The breaking of internal solitary waves (ISWs) of depression shoaling upon a uniformly sloping boundary in a smoothed two-layer density field was investigated using high-resolution two-dimensional simulations. The simulations were performed for a wide range of boundary slopes S∈[0.01,0.3] and wave slopes. Over steep slopes (S≥0.1), three distinct breaking processes were observed; surging, plunging and collapsing breakers which are associated with reflection, convective instability and boundary layer separation, respectively. Over mild slopes (S≤0.05), nonlinearity varies gradually and the wave fissions into a train of waves of elevation after it passes through the turning point where solitary waves reverse polarity. The dynamics of each breaker type were investigated and the predominance of a particular mechanism was associated with a relative developmental timescale. The breaker type was characterized in wave slope S_w versus S space and the reflection coefficient (R), modeled as a function of the internal Iribarren number, was in agreement with other studies. The same 2D model was applied to investigate boundary layer separation-driven global instability, which is shown to play an important role in breaking of shoaling ISWs. The simulations were conducted with waves propagating over a flat bottom and shoaling over relatively mild (S=0.05) and steep (S=0.1) slopes. Combining the results over flat and sloping boundaries, a unified criterion for vortex shedding is proposed, which depends on the momentum thickness Reynolds number and the non-dimensionalized ISW-induced pressure gradient at the point of separation. The criterion is generalized to a form that may be readily computed from field data and compared to published laboratory and field observations. During vortex shedding, the bed shear stress, vertical velocity and near-bed Reynolds stress were elevated, implying potential for sediment re-suspension. Laboratory experiments were also performed to study three-dimensionality (3D) of global instability. Our results agree with previous laboratory experiments, using the proposed pressure gradient parameter and Reynolds number. The 3D effects prevent the vortices from ascending as high as they do in 2D simulations. The instabilities were not able to re-suspend sediments with 20 µm median diameters, which suggests applying lighter sediments, as finer sediments will be cohesive and dynamically different. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2011-12-23 15:03:29.76

A computational fluid dynamics (CFD) methodology is presented to predict density stratified flows in the near-field of ships and submarines. The density is solved using a higher-order transport equation coupled with mass and momentum conservation. Turbulence is implemented with a k-ε/k-ω based Delayed Detached Eddy Simulation (DDES) approach, enabling explicit solution of larger energy-containing vortices in the wake. Validation tests are performed for a two-dimensional square cavity and the three-dimensional stratified flow past a sphere, showing good agreement with available data. The near-field flow of the self-propelled Research Vessel Athena advancing in a stably stratified fluid is studied, as well as the operation in stratified flow of the notional submarine Joubert BB2 also in self-propelled condition. The resulting density, velocity, pressure and turbulent quantities at the exit plane of the near-field computation contain a description of the relevant scales of the flow and can be used to compute the far-field stratified flow, including internal waves. The generation of internal waves is shown in the case of the submarine for two different conditions, one with the pycnocline located at the propeller centerline, and the second with the pycnocline located slightly below the submarine, concluding that distance to the pycnocline strongly affects the internal wave generation due to the presence of the vessel. It is also shown that, as in the case of surface waves, the generation of internal waves requires energy that results in an increase in resistance. For the case of the surface ship the near field wakes are mostly affected by the separation at the wet transom and propeller mixing. However, in the case of the underwater vessel, the disturbance of the background density profile by the presence of the submarine affects the near-field wakes. Finally, the dead-water phenomenon, which occurs at very low Froude numbers, is studied for R/V Athena. Though the dead water problem has been studied in the literature using potential flow methods, this thesis presents the first attempt at using computational fluid dynamics (CFD) to analyze the flow. Results show that, while CFD can reproduce trends observed in potential flow studies, viscous effects are significant in the wake and the friction coefficient.

