in an anatomically-realistic human-ventricular heart model with an ionic gradient along the apico-basal direction. Finally, we show that gradients in the ion-channel densities can also lead to spontaneous initiation of spiral waves when we pace the medium at high frequency. Chapter 3: In this chapter we study the effects of gradients in the density of fibroblasts on wave-dynamics in cardiac tissue. The existence of fibroblast-myocyte coupling can modulate electrical-wave dynamics in cardiac tissue. In diseased hearts, the distribution of fibroblasts is heterogeneous, so there can be gradients in the fibroblast density (henceforth we call this GFD) especially from highly injured regions, like infarcted or ischemic zones, to less-wounded regions of the tissue. Fibrotic hearts are known to be prone to arrhythmias, so it is important to understand the effects of GFD in the formation and sustenance of arrhythmic re-entrant waves, like spiral or scroll waves. Therefore, we investigate the effects of GFD on the stability of spiral and scroll waves of electrical activation in a state-of-the-art mathematical model for cardiac tissue in which we also include fibroblasts. By introducing GFD in controlled ways, we show that spiral and scroll waves can be unstable in the presence of GFDs because of regions with varying spiral or scroll-wave frequency ω, induced by the GFD. We examine the effects of the resting membrane potential of the fibroblast and the number of fibroblasts attached to the myocytes on the stability of these waves. Finally, we show that the presence of GFDs can lead to the formation of spiral waves at high-frequency pacing. Chapter 4: In this chapter we study the arrhythmogenic effects of lo-calized fibrobblast clumps. Localized heterogeneities, caused by the regional proliferation of fibroblasts, occur in mammalian hearts because of diseases like myocardial infarction. Such fibroblast clumps can become sources of pathological reentrant activities, e.g., spiral or scroll waves of electrical activation in cardiac tissue. The occurrence of reentry in cardiac tissue with heterogeneities, such as fibroblast clumps, can depend on the frequency at which the medium is paced. Therefore, it is important to study the reentry-initiating potential of such fibroblast clumps at different frequencies of pacing. We investigate the arrhythmogenic effects of fibroblast clumps at high- and low-frequency pacing. We find that reentrant waves are induced in the medium more prominently at high-frequency pacing than with low-frequency pacing. We also study the other factors that affect the potential of fibroblast clumps to induce reentry in cardiac tissue. In particular, we show that the ability of a fibroblast clump to induce reentry depends on the size of the clump, the distribution and percentage of fibroblasts in the clump, and the excitability of the medium. We study the process of reentry in two-dimensional and a three-dimensional mathematical models for cardiac tissue. Chapter 5: In this chapter we investigate the role of early afterdepolarizations (EADs) on the formation of spiral and scroll waves. Early after depolarizations, which are abnormal oscillations of the membrane poten-tial at the plateau phase of an action potential, are implicated in the de-velopment of cardiac arrhythmias like Torsade de Pointes. We carry out extensive numerical simulations of the TP06 and ORd mathematical models for human ventricular cells with EADs. We investigate the different regimes in both these models, namely, the parameter regimes where they exhibit (1) a normal action potential (AP) with no EADs, (2) an AP with EADs, and (3) an AP with EADs that does not go back to the resting potential. We also study the dependence of EADs on the rate of at which we pace a cell, with the specific goal of elucidating EADs that are induced by slow or fast rate pacing. In our simulations in two- and three-dimensional domains, in the presence of EADs, we find the following wave types: (A) waves driven by the fast sodium current and the L-type calcium current (Na-Ca-mediated waves); (B) waves driven only by the L-type calcium current (Ca-mediated waves); (C) phase waves, which are pseudo-travelling waves. Furthermore, we compare the wave patterns of the various wave-types (Na-Ca-mediated, Ca-mediated, and phase waves) in both these models. We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca- mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves. However, there are quantitative differences in the wave patterns of each wave type. The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not. The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model. Chapter 6: In this chapter we study the role of EAD-capable cells, and fibroblasts on the trigerring of abnormal electrical pulses called premature ventricular complexes (PVCs). Premature ventricular complexes, which are abnormal impulse propagations in cardiac tissue, can develop because of various reasons including early afterdepolarizations (EADs). We show how a cluster of EAD-generating cells (EAD clump) can lead to PVCs in a model