Modal analysis for strongly stratified lakes was extended to obtain a better understanding of the dynamics of the basin-scale motions. By viewing the basin-scale motions as a superposition of modes, that have distinct periods and three-dimensional structures, the method provides a conceptual understanding for the excitation, evolution, and damping of the basin-scale motions. Once the motion has been decomposed into modes, their evolution and energetics may be extracted from hydrodynamic simulation results and field data. The method was applied to Lake Biwa, Japan, and Lake Kinneret, Israel, and used for a theoretical study. The real lake applications showed that winds excited basin-scale motions that had a surface layer velocity structure similar to the wind stress pattern. Three-dimensional hydrodynamics simulations of Lake Biwa indicated that most of the energy input from winds was partitioned into the internal waves that decayed within a few days. The gyres, on the other hand, received much less energy but dominated the dynamics during calm periods due to their slow damping. Analyses of field data from Lake Kinneret suggested that the internal waves, excited by the strong winds every afternoon, were damped over a few days primarily due to bottom friction. Theoretical investigations of damping mechanisms of internal waves revealed that bottom friction induced a velocity anomaly at the top of the boundary layer that drained energy from the nearly inviscid interior by a combination of internal wave cancelling and spin-down. These results indicate that gyres induce long-term horizontal transport near the surface and internal waves transfer energy from winds to near-bottom mixing. Modal structure of dominant basin-scale internal waves can induce large heterogeneity of nearbottom mass transfer processes. The method presented here provides a tool to determine how basin-scale motions impact on biogeochemical processes in stratified lakes.

The barotropic tide dissipates a well established estimate of 2.5 TW of energy at the M2 frequency. Bottom topography is responsible for part of this dissipation, and the generation of the internal tide is also partly responsible. The fate of this energy is largely described by a cascade from large scales to small scales by non-linear wave-wave interactions where it gets dissipated. This thesis aims to investigate how the presence of mesoscale eddies (vortices) in the ocean affect the internal tide. Previous work has looked at the interaction of the barotropic tide with eddies. Krauss (1999) found that the interaction can produce a modulated internal tide, however a scaling analysis suggests that the effect may not be as strong as reported. The MITgcm is used to simulate internal wave generation by barotropic flow over topography and comparisons are made with Dr. Lamb's IGW model. Baroclinic eddies are analytically prescribed and then geostrophically adjusted also using the MITgcm. Finally, the two are combined, and the internal tide field is analysed with and without the presence of eddies of various magnitude and length scales. The results of this investigation do not find a strong transfer of energy between modes; the modal distribution of energy in the internal tide remains the same when an eddy is added. However, focusing and shadow beams of internal waves are produced in the wake of an eddy as the internal waves pass through it. The beams show very strong variations in intensity, vertically integrated energy flux can reduce almost to zero in the shadow regions and increase more than double in the focusing regions. Modal decomposition of the horizontal flow field reveals that mode 2 and 3 waves are most strongly affected by the eddies and contribute strongly to the formation of the beams. Mode 1 appears to be less affected by the eddy. The larger wavelength and faster group velocity of mode 1 supports the notion that the eddy interacts with it less.

The barotropic tide dissipates a well established estimate of 2.5 TW of energy at the M2 frequency. Bottom topography is responsible for part of this dissipation, and the generation of the internal tide is also partly responsible. The fate of this energy is largely described by a cascade from large scales to small scales by non-linear wave-wave interactions where it gets dissipated. This thesis aims to investigate how the presence of mesoscale eddies (vortices) in the ocean affect the internal tide. Previous work has looked at the interaction of the barotropic tide with eddies. Krauss (1999) found that the interaction can produce a modulated internal tide, however a scaling analysis suggests that the effect may not be as strong as reported. The MITgcm is used to simulate internal wave generation by barotropic flow over topography and comparisons are made with Dr. Lamb's IGW model. Baroclinic eddies are analytically prescribed and then geostrophically adjusted also using the MITgcm. Finally, the two are combined, and the internal tide field is analysed with and without the presence of eddies of various magnitude and length scales. The results of this investigation do not find a strong transfer of energy between modes; the modal distribution of energy in the internal tide remains the same when an eddy is added. However, focusing and shadow beams of internal waves are produced in the wake of an eddy as the internal waves pass through it. The beams show very strong variations in intensity, vertically integrated energy flux can reduce almost to zero in the shadow regions and increase more than double in the focusing regions. Modal decomposition of the horizontal flow field reveals that mode 2 and 3 waves are most strongly affected by the eddies and contribute strongly to the formation of the beams. Mode 1 appears to be less affected by the eddy. The larger wavelength and faster group velocity of mode 1 supports the notion that the eddy interacts with it less.

