Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Sciences, 1980. / Microfiche copy available in Archives and Science. / Bibliography: leaves 92-98. / by Eric Arthur D'Asaro. / Ph.D.

Although the leading-order motion of waves is periodic - in other words backwards and forwards - many types of waves including those driven by gravity induce a mean flow as a higher-order effect. It is the induced mean flow of three types of gravity waves that this thesis examines: surface (part I), internal (part II) and interfacial gravity waves (part III). In particular, this thesis examines wave groups. Because they transport energy, momentum and other tracers, wave-induced mean flows have important consequences for climate, environment, air traffic, fisheries, offshore oil and other industries. In this thesis perturbation methods are used to develop a simplified understanding of the physics of the induced mean flow for each of these three types of gravity wave groups. Leading-order estimates of different transport quantities are developed. For surface gravity wave groups (part I), the induced mean flow consists of two compo- nents: the Stokes drift dominant near the surface and the Eulerian return flow acting in the opposite direction and dominant at depth. By considering subsequent orders in a separation of scales expansion and by comparing to the Fourier-space solutions of Longuet-Higgins and Stewart (1962), this thesis shows that the effects of frequency dis- persion can be ignored for deep-water waves with realistic bandwidths. An approximate depth scale is developed and validated above which the Stokes drift is dominant and below which the return flow wins: the transition depth. Results are extended to include the effects of finite depth and directional spreading. Internal gravity wave groups (part II) do not display Stokes drift, but a quantity analogous to Stokes transport for surface gravity waves can still be developed, termed the “divergent- flux induced flow” herein. The divergent-flux induced flow it itself a divergent flow and induces a response. In a three-dimensional geometry, the divergent-flux induced flow and the return flow form a balanced circulation in the horizontal plane with the former transporting fluid through the centre of the group and the latter acting in the opposite direction around the group. In a two-dimensional geometry, stratification inhibits a balanced circulation and a second type of waves are generated that travel far ahead and in the lee of the wave group. The results in the seminal work of Bretherton (1969b) are thus validated, explicit expressions for the response and return flow are developed and compared to numerical simulations in the two-dimensional case. Finally, for interfacial wave groups (part III) the induced mean flow is shown to behave analogously to the surface wave problem of part I. Exploring both pure interfacial waves in a channel with a closed lid and interacting surface and interfacial waves, expressions for the Stokes drift and return flow are found for different configurations with the mean set-up or set-down of the interface playing an important role.

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.

In shallow water environments, sound propagation experiences multiple interactions with the surface/bottom interfaces, with hydrodynamic disturbances such as internal waves, and with tides and fronts. It is thus very difficult to make satisfactory predictions of sound propagation in shallow water. Given that many of the ocean characteristics can be modeled as stochastic processes, the statistical measure, spatial coherence, is consequently an important quantity. Spatial coherence provides valuable information for array performance predictions. However, for the case of long-range, low frequency propagation, studies of spatial coherence influenced by various environmental parameters are limited insofar as having the appropriate environmental data with which to model and interpret the results. The comprehensive Asian Seas International Experiment 2001 (ASIAEX01) examined acoustic propagation and scattering in shallow water. Environmental oceanographic data were taken simultaneously with the acoustic data. ASIAEX01 provided a unique data set which enabled separate study of the characteristics of the oceanographic features and their influence on long range sound propagation. In this thesis, the environmental descriptors considered include sediment sound speed and attenuation, background internal waves, episodic non-linear internal waves, and air-sea interface conditions. Using this environmental data, the acoustic data are analyzed to show the characteristics of spatial coherence in a shallow water waveguide. It is shown that spatial coherence can be used as an inversion parameter to extract geoacoustic information for the seabed. Environmental phenomena including internal waves and wind-generated surface waves are also studied. The spatial and temporal variations in the sound field induced by them are presented. In addition, a tank experiment is presented which simulates propagation in a shallow water waveguide over a short range. Based on the data model comparison results, the model proposed here is effective in addressing the major environmental effects on sound propagation in shallow water.