of cardiac tissue, and also investigate the factors that assist such clumps in triggering PVCs. In particular, we study, through computer simulations, the effects of the following factors on the PVC-triggering ability of an EAD clump: (1) the repolarization reserve (RR) of the EAD cells; (2) the size of the EAD clump; (3) the coupling strength between the EAD cells in the clump; and (4) the presence of fibroblasts in the EAD clump. We find that, although a low value of RR is necessary to generate EADs and hence PVCs, a very low value of RR leads to low-amplitude EAD oscillations that decay with time and do not lead to PVCs. We demonstrate that a certain threshold size of the EAD clump, or a reduction in the coupling strength between the EAD cells, in the clump, is required to trigger PVCs. We illustrate how randomly distributed inexcitable obstacles, which we use to model collagen deposits, affect PVC-triggering by an EAD clump. We show that the gap-junctional coupling of fibroblasts with myocytes can either assist or impede the PVC-triggering ability of an EAD clump, depending on the resting membrane potential of the fibroblasts and the coupling strength between the myocyte and fibroblasts. We also find that the triggering of PVCs by an EAD clump depends sensitively on factors like the pacing cycle length and the distribution pattern of the fibroblasts.

There is a growing consensus that life-threatening cardiac arrhythmias like ven- tricular tachycardia (VT) or ventricular fibrillation (VF) arise because of the formation of spiral waves of electrical activation in cardiac tissue; unbroken spiral waves are associated with VT and broken ones with VF. Several experimental studies have shown that in homogeneities in cardiac tissue can have dramatic effects on such spiral waves. In this thesis we focus on spiral-wave dynamics in mathematical models of human ventricular tissue which contain (a) conduction in homogeneities, (b) ionic in- homogeneities, (c) fibroblasts, (d) Purkinje fibers. We also study the effect of a periodic deformation of the simulation domain on spiral wave-dynamics. Chapter 2 contains our study of “Spiral-Wave Dynamics and Its Control in the Presence of In homogeneities in Two Mathematical Models for Human Cardiac Tissue”; this chapter follows closely parts of a paper we have published [1]. Chapter 3 contains our study of “Spiral-wave dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts”; this chapter follows closely a paper that we have submitted for publication. Chapter 4 contains our study of “Spiral-wave Dynamics in Ionically Realistic Mathematical Models for Human Ventricular Tis- sue: The Effects of Periodic Deformation”; this chapter follows closely a paper that we have submitted for publication. Chapter 5 contains our study of “Spiral-wave dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Purkinje fibers”; this chapter follows closely a paper that we will submit for publication soon. In chapter 2, we study systematically the AP morphology in a state-of-the-art mathematical model of human ventricular tissue due to ten-Tusscher, Noble, Noble, and Panfilov (the TNNP04 model); we also look at the contribution of individual ionic currents to the AP by partially or completely blocking ion channels associated with the ionic currents. We then carry out systematic studies of plane- wave and circular-wave dynamics in the TNNP04 model for cardiac tissue model. We present a detailed and systematic study of spiral-wave turbulence and spa- tiotemporal chaos in two mathematical models for human cardiac tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNP04 model). In particular, we use extensive numerical simulations to elucidate the interaction of spiral waves in these models with conduction and ionic in homogeneities. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such in homogeneities. A major goal here is to develop low amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of in homogeneities that occur commonly in cardiac tissue. Therefore, we study a control scheme that has been suggested for the control of spiral turbulence, via low-amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control scheme in the presence of in homogeneities in biophysical realistic models. We find that a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence than other control schemes. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation. In chapter 3, we study the role of cardiac fibroblasts in ventricular tissue; we use the TNNP04 model for the myocyte cell, and the fibroblasts are modelled as passive cells. Cardiac fibroblasts, when coupled functionally with myocytes, can modulate their electrophysiological properties at both cellular and tissue levels. Therefore, it is important to study the effects of such fibroblasts when they are coupled with myocytes. Chapter 3 contains our detailed and systematic study of spiral-wave dynamics in the presence of fibroblasts in both homogeneous and inhomogeneous domains of the TNNP04 model for cardiac tissue. We carry out extensive numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for no, one-way, or two-way MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as Ef , the fibroblast resting membrane potential, the fibroblast conductance Gf , and the MF gap-junctional coupling Ggap. Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as Ggap, Gf , and Ef , and (c) intercellular couplings that can be no, one-way, and two-way connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity CV decreases as a function of Ggap, for no and one-way couplings; however, for two-sided coupling, CV decreases initially and then increases as a function of Ggap, and, eventually, we observe that conduction failure occurs for low values of Ggap. In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling Ggap or Ef . Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities. In chapter 4, we carry out a detailed, systematic study of spiral-wave dynamics in the presence of periodic deformation (PD) in two state-of-the-art mathematical models of human ventricular tissue, namely, the TNNP04 model and the TP06 model. To the best of our knowledge, our work is the first, systematic study of the dynamics of spiral waves of electrical activation and their transitions, in the presence of PD, in such biophysically realistic mathematical models of cardiac tissue. In our studies, we use three types of initial conditions whose time evolutions lead to the following states in the absence of PD: (a) a single rotating spiral (RS), (b) a spiral-turbulence (ST) state, with a single meandering spiral, and (c) an ST state with multiple broken spirals for both these models. We then show that the imposition of PD in these three cases leads to a rich variety of spatiotemporal pat- terns in the transmembrane potential including states with (a) an RS state with n-cycle temporal evolution (here n is a positive integer), (b) rotating-spiral states with quasiperiodic (QP) temporal evolution, (c) a state with a single meandering spiral MS, which displays spatiotemporal chaos, (d) an ST state, with multiple bro- ken spirals, and (e) a quiescent state in which all spirals are absorbed (SA). For all three initial conditions, precisely which one of the states is obtained depends on the amplitudes and the frequencies of the PD in the x and y directions. We also suggest specific experiments that can test the results of our simulations. We also study, in the presence of PD, the efficacy of a low-amplitude control scheme that has been suggested, hitherto only without PD, for the control of spiral-wave turbulence, via low-amplitude current pulses applied on a square mesh, in mathematical models for cardiac tissue. We also develop line-mesh and rectangular-mesh variants of this control scheme. We find that square- and line-mesh-based, low-amplitude control schemes suppress spiral-wave turbulence in both the TP06 and TNNP04 models in the absence of PD; however, we show that the line-based scheme works with PD only if the PD is applied along one spatial direction. We then demonstrate that a minor modification of our line-based control scheme can suppress spiral-wave turbulence: in particular, we introduce a rectangular-mesh-based control scheme, in which we add a few control lines perpendicular to the parallel lines of the line- based control scheme; this rectangular-mesh scheme is a significant improvement over the square-mesh scheme because it uses fewer control lines than the one based on a square mesh. In chapter 5, we have carried out detailed numerical studies of (a) a single unit of an endocardial cell and Purkinje cell (EP) composite and (b) a two-dimensional bilayer, which contains such EP composites at each site. We have considered bio- physically realistic ionic models for human endocardial cells (Ecells) and Purkinje cells (Pcells) to model EP composites. Our study has been designed to elucidate the sensitive dependence, on parameters and initial conditions, of (a) the dynamics of EP composites and (b) the spatiotemporal evolution of spiral waves of electrical activation in EP-bilayer domains. We examine this dependence on myocyte parameters by using the three different parameter sets P1, P2, and P3; to elucidate the initial-condition dependence we vary the time at which we apply the S2 pulse in our S1-S2 protocol; we also investigate the dependence of the spatiotemporal dynamics of our system on the EP coupling Dgap, and on the number of Purkinje- ventricular junctions (PVJs), which are measured here by the ratio R, the ratio of the total number of sites to the number of PVJs in our simulation domain. Our studies on EP composites show that the frequency of autorhythmic activity of a P cell depends on the diffusive gap-junctional conductance Dgap. We perform a set of simulations to understand the source-sink relation between the E and P cells in an EP composite; such a source-sink relation is an important determinant of wave dynamics at the tissue level. Furthermore, we have studied the restitution properties of an isolated E cell and a composite EP unit to uncover this effect on wave dynamics in 2D, bilayers of EP composites. Autorhythmicity is an important property of