Tide-topography coupling is important for understanding surface-tide energy loss, the intermittency of internal tides, and the cascade of internal-tide energy from large to small scales. Although tide-topography coupling has been observed and modeled for 50 years, the identification of surface and internal tides over arbitrary topography has not been standardized. Here, we begin by examining five surface/internal-tide decompositions and find that only one is (i) consistent with the normal-mode description of tides over a flat bottom, (ii) produces a physically meaningful depth-structure of internal-tide energy flux, and (iii) results in an established expression for internal-tide generation. Next, we examine the expression for internal-tide generation and identify how it is influenced by remotely-generated shoaling internal tides. We show that internal-tide generation is subject to both resonance and intermittency, and can not always be predicted from isolated regional models. Lastly, we quantify internal-tide generation and scattering on the Oregon Continental slope. First, we derive a previously unpublished expression for inter-modal energy conversion. Then we evaluate it using observations and numerical simulations. We find that the surface tide generates internal tides, which propagate offshore; while at the same time, low-mode internal tides shoal on the slope, scatter, and drive turbulent mixing. These results suggest that internal tides are unlikely to survive reflection from continental slopes, and that continental margins play an important role in deep-ocean tidal-energy dissipation. / Graduation date: 2011

Small- and fine-scale biological and oceanographic processes may have a measurable electromagnetic signature. These types of processes inherently involve turbulence and three-dimensional dynamics. Traditional models of the electromagnetic signature of oceanographic processes are of an analytical nature, do not account for three-dimensional boundary layer dynamics or turbulence, self-inductance, and may not describe the variety of the environmental conditions occurring in the ocean. In order to address this problem, I have implemented magnetohydrodynamic (MHD) computational fluid dynamics (CFD) tools, which has allowed for the evaluation of the electromagnetic signature of a number of small- and fine-scale biological and oceanographic processes in the ocean. The suite of computational tools has included the commercial models ANSYS Fluent, coupled with the MHD module, and ANSYS Maxwell. These computational tools have been well-established in fluid and electromagnetic engineering. The application of CFD and MHD tools in oceanography is new but is undergoing rapid development. In this work, substantial effort was made toward the CFD, MHD, and magnetostatic model verification and identification of model limitations. Verifications of the CFD, MHD, and magnetostatic models were conducted by successfully comparing their results with the field measurements and laboratory experiments. Comparison with the traditional (analytical) models for surface and internal waves, has revealed their limitations related to bottom boundary layer physics, effect of self-inductance, and, to a lesser extent, the magnetic permeability difference at the air-sea interface. These limitations become important for shallow water internal waves. As a result, the traditional models significantly overestimate the magnetic signature of internal waves observed at the Electromagnetic Observatory. After model verification with the field and laboratory data, the computational models were then applied to evaluate the magnetic signature of diel vertical migration (DVM) of zooplankton, surface waves, internal wave solitons, freshwater lens spreading, and Langmuir circulation. The quantitative estimates have been made for typical environmental conditions. In other environmental conditions, their magnetic signature may be somewhat different. The suite of computational models developed in this dissertation work allows for the estimation of the magnetic signature of fine- and small-scale oceanographic processes in virtually any environmental conditions (e.g., in oil emulsions). I anticipate the result of this study will have Naval, environmental, and oil exploration applications.