Full-depth profile data reveal semidiurnal internal waves radiating from Mendocino Escarpment. Energy- and momentum-fluxes are lost between stations bracketing the first surface reflection to the north. A plausible interpretation is that wave energy is dissipated as a consequence of superposition of incident and reflected waves. Because there are no profiler data in the superposition region, a theoretical approach is used to bridge the gap. Assuming zonal independence, constant stratification and linear decay in the dissipation region, the forcing on the mean equations is evaluated with parameters consistent with Mendocino Escarpment data. Both superposition and dissipation cause momentum-flux divergence forcing. An Ekman-like balance is anticipated with predicted mean zonal flows u~O(1-2 cm/s), comparable to surface wind-forced Ekman currents.

In Saanich Inlet, a fjord located in southern Vancouver Island, British Columbia, dense aggregations of euphausiids exhibit diel vertical migration behavior and their capability of generating turbulence has been suggested. Despite decades of research on diel vertical migration of zooplankton, its variability has not been well studied. In addition, the physical oceanographic environment in Saanich Inlet has not been thoroughly quantified, which raises the possibility of previously observed turbulent bursts of O(10^-5 – 10^-4 W kg^-1) having physical (rather than biological) origin. This work characterizes variability of diel vertical migration behavior using a moored 200-kHz echosounder, complemented by plankton sampling. Physical properties such as barotropic, baroclinic and turbulent signals are described, and the relationship between turbulence and internal waves/scattering layer examined. A two-year high-resolution biacoustic time-series provided by the Victoria Experimental Network Under the Sea (VENUS) cabled observatory allowed quantification of the seasonal variability in migration timing of euphausiids. During spring – fall, early dusk ascent and late dawn descent relative to civil twilight occur. During winter, late dusk ascent and early dawn descent occur. Factors regulating the seasonal changes in migration timing are light availability at the daytime depth of the scattering layers, and size-dependent visual predation risk of euphausiids. Instead of the traditional view of diel vertical migration timing correlated solely with civil twilight, euphausiids also adapt their migration timing to accommodate changes in environmental cues as well as their growth. The pre-spawning period (February – April) is an exception to this seasonal pattern, likely due to the higher energy demands for reproduction. Turbulence and internal waves in Saanich Inlet are characterized based on a one-month mooring deployment. Average dissipation rates are nearly an order of magnitude larger than previously reported values and higher dissipation rates of O(10^-7 – 10^-6 W kg^-1) are occasionally observed. A weak correlation is observed between turbulent dissipation rates and baroclinic velocity/shear. To examine the possibility of biological generation of turbulence, an echosounder at the VENUS cabled observatory is used to simultaneously measure the intensity of the euphausiid scattering layer and its vertical position. Turbulent bursts of the sort previously reported are not observed, and no relation between diel vertical migration and turbulent dissipation rates is found. Physical forcing at the main channel remains as a possible cause of the turbulent bursts. / Graduate / 0416 / 0415