Purkinje cell; it helps to carry electrical signals rapidly from bundle of His to the endocardium. Our investigation of an EP composite shows that the cycle length (CL) of autorhythmic activity decreases, compared to that of an uncoupled Purkinje cell. Furthermore, we find that the APD increases for an EP composite, compared to that of an uncoupled P cell. In our second set of simulations for an EP-composite unit, we have obtained the AP behaviors and the amount of flux that flows from the E to the P cell during the course of the AP. The direction of flow of this flux is an important quantity that identifies which one of these cells act as a source or a sink in this EP composite. We have found that the P cell in an EP composite acts as a stimulation-current source for the E cell in the depolarization phase of the AP, when the stimulus is applied to both cells or to the P cell only. However, the P cell behaves both as a source and a sink when the stimulus is applied to the E cell only. In our third set of simulations for an EP composite unit, we have calculated the restitution of the APD; this plays an important role in deciding the stability of spiral waves in mathematical models for cardiac tissue. Our simulation shows that, for the EP composite with high coupling (Dgap = Dmm~10), the APDR slope decreases, relative to its value for an isolated E cell, for parameter sets P1 and P2, and first increases (for 50 ≤ DI ≤ 100 ms) and then decreases for the parameter set P3 ; however, for low coupling (Dgap = Dmm~100), the variation of the AP D as function of DI, for an EP composite, shows biphasic behavior for all these three parameter sets. We found that the above dynamics in EP cable type domains, with EP composites, depends sensitively on R. We hope our in silico studies of spiral-wave dynamics in a variety of state-of-the- art ionic models for ventricular tissue will stimulate more experimental studies that examine such dynamics.

Les cristaux granulaires sont des structures périodiques de particules disposées en réseau cristallin. Les interactions entre ces billes peuvent être modélisées par leurs contacts, qui ont des dimensions et des masses effectives beaucoup plus petites que celles des billes. Ceci induit une propagation d'ondes élastiques dans les structures granulaires avec des vitesses significativement plus lentes que dans le matériau des grains individuels. En outre, en raison de forces de cisaillement non centrales, les rotations de particules peuvent être initiées, conduisant à des modes de phononiques supplémentaires dans ces cristaux. Dans ce manuscrit, on étudie la propagation d’ondes dans les cristaux granulaires monocouche bidimensionnels avec un mouvement des particules hors-plan ou dans le plan. Les propriétés phononiques sont étudiées, y compris les points de Dirac, les modes de fréquence nulle, les modes à vitesse de groupe nulle et leur transformation en modes de propagation lente. En outre, en présence de bords, on peut prévoir également des ondes de bord élastiques à fréquence nulle et extrêmement lentes dans des cristaux granulaires en « nid d'abeille » (graphène granulaire). En outre, les propriétés topologiques des ondes de bord rotationelles-transverses dans un graphène granulaire sont théoriquement démontrées. En induisant une transition topologique, qui transforme l'ordre topologique du graphène granulaire de trivial en non trivial, on peut observer le transport de bord topologique dans le graphène granulaire. Les théories développées pourraient mener potentiellement à des applications sur le contrôle des ondes élastiques par des structures granulaires. / Granular crystals are spatially periodic structures of elastic particles arranged in crystal lattices. The interactions between particles take place via their elastic interconnections, which are of much smaller dimensions and weights than the beads. This induces propagation of elastic waves in granular structures at significantly slower velocities than in the individual grains. In addition, due to the existence of non-central shear forces, rotations of particles can be initiated, leading to extra phononic modes in the crystals. In the manuscript, wave dynamics in two-dimensional monolayer granular crystals with either out-of-plane or in-plane particle motion is studied. The phononic properties are investigated, including Dirac points, zero-frequency modes, zero-group-velocity modes and their transformation into slow propagating phononic modes. Furthermore, in the presence of edges/boundaries, zero-frequency and extremely slow elastic edge waves can be also predicted in mechanical granular honeycomb crystals (granular graphene). In addition, topological properties of rotational edge waves in a granular graphene are theoretically demonstrated. By inducing topological transition, which turns the topological order of granular graphene from trivial to nontrivial, topological edge transport in the granular graphene can be observed. The developed theories could promote the potential applications of designed granular structures with novel elastic wave propagation properties.

