Thesis. 1975. M.S.--Massachusetts Institute of Technology. Dept. of Meteorology. / Bibliography: leaves 70-72. / M.S.

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Meteorology. / Microfiche copy available in Archives and Science. / Vita. / Bibliography : p. [323-328]. / Ph.D.

Thesis (Ph. D.)--Joint Program in Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and the Woods Hole Oceanographic Institution), 2011. / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 185-193). / This thesis describes the physics of fully three-dimensional low frequency acoustic interaction with internal waves, bottom sediment waves and surface swell waves that are often observed in shallow waters and on continental slopes. A simple idealized model of the ocean waveguide is used to analytically study the properties of acoustic normal modes and their perturbations due to waves of each type. The combined approach of a semi-quantitative study based on the geometrical acoustics approximation and on fully three-dimensional coupled mode numerical modeling is used to examine the azimuthal dependence of sound wave horizontal reflection from, transmission through and ducting between straight parallel waves of each type. The impact of the natural crossings of nonlinear internal waves on horizontally ducted sound energy is studied theoretically and modeled numerically using a three-dimensional parabolic equation acoustic propagation code. A realistic sea surface elevation is synthesized from the directional spectrum of long swells and used for three-dimensional numerical modeling of acoustic propagation. As a result, considerable normal mode amplitude scintillations were observed and shown to be strongly dependent on horizontal azimuth, range and mode number. Full field numerical modeling of low frequency sound propagation through large sand waves located on a sloped bottom was performed using the high resolution bathymetry of the mouth of San Francisco Bay. Very strong acoustic ducting is shown to steer acoustic energy beams along the sand wave's curved crests. / by Alexey Alexandrovich Shmelev. / Ph.D.

Internal waves are prominent fluid phenomena in both the atmosphere and ocean. Because internal waves have the ability to transfer a large amount of energy, they contribute to the global distribution of energy. This causes internal waves to influence global climate patterns and critical ocean mixing. Therefore, studying internal waves provides additional insight in how to model geophysical phenomena that directly impact our lives. There is a myriad of fluid phenomena with which internal waves can interact, including other internal waves. Equipment and processes are developed to perform laboratory experiments analyzing the interaction of two colliding nonresonant internal waves. Nonresonant interactions have not been a major focus in previous research. The goal of this study is to visualize the flow field, compare qualitative results to Tabaei et al., and determine the energy partition to the second-harmonic for eight unique interaction configurations. When two non-resonant internal waves collide, harmonics are formed at the sum and difference of multiples of the colliding waves' frequencies. In order to create the wave-wave interaction, two identical wave generators were designed and manufactured. The interaction flow field is visualized using synthetic schlieren and the energy entering and leaving the interaction region is analyzed. It is found that the energy partitioned to the harmonics is much more dependent on the general direction the colliding waves approach each other than on the angle. Depending on the configurations, between 0.5 and 7 percent of the energy within the colliding waves is partitioned to the second-harmonics. Interactions in which the colliding waves have opposite signed vertical wavenumber partition much more energy to the harmonics. Most of the energy entering the interaction is dissipated by viscous forces or leaves the interaction within the colliding waves. For all eight configurations studied, 5 to 8 percent of the energy entering the interaction has an unknown fate.

Internal waves exist everywhere in stratified fluids - fluids whose density changes with depth. The two largest bodies of stratified fluid are the atmosphere and ocean. Internal waves are generated from a variety of mechanisms. One common mechanism is wind forcing over repeated sinusoidal topography, like a series of hills. When modeling these waves, linear theory has been employed due to its ease and low computational cost. However, recent research has shown that non-linear effects, such as boundary layer separation, may have a dramatic impact on wave generation. This research has consisted of experimentation on sloped, sinusoidal hills. As of yet, no experimental research has been done to characterize internal wave generation when repeated sinusoidal hills lie on a sloped surface such as a continental slope or a foothill. In order to perform this experiment, a laboratory was built which employed the synthetic schlieren method of wave visualization. Measurements were taken to find wind speed, boundary layer thickness, and density perturbation. From these data, an analysis was performed on wave propagation angle, wave amplitude, and pressure drag. The result of the analysis shows that when wind blows across a series of sloped sinusoidal hills, fluid becomes trapped in the troughs of the hills resulting in a lower apparent forcing amplitude. The generated waves contain less energy than linear predictions. Additionally, the sloped hills produce waves which propagate at an angle away from the viewer. A necessary correction, which shifts from the reference frame of the observer to the reference plane of the waves is described. When this correction is applied, it is shown that linear theory may only be applied for low Froude numbers. At high Froude numbers, the effect of the boundary layer is great enough that the wave characteristics deviate significantly from linear theory predictions. The analyzed data agrees well with previous studies which show a similar deviation from linear theory.