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

Les océans de la Terre sont stratifiés en densité par les gradients de température et de salinité.L'interaction des courants de marée avec la topographie du fond océanique entraîne donc le rayonnement des ondes de gravité interne dans l'intérieur de l'océan. Ces ondes sont appelées marées internes et leur dissipation due à le déferlement des ondes nonlinéaires joue un rôle important dans le mélange de l'océan abyssal, et donc dans la circulation océanique à la grande échelle.Dans ce contexte, nous étudions la génération des ondes internes par l’oscillation d’objet de différentes géométries simplifiées afin de modéliser le marée barotropique sur la topographie océanique et considérons les effets linéaires et nonlinéaires sur ces ondes résultant d’interactions avec l'objet et entre ces ondes.La contribution relativement nouvelle de cette thèse est l'étude des aspects de flux tridimensionnels qui étaient accessibles avec notre approche expérimentale, et sont généralement difficiles à étudier par modélisation numérique et analytique.Nous étudions d'abord la structure des ondes fundamentale et des harmoniques supérieur pour un sphéroïde oscillant, émettant des ondes divergentes. Les harmoniques supérieures sont générées par l'instabilité non linéaire à la surface de l'objet avec des effets nonlinéaires dans la zone d'intersection des faisceaux fundamentales. Ils peuvent se croiser et se concentrer, donc augmenter d'énergie, et devenir dominant sur les ondes fundamentales. On détermine les structures horizontales des ondes fundamentale et des harmoniques supérieures.Subséquemment, nous considérons les ondes générées par un tore oscillant, qui convergent vers un point focal. En dehors de cette région focale, les résultats expérimentaux et les prédictions théoriques sont en bon accord, mais dans la région focale, l'amplitude de l'onde est deux fois plus grande que près du tore, conduisant à une amplification locale nonlinéaire et à un déferlement des onde pour les grandes amplitudes d'oscillations. En conséquence, la propagation des ondes fundamentales se trouve entravée dans la région focale. L'onde stationnaire se forme alors que de nouvelles ondes sont générées et émises de cette région focale.Un tore plus grand a été testé sur la plate-forme Coriolis pour comparer la focalisation des ondes de gravité internes, inertie-gravité et des ondes inertielles dans un régime faiblement visqueux. En raison de la complexité de la zone focale, une seconde harmonique est observée même quand l'amplitude d'oscillation est faible. Le champ de vorticité verticale des ondes de gravité interne présente une structure dipolaire dans la zone focale, qui se transforme dans le cas tournant en une structure de vortex "Yin-Yang". La structure globale des faisceaux des ondes inertiels est proche de celle pour des ondes de gravité internes, bien q'elle est relativement plus intense. / The Earth's oceans are stratified in density by temperature and salinity gradients.The interaction of tidal currents with ocean bottom topography results therefore in the radiation of internal gravity waves into the ocean interior. These waves are called internal tides and their dissipation owing to nonlinear wave breaking plays an important role in the mixing of the abyssal ocean, and hence in the large-scale ocean circulation.In this context we investigate the generation of internal waves by oscillating objects of different idealized geometries as a model of barotropic flow over ocean topography, and consider linear as well as nonlinear effects on these waves resulting from interactions with the object and from wave--wave interactions.The relatively novel contribution of this thesis is the investigation of three-dimensional flow aspects that were accessible with our experimental approach, and are generally difficult to investigate by numerical and analytical modelling.First we investigate the wave structure of the first and higher harmonics for an oscillating spheroid, emitting diverging waves. Higher harmonics are generated by nonlinear instability at the surface of the object together with nonlinear effects in the zone of intersection of the primary beams. They may intersect and focus, therefore increase in energy, and become dominant over the first harmonic. The horizontal structures of both, first and higher harmonics are determined.We then consider waves generated by an oscillating torus, that are converging to a focal point. Outside this focal region experimental results and theoretical predictions are in good agreement, but in the focal region the wave amplitude is twice as large as it is close to the torus, leading to local nonlinear wave amplification and incipient wave breaking for large oscillation amplitudes. As a result, the propagation of the first harmonic waves is found to be hindered in the focal region. A standing pattern forms, while new waves are generated and emitted away from this focal region.A larger torus has been tested at the Coriolis platform to compare the focusing of internal gravity, inertia--gravity and inertial waves in a low viscous regime. Owing to the complexity of the focal region, a second harmonic is observed even at low oscillation amplitude. The vertical vorticity field of internal gravity waves exhibits a dipolar structure in the focal zone, which transforms in the rotating case into a ``Yin--Yang-shaped'' monopolar vortex structure. The overall structure of the inertial wave beams is close to that for internal gravity waves, though relatively more intense.