Shock-shock interactions are among the most basic gas-dynamic problem, and are almost unavoidable in any high speed light, where shock waves generating from different sources crosses each other paths. These interactions when present very close to the solid surface lead to very high pressure and thermal loads on the surface. The related practical problem is that experienced at the cowl lip of a scramjet engine, where the interfering shock waves leads to high heat transfer rates which may also lead to the damage of the material. The classification by Edney (1968) on the shock-shock interaction patterns based on the visualization has since then served the basis for such studies. Though the problem of high heating on the surface in the vicinity of the shock-shock interactions has been studied at length at supersonic Mach numbers, the study on the topic at the hypersonic Mach numbers is little sparse. Even in the studies at hypersonic Mach numbers, the high speeds are not simulated, which is the measure of the kinetic energy of the ow. Very few experimental studies have addressed this problem by simulating the energy content of the ow. Also, some of the numerical studies on the shock-shock interactions suggest the presence of unsteadiness in the shock-shock interaction patterns as observed by Edney (1968), though this observation is not made very clearly in the experimental studies undertaken so far. In the present study, experiments are carried out in a conventional shock tunnel at Mach number of 5.62 (total enthalpy of 1.07 MJ/kg; freestream velocity of 1361 m/s), with the objective of mapping the surface pressure distribution and surface convective heat transfer rate distribution on the hemispherical body in the presence of the shock-shock interactions. A shock generator which is basically a wedge of angle = 25 , is placed at some dis-dance in front of the hemispherical body such that the planar oblique shock wave from the shock generator hits the bow shock wave in front of the hemi-spherical body. The relative distance between the wedge tip and the nose of the hemispherical body is allowed to change in di erent experiments to capture the whole realm of shock-shock interaction by making the planar oblique shock wave interact with the bow shock wave at different locations along its trajectory. The study results in a bulk of data for the surface pressure and heat transfer rates which were obtained by placing 5 kulites pressure transducers, 1 PCB pressure transducer and 21 platinum thin lm gauges along the surface of the hemispherical body in a plane normal to the freestream velocity direction. Along with the measurement of the surface pressure and the surface heat transfer rates, the schlieren visualization is carried out to capture the shock waves, expansion fans, slip lines, present in a certain shock-shock interaction pattern and the measured values were correlated with the captured schlieren images to evaluate the ow build up and steady and useful test time thereby helping in understanding the ow physics in the presence of the shock-shock interactions. From the present study it has been observed that in the presence of Edney Type-I and Edney Type-II interaction, the heat transfer rates on the hemi-spherical body are symmetrical about the centerline of the body, with the peak heating at the centerline which drops towards the shoulder. For Edney Type-III, Edney Type-IV, Edney Type-V and Edney Type-VI interaction pattern, the distribution in not symmetrical and shifts in peak heat transfer rates being on the side of the hemispherical from which planar oblique shock wave is incident. Also, it is observed that for the interactions which appear within the sonic circle, Edney Type-III and Edney Type-IV, the heat transfer rates observe an unsteadiness, such that the gauges located close to the interaction region experiencing varying heat transfer rates during the useful test time of the shock tunnel. Few experiments were conducted at Mach 8.36 (total enthalpy of 1.29 MJ/kg; freestream velocity of 1555.25 m/s) and Mach 10.14 (total enthalpy of 2.67 MJ/kg; freestream velocity of 2258.51 m/s) for the con gurations representing Edney Type-III interaction pattern to further evaluate the unsteady nature observed at Mach 5.62 ows. The unsteadiness was evident in both the cases. It is realized that the short test times in the shock tunnels pose a constraint in the study of unsteady flow fields, and the use of tailored mode operation of shock tunnel can alleviate this constraint. Also, limited number of experiments in the present study, which are carried out in a Free Piston Shock Tunnel, helps to understand the need to conduct such study in high enthalpy test conditions.