Submarine canyons incising the continental shelf and slope are hot spots for topography-internal wave interactions, with elevated dissipation and mixing contributing to regional transport and biological productivity. At two Barkley Canyon sites (the continental slope below the shelf-break, and deep within the canyon), four overlapping years of horizontal velocity time-series data are used to examine the effects of irregular topography on the internal wave field. Mean currents are topographically guided at both sites, and in the canyon there is an inter-annually consistent, periodic (about a week) up-canyon flow (-700 to -900 m) above a near-bottom down-canyon layer. There is elevation of internal wave energy near topography, up to a factor of 10, 130 m above the slope, and up to a factor of 100, 230 m above the canyon bottom. All bands display weak inter-annual variability, but significant seasonality. Sub-diurnal and diurnal flows are presumably sub-inertially trapped along topography, and the diurnal band appears to be forced locally (barotropically). Both sites have high near-inertial energy. At the slope site, near-inertial energy is attenuated with depth, while in the canyon it is amplified near the bottom. Both sites show intermittent near-inertial forcing associated with wind events, downward propagation of high-mode internal waves, and the seasonal mixed-layer depth, though fewer events are observed in the canyon. Free semidiurnal internal tides are focused and reflected near critical shelf-break and canyon floor topography, and appear to experience both local and remote (baroclinic) forcing. The high-frequency internal wave continuum has enhanced energy near bottom at both sites (up to 7 times the open-ocean Garrett-Munk spectrum), and inferred dissipation rates increasing from a background of less than 10^-9 W kg^-1 and reaching 10^-7 W kg^-1 near topography. Dissipation is most strongly correlated with the semidiurnal (M2) constituent at both sites, with secondary contributions from the sub-diurnal (Sub_K1) band on the slope, and the near-inertial (NI) band in the canyon. Power laws for these dependencies are dissipation ~ M2^0.83 + Sub_K1^0.59 at the slope, and dissipation ~ M2^1.47 + NI^0.24 in the canyon. There is evidence in spectra of a near-buoyancy frequency build-up of energy correlated with high-frequency continuum variability, with a power law fit of 'shoulder' power ~ dissipation^0.34 that is independent of site topography. Though some general results are expected from observations at other slope and canyon sites, the greater temporal extent of these data provide a uniquely long-term evaluation of such processes. / Graduate

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Science, 1980. / Microfiche copy available in Archives and Science. / Vita. / Bibliography: leaves 111-115. / by Frances Luellen Stephenson Hotchkiss. / M.S.

Mathematical modeling of ocean waves is based on the formulation and solution of the appropriate equations of continuity, momentum and the choice of proper initial and boundary conditions. Under the influence of gravity, many free surface water waves can be modeled by the shallow water equations (SWE) with the assumption that the horizontal length scale of the wave is much greater than the depth scale and the wave height is much less than the fluid's mean depth. Furthermore, to describe three dimensional flows in the hydrostatic and Boussinesq limits, the multilayer SWE model is used, where the fluid is discretized horizontally into a set of vertical layers, each having its own height, density, horizontal velocity and geopotential. In this study, we used an explicit staggered finite volume method to solve single and multilayer SWE, with and without density stratification and bathymetry, to understand the dynamic of surface waves and internal waves. We implemented a two-dimensional version of the incompressible DYNAMICO method and compare it with a one-dimensional SWE. For multilayer SWE, we considered both two layer and a linear stratification of density, with very small density gradient, consistent with Boussinesq approximation. We used Lagrangian vertical coordinate which doesn't allow mass to flow across vertical layers. Numerical examples are presented to verify multilayer SWE model against single layer SWE, in terms of the phase speed and the steepness criteria of wave profile. In addition, the phase speed of the barotropic and baroclinic mode of two-layer SWE also verified our multilayer SWE model. We found that, for multilayer SWE, waves move slower than single layer SWE and get steeper than normal when they flow across bathymetry. A series of numerical experiment were carried out to compare 1-D shallow water solutions to 2-D solutions with and without density as well as to explain the dynamics of surface wave and internal wave. We found that, a positive fluctuations on free surface causes water to rise above surface level, gravity pulls it back and the forces that acquired during the falling movement causes the water to penetrate beneath it's equilibrium level, influences the generation of internal waves. Internal waves travel considerably more slowly than surface waves. On the other hand, a bumpy or a slicky formation of surface waves is associated with the propagation of internal waves. The interaction between these two waves is therefore demonstrated and discussed. / Thesis / Master of Science (MSc) / In the modelling of ocean wave, the formulation and solution of appropriate equations and proper initial and boundary conditions are required. The shallow water equations (SWE) are derived from the conservation of mass and momentum equations, in the case where the horizontal length scale of the wave is much greater than the depth scale and the wave height is much less than the fluid's mean depth. In multilayer SWE, the fluid is discretized horizontally into a set of vertical layers, each having its own height, density, horizontal velocity and geopotential. In this study, we used an explicit staggered finite volume method to solve single and multilayer SWE, with and without density stratification and bathymetry, to understand the dynamic of surface waves and internal waves. A series of numerical experiments were carried out to validate our multilayer model. It is found that, in the presence of density differences, surface waves for the multilayer SWE move slowly and get more steep than normal when they flow across bathymetry. Also, a positive fluctuations on free surface generates internal waves at the interior of ocean which propagate along the line of density gradient.

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Earth and Planetary Sciences. / Vita. / Bibliography: leaves 324-329. / Ph.D.

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Earth and Planetary Sciences. / Microfiche copy available in Archives and Science. / Vita. / Bibliography : leaves 162-165. / Ph.D.