Internal waves (IWs) owe their existence to the stratification in the medium. These waves affect acoustic transmission greatly. Impact of these waves on acoustic transmission in deep water is fairly well understood due to better performance of well-celebrated Garrett-Munk (GM) model. However, in shallow waters, predicting these waves is not as easy, because of interactions with the bottom and surface. Hence two experiments, one during October 2002 and the other during October 2004 were conducted to characterize IWs in the shallow waters of northeastern Arabian Sea. The first experiment was carried out during October 2002 south of Gulf of Kutch (GOK) and the second experiment during October 2004 both south and north of GOK. During these experiments CTD moorings were deployed and temperature and salinity (TS) data were collected at 5 seconds interval. CTD Yo-Yo collected vertical profiles of TS at a sampling interval of 2.5 minutes for 3.5 hours during October 2002 and 1 hour during October 2004 experiment. In addition, during the first experiment, currents were measured using a vessel mounted Acoustic Doppler Current Profiler (ADCP), and in both experiments CTD TS profiles were taken from the ship. This data set has been used for characterizing internal waves in the northeastern Arabian Sea. Experiment conducted during October 2002, south of GOK has revealed large tidal ranges. The barotropic tidal range at the experimental site was 1.5m. Current observations made using the vessel mounted ADCP, along the shore and across the shore, showed signs of first mode (baroclinic) oscillations; currents in the top and bottom layers were in opposing directions. They were found to be southwesterly in the top layer and northeasterly in the bottom layer. Time - depth sections of TS profiles from CTD yo-yo data, revealed the presence of high frequency internal waves and solitons overriding on low frequency trend. Moored CTD time series of temperature records showed the presence of internal solitons, which caused a vertical displacement of about 8m in the isotherms, which is equivalent to 3OC change in temperature, in less than 10 minutes. Passage of internal solitons induced vertical mixing causing the mixed layer to deepen by about 10m and current speed increased by about 0.1 m/s. Internal solitons were traveling towards northwest and current vectors suggest that they were generated when the internal tide is reflected from the bottom. Vertical displacement spectra agreed well with GM spectra when solitons were not present. However, when the solitons were present the displacement spectra had higher energy levels compared to the GM spectra. Another experiment was done in October 2004, mainly aimed at characterizing internal solitons and to verify the consistency of the results obtained during October 2002 experiment. This experiment also showed that IWs of both high and low frequency along with internal solitons were present at the experimental site. It was found that internal solitons were more energetic during spring tide than the neap. The observed amplitudes of these solitons were around 12m and were not rank ordered suggesting that the experimental site is close to the generation point. It is believed that, generally, solitons get phase locked to the barotropic tide’s trough and travel. Such phase locking was not observed at the experimental site. They were observed riding on both troughs and crests of barotropic tide. One of the aims of this thesis is to develop a simulation model based on Garrett-Munk steady state internal wave spectrum. Hence, an internal wave model IWAVE was developed to simulate the sound speed structure due to internal waves. Sound speed structure is simulated instead of TS structure, because of their direct utility in sonar range prediction models. Since the GM model is a deep-water and mid-latitude model, it was calibrated to suite shallow-water tropical environment by incorporating the site and region specific parameters. EOFs and Dynamical modes estimated using TS profiles were used to identify the site-specific parameters of the GM model. Values for characteristic mode number and spectral slope used in the GM model are 3 and 2 respectively. However, it was found that they are different in the northeastern Arabian Sea. At this site, the characteristic mode number was found to be 1 and the spectral slope was found to be 3. The modified model was validated against the measured sound speed profiles. In the first case, the first sound speed profile (TS) of the CTD yo-yo data (20 October 2002) was used for predicting the remaining profiles and compared them with observations. This was done to verify the model’s ability to predict high frequency case (TS profiles are measured at every 2.5min.). In the second case, during October 2004, TS profiles collected at every one-hour for 24 hours were used. This gives an idea of the model’s performance for the low frequency case. The variances of the measured and simulated sound speed profiles matched well in both cases with the modified GM model.