Exchange of mass (water vapor), momentum, and energy between atmosphere andocean has profound influence on weather and climate. This exchange takes place at the air-sea interface, which is part of the marine atmospheric boundary layer. Various empirical relations are being used for estimating these fluxes in numericalweather and climate models but their accuracies are not sufficiently verified or tested over the Indian Ocean. The main difficulty is that vast areas of open oceans are not easily accessible. The marine environment is very corrosive and unattended long term and accurate measurements are extremely expensive. India has research ships that spend most of their time over the seas around India but that opportunity is yet to be exploited. To address this, an air-sea flux measurement system for operation on board research ships was planned. The system was tested on board Indian Research Vessels ORV SagarKanya during its cruise SK-296 in the Bay of Bengal (BoB) in July-August 2012, and NIO ship Sindhu Sadhana in June-July 2016. The complete set included instruments for measuring wind velocity, windspeed and direction, air and water temperature, humidity, pressure, all components of radiation and rainfall. In addition, ship motion was recorded at required sampling rate to correct for wind velocity. The set up facilitates the direct computation of sensible and latent heat fluxes using the eddy covariance method. In this thesis, design and installation of meteorological and ship motion sensors onboard research ships, data collection and quality control, computation of fluxes of heat, moisture and momentum using eddy covariance method and their comparison with those derived from bulk method are described. A set of sensors (hereafter, flux measuring system) were mounted on a retractable boom, ~7 m long forward of the bow to minimize the flow disturbance caused by the ship superstructures. The wind observed in the ship frame was corrected for ship motion contaminations. During the CTCZ cruise period true mean wind speed was over 10 m/s and true wind direction was South/South-Westerly. True windspeedis computed combiningdata from the anemometer a compass connected to AWS and a GPS. Turbulent fluxes were computed from motion-corrected time-series of high frequency velocity, water vapor, and air temperature data. Covariance latent heat flux, sensible heat flux, and wind stress were obtained by cross-correlating the motion-corrected vertical velocity with fast humidity fluctuations measured with anIR hygrometer, temperate fluctuation from sonic anemometer and motion-corrected horizontal windfluctuations from sonic anemometer, respectively. During the first attempt made in July-August 2012 as part of a cruise of CTCZ monsoonresearch program, observations were mainly taken in the North Bay of Bengal. The mean air-temperature and surface pressure were ~28 Deg C and ~998 hPa, respectively. Relative humidity was ~80%. Average wind speed varied in the range 4-12 m/s. The mean latent heat flux was 145 W/m2 , sensible heat flux was ~3 W/m2 and average sea-air temperature difference was ~ 0.7°C. The Bay of Bengal boundary layer experiment (BoBBLE) was conducted during June-July 2016 and the NIO research ship Sindhu Sadhana was deployed. The same suite of sensors installed during CTCZ were used during BoBBLE. During daytime, peaks of hourly net heat fluxes (Qnet ) were around 600 Wm-2(positive if into the sea), whereas, night time values were around -250 W m-2. Sea surface temperature was always >28°C and maximum air temperature exceeded 29°C. During the experimental period the mean Qnet was around -24 Wm-2 from both eddy covariance and conventional bulk methods, but there are significant differences on individual days.The new flux system gives fluxes which are superior to what was available before.