La thèse concerne la modélisation de deux écoulements issus de problèmes géophysiques. Un premier problème a trait à la présence de tourbillons longitudinaux apparaissant dans les cours d'eau. L'origine de ces structures reste indéterminée. On aborde ce problème par une simulation numérique d'un écoulement turbulent cisaillé dans un canal ouvert utilisant un code pseudo-spectral. On tente de voir si un cisaillement de surface même faible est capable ou non de comprendre ces observations. Le second problème est lié à la resuspension des sédiments sur les bords d'une mer ou d'un lac par des ondes internes. Ces ondes existent à cause de la stratification en densité de la colonne d'eau. Lorsque elles s'approchent de la côte, elles se déstructurent générant un cisaillement sur le fond capable de resuspendre du sédiment. On a envisagé à nouveau cette étude par le biais de la simulation numérique directe. On examine comment l'onde interne se brise sur les bords en fonction de (a) la nature de la stratification, (b) la forme de la topographie du fond et (c) l'amplitude des ondes. On calcule dans chaque cas le cisaillement sur le fond. On en déduit le flux et le transport de sédiment dans toute la colonne d'eau. / This thesis studies the modeling of two problems that take their origin from a geophysical context. A first problem is related to the presence of longitudinal vortices which have been measured in rivers. The origin of these structures remains unknown. We address this problem by numerical simulations of a sheared turbulent flows in an open channel using a pseudo-spectral code. We try to determine if the presence of an imposed shear at the surface coupled with a pressure gradient is capable or not to explain these observations. The second study focuses on the sediment resuspension on shores of seas or lakes by the action of internal waves. These waves exist because of density stratification of the water column. When waves approach the shore, their patterns evolve generating a shear on the bottom capable to resuspend sediment. By direct numerical simulations, we analyse how internal waves breaking changes according to (a) stratification, (b) bottom topography and (c) wave amplitude. We compute for each case the shear exerted on the bottom, the sediment flux and transport throughout the water column.

Les différents projets présentés dans cette thèse contribuent à la compréhension de plusieurs aspects clés de la circulation océanique. Le premier aspect que nous étudions porte sur les processus physiques à l'origine du mélange lié à la marée; deux processus ont été mis en évidence. Depuis la latitude critique vers l'équateur, la marée interne transfert son énergie à des ondes plus petite échelle via des instabilités triadiques résonnantes impliquant les ondes proche inertielles. Depuis la latitude critique vers le pôle, les ondes de marée interne continuent de transférer leur énergie à des ondes plus petite échelle, mais étonnamment ce transfert se fait entre la marée interne et des ondes évanescentes.Dans la deuxième étude, nous étudions l'effet d'un courant moyen sur la propagation et la dissipation des ondes de marée interne, générées à la topographie dans des simulations haute résolution. Dans ce cas, la dépendance en latitude de la dissipation de la marée interne est plus lisse et plus proche d'une constante. Ce changement de la dépendance en latitude peut être lié au décalage des fréquences des ondes de marée interne par effet Doppler, ce qui induit la génération d'ondes secondaires plus petite échelle.Dans la troisième étude, nous étudions l'effet d'une perturbation générée en amont sur la circulation dans le bassin amont dû à l'interaction entre la perturbation et un seuil hydrauliquement contrôlé. Les ondes de Kelvin et topographiques de Rossby, générées par une variation de l'afflux d'eau dans le bassin amont, perturbent l'écoulement au dessus du seuil et ainsi l'export d'eau. Cette perturbation est due à la réfraction des ondes sur le seuil à chaque passage, une fois qu'elles ont fait le tour du bassin amont. / The various projects presented in this thesis contribute to our understanding of various key aspects of the oceanic circulation. The first aspect that we investigate is the physical processes responsible for this tidal mixing, and we identify two processes. Equatorward of the critical latitude, internal tides transfer their energy to smaller-scale waves via triadic resonant instabilities involving near-inertial waves. Poleward of the critical latitude, internal tides still transfer energy to smaller-scale waves, but surprisingly this transfer takes place between the internal tide and evanescent waves.In the second study, we investigate the effect of a mean current on the propagation and the dissipation of internal tides generated at the topography in high-resolution simulations. In that case, the latitudinal dependence of the tidal energy dissipation is found to be smoother and closer to a constant. This change in the latitudinal dependence can be linked to the Doppler shift of the frequency of the internal tides, which impacts the generation of smaller-scale secondary waves.In the third study, we study the effect of an upstream disturbance on the upstream circulation by interaction with a hydraulically controlled sill. The Kelvin and topographic Rossby waves, generated by a change in the upstream inflow, perturb the flow through the channel and hence the water export. This perturbation is due to the refraction of the waves at the sill at each passage, once they go around the upstream basin.