Les ondes internes sont produites par suite de l’équilibre dynamique entre les forces de flottabilité et la gravité quand une particule de fluide est déplacée verticalement dans un milieu stratifié stable. Les systèmes géophysiques tels que océan et l’atmosphère sont naturellement stratifiés et donc favorables à la propagation des ondes internes. En outre, ces deux environnements stockent une grande quantité de particules tant dans leur intérieur que sur les bords. Par conséquent, les ondes internes et les particules vont inévitablement interagir dans ces systèmes. Au cours de ce travail, des expériences exploratoires sont réalisées pour étudier le transport par érosion des particules, généré par les ondes internes. Afin de déterminer un seuil de transport, les propriétés particulières des réflexions d’ondes internes («réflexion critique ») sont utilisées pour augmenter l’intensité du champ d’ondes à la surface de réflexion. Une méthode a été développée en collaboration avec une équipe de traitement du signal pour améliorer la détermination des composantes de l’onde impliquées dans une réflexion quasi critique. Cela nous a permis de comparer nos résultats expérimentaux avec une théorie de la réflexion critique, montrant un bon accord et permettant d’extrapoler ces résultats à des expériences au-delà de la nôtre et à des conditions océaniques. Nous avons aussi étudié l’interaction des ondes internes avec une colonne de particules en sédimentation. Deux effets principaux ont été observés : la colonne oscille autour d’une position d’équilibre, et elle est déplacée dans son ensemble. La direction du déplacement de la colonne est expliquée par le calcul de l’effet de la dérive Lagrangienne produite pour des ondes. Cet effet pourrait également expliquer la dépendance en fréquence du déplacement. / Internal waves are produced as a consequence of the dynamic balance between buoyancy and gravity forces when a particle of fluid is vertically displaced in a stably stratified environment. Geophysical systems such as ocean and atmosphere are naturally stratified and therefore suitable for internal waves propagation. Furthermore, these two environments stock a vast amount of particles at their boundaries and in their bulk. Therefore, internal waves and particles will inexorably interact in these systems. In this work, exploratory experiments are performed to study wave generated erosive transport of particles. In order to determine a transport threshold, the peculiar properties of internal waves (“critical reflection”) are employed to increase the intensity of the wave field at the boundaries. A method was developed in collaboration with a signal processing team to improve the determination of the wave components involved in near-critical reflection. This method enabled us to compare our experimental results with a theory of critical reflection, showing good agreement and allowing to extrapolate these results to experiments beyond ours and to oceanic conditions. In addition, we study the interaction of internal waves with a column of particles in sedimentation. Two main effects are observed: the column oscillates around an equilibrium position, and it is displaced as a whole. The direction of the displacement of the column is explained by computing the effect of the Lagrangian drift of the waves. This effect could also explain the frequency dependence of the displacement.

La cascade d’énergie qui a lieu dans les océans, depuis les grandes vers les petites échelles, est capitale pour comprendre leur dynamique et le mélange irréversible associé. Les attracteurs d’ondes internes font partie des mécanismes conduisant potentiellement à une telle cascade. Dans ce manuscrit, nous étudions expérimentalement les attracteurs d’ondes internes, dans une cuve trapézoïdale remplie d’un fluide stratifié linéairement en densité. Dans cette géométrie, les ondes peuvent être focalisées vers un cycle limite : l’attracteur. Nous montrons que la formation de l’attracteur est purement linéaire : des petites échelles sont donc créées grâce à la focalisation des ondes. Les principales caractéristiques de l’attracteur dépendent uniquement de la géométrie trapézoïdale de la cuve. A l’échelle de l’océan, nous montrons que les attracteurs d’ondes internes sont très probablement instables. En effet, ceux-ci sont sujets à une instabilité de résonance triadique, qui transfère de l’énergie depuis l’attracteur vers un couple d’ondes secondaires. Cette instabilité et ses principales caractéristiques sont décrites en fonction de la géométrie du bassin. Pour des expériences de longue durée, l’instabilité produit plusieurs paires d’ondes secondaires, créant une cascade d’instabilités triadiques et transférant l’énergie injectée à grandes échelles vers des échelles plus petites. Nous montrons, pour la première fois de façon expérimentale, de très fortes signatures de turbulence d’ondes internes. Au delà de cet état, la cascade atteint un régime de mélange partiel du fluide stratifié. Cet ultime régime apparait indépendant de la géométrie trapézoïdale du bassin, et donc, universel. Cette thèse est complétée par une étude sur la masse ajoutée et l’amortissement par émission d’ondes d’objets oscillant horizontalement dans un fluide stratifié en densité. Cela a des applications concernant la conversion de l’énergie des marées en ondes internes. / A question of paramount importance in the dynamics of oceans is related to the energy cascade from large to small scales and its contribution to mixing. Internal wave attractors may be one of the possible mechanisms responsible for such a cascade. In this manuscript, we study experimentally internal wave attractors in a trapezoidal test tank filled with linearly stratified fluid. In such a geometry, the waves can form closed loops called attractors. We show that the attractor formation is purely linear: small scales are thus created by wave focusing. The attractor characteristics are found to only depend on the trapezoidal geometry of the tank. At the ocean scale, we show that attractors are very likely to be unstable. Indeed, internal wave attractors are prone to a triadic resonance instability, which transfers energy from the attractor to a pair of secondary waves. This instability and its main characteristics are described as a function of the geometry of the basin. For long-term experiments, the instability produces several pairs of secondary waves, creating a cascade of triadic interactions and transferring energy from large-scale monochromatic input to multi-scale internal-wave motion. We reveal, for the first time, experimental convincing signatures of internal wave turbulence. Beyond this cascade, we have a mixing regime, which appears to be independent of the trapezoidal geometry and, thus, universal. This manuscript is completed by a study on added mass and wave damping coefficient of bodies oscillating horizontally in a stratified fluid, with applications to tidal conversion.

Au travers de leurs instabilités, les ondes internes de gravité, qui se propagent dans les fluides stratifiés, jouent un rôle crucial dans la dynamique océanique. En effet, ces instabilités transfèrent de l'énergie vers les petites échelles et créent ainsi du mélange. Parmi ces mécanismes, nous avons étudié l'instabilité triadique résonante (TRI). Ce processus se caractérise par l'émission à partir d'une onde-mère de deux ondes-filles, dont les fréquences et vecteurs d'onde vérifient avec l'onde-mère des conditions de résonance temporelle et spatiale. Dans le cas où une rotation globale du fluide (cas général en géophysique) s'ajoute à la rotation, celle-ci va changer les propriétés non seulement des ondes internes, on les appellera alors ondes gravito-inertielles, mais aussi de la TRI. L’étude expérimentale sur table tournante de l'instabilité d'un faisceau de forme contrôlée d'onde gravito-inertielle a mis en évidence l’importance de la rotation sur les caractéristiques de la TRI, comme le seuil d'instabilité ou les caractéristiques des ondes secondaires. En outre, ces résultats sont en très bon accord avec un développement asymptotique de cette instabilité qui prend en compte la taille finie du faisceau, paramètre déterminant au laboratoire et dans un contexte océanique. Cet effet est responsable notamment de l'existence d'une latitude critique dans l'océan.Dans un second temps, la réalisation d'un nouveau type de générateur d'onde axisymétrique a permis d'étudier la propagation d'ondes axisymétriques à trois dimensions. Les modes axisymétriques générés par ce nouveau dispositif ont été caractérisés et comparés aux solutions analytiques. Ce dispositif permet également de créer une excitation annulaire localisée qui focalise les ondes internes au centre de la cuve. En changeant la vitesse de groupe de ces ondes, au travers d'une stratification non-linéaire, nous pouvons créer une forte accumulation d'énergie au point de focalisation. En fonction de l'amplitude de l'excitation, on observe la transition entre un état stable vers un état fortement instable. / Through their instabilities, internal gravity waves, which propagate in stratified fluids, play a paramount role in the oceanic dynamics. Indeed, their instabilities transfer energy to small scales and lead to mixing. Among these instabilities, we studied the triadic resonant instability (TRI). This process is characterized by the generation from a primary wave of two secondary internal waves, whose frequencies and wave vectors fulfill the spatial and time resonance conditions. If the fluid is also rotating (which is in generally the case in geophysics), rotation changes not only the properties of internal waves, which, in this case, are named inertia-gravity waves, but also the properties of the TRI. The experimental study on a rotating plateform of the instability of a controlled internal wave beam highlighted the role played by rotation on TRI features, such as the instability threshold or the characteristics of the secondary waves. Moreover, these results are in excellent agreement with an asymptotic development of the instability that takes into account the finite width of the wave beam, key parameter in a laboratory and oceanic context. this effect is responsible for the existence of a critical latitude in the ocean.In a second part of this work, we built a new wave generator, which allowed for the study of tridimensional axisymmetric waves. The axisymmetric modes generated by this new set-up were characterized and compared to analytical solutions. The generator can also produce a localized axisymmetric bump which focalises the wave in the center of the tank. By changing the group velocity of the waves, through a non-linear stratification, we are able to create a large energy build-up at the point of focalisation. Depending on the amplitude of the wave, we observe the transition from a stable state to a strongly unstable one.

Les ondes internes jouent un rôle essentiel dans la dynamique de l'atmosphère et de l'océan. Elles sont entres autres invoquées pour expliquer le mélange irréversible de ce dernier. Dans des géométries particulières, ces ondes sont susceptibles de converger vers des trajectoires limites appelées attracteurs. Dans cette thèse, nous étudions expérimentalement ces attracteurs dans une cuve trapézoïdale. Dans un premier temps, nous nous intéressons à leur bilan énergétique, en mesurant les différentes dissipations ainsi que la puissance injectée par le générateur d'onde. Si cette puissance est suffisante, l'attracteur est susceptible de se déstabiliser par interactions triadiques. Nous quantifions la part de dissipation portée par ces ondes secondaires ainsi générées. La mesure de la puissance injectée en régime linéaire a montré qu'elle est plus importante pour les attracteurs. Cette résonance, observée jusqu'ici sous une excitation monochromatique, est ici observée en étudiant la réponse du système à une impulsion. Un développement théorique est proposé et permet de comparer quantitativement les deux méthodes. Enfin, nous étudions le régime non linéaire des attracteurs, qui présente des spectres temporel et spatial très riches. Après avoir caractérisé le régime non linéaire, nous exhibons deux comportements non linéaires très différents et apportons des pistes d'explication à leur existence / Internal waves are very important to atmospheric and oceanic dynamics. Among others, they might explain the irreversible mixing of the oceans. In particular geometries, these waves can focus on limit cycles called attractors. Firstly, we investigate the energy budget of these attractor by measuring the different dissipative terms and the injected power coming from the waves source. If this power is sufficient, the attractor destibilise throught triadic instabilities. We quantify how much these secondary are important to the global dissipation rate.The measurement of injected power in the linear regime has shown that it is bigger for the attractors. This resonance, which had been observed under a monochromatic excitation, is here study by analysing the response of the system to an impulse. A theoretical development is proposed to compare quantitatively these two methods. Finally, we study the non linear regime of attractors, which present some complex spatial and temporal spectrum. We caracterise this non linear regime and show that two very different non linear beahviors exist. We bring up some explanation to these behaviors