Internal waves are generated in stratified fluids, like the ocean, where density increases with depth. Tides are one of the major generation mechanisms of internal waves. As the tides move water back and forth over underwater topography, internal waves can be generated. The shape of the topography plays a major part in the properties of the generated internal wave and the type of wave and energy is known for multiple symmetric topographies, such as Gaussian or sinusoidal. In order to further understand the effects topographic shape plays, the effect of asymmetry on internal waves is investigated. First, two experimental methods are compared to evaluate which will capture the relevant information for comparing waves generated from oscillating asymmetric topographies. Two experimental methods are often used in internal wave research, Synthetic Schlieren (SS) and Particle Image Velocimetry (PIV). Both SS and PIV experimental methods are used to analyze a set of experiments in a variety of density profiles and with a variety of topographies. The results from these experiments are then compared both qualitatively and quantitatively to decide which method to use for further research. In the setup, the larger field of view of SS results in superior resolution in wavenumber analysis, when compared to PIV. In addition, SS is 25% faster to setup and significantly cheaper. These are the deciding factors leading to the selection of SS as the preferred experimental method for further tests regarding tidally generated internal waves from asymmetric topographies. Previous experimental and theoretical research on tidally generated internal waves has most often used symmetric topographies. However, due to the complex nature of real ocean topography, the effect of asymmetry can not be overlooked. A few studies have shown that asymmetry can have a significant effect on internal wave generation, but topographic asymmetry has not been studied in a systematic manner up to this point. This work presents a comparison of tidally generated internal waves from nine different asymmetric topographies, consisting of a steeper Gaussian curve on one side, and a wider Gaussian curve on the other. The wider curve has varying amplitude from 1 to 0.6 of the steeper curve's amplitude, and two oscillation frequencies are explored. First, kinetic energy density in tidally generated internal waves is compared qualitatively and quantitatively, in both physical and Fourier space. When compared to similar symmetric topographies, the asymmetric topographies varied distinctly in the amount of internal wave kinetic energy generated. In general, internal wave kinetic energy generated from asymmetric topographies is higher for waves generated at a lower frequency than at a higher frequency. Also, kinetic energy is higher in internal waves on the relatively steeper side of the topography. There is very little kinetic energy in the higher wavenumbers, with most of the internal waves being generated at the lower wavenumbers. The amplitude does not make an appreciable difference in the wavenumber at which the internal waves are generated. Thus, the differences quantified here are due solely to changing slope, showing a significant impact of a relatively slight asymmetry.

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.

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 onset of summer stratification in temperate lakes and reservoirs forces a decoupling of the hypolimnion from the epilimnion that is sustained by strong density gradients in the metalimnion. These strong gradients act as a barrier to the vertical transport of mass and scalars leading to bottom anoxia and subsequent nutrient release from the sediments. The stratification is intermittently overcome by turbulent mixing events that redistribute mass, heat, dissolved parameters and particulates in the vertical. The redistribution of ecological parameters then exerts some control over the ecological response of the lake. This dissertation is focused on the physics of deep vertical mixing that occurs beneath the well-mixed surface layer in stratified lakes and reservoirs. The overall aim is to improve the ability of numerical models to reproduce deep vertical mixing, thus providing better tools for water quality prediction and management. In the first part of this research the framework of a one-dimensional mixed-layer hydrodynamic model was used to construct a pseudo two-dimensional model that computes vertical fluxes generated by deep mixing processes. The parameterisations developed for the model were based on the relationship found between lake-wide vertical buoyancy flux and the first-order internal wave response of the lake to surface wind forcing. The ability of the model to reproduce the observed thermal structure in a range of lakes and reservoirs was greatly improved by incorporating an explicit turbulent benthic boundary layer routine. Although laterally-integrated models reproduce the net effect of turbulent mixing in a vertical sense, they fail to resolve the transient distribution of turbulent mixing events triggered by local flow properties defined at far smaller scales. Importantly, the distribution of events may promote tertiary motions and ecological niches. In the second part of the study a large body of microstructure data collected in Lake Kinneret, Israel, was used to show that the nature of turbulent mixing events varied considerably between the epilimnion, metalimnion, hypolimnion and benthic boundary layer, yet the turbulent scales of the events and the buoyancy flux they produced collapsed into functions of the local gradient Richardson number. It was found that the most intense events in the metalimnion were triggered by high-frequency waves generated near the surface that grew and imparted a strain on the metalimnion density field, which led to secondary instabilities with low gradient Richardson numbers. The microstructure observations suggest that the local gradient Richardson number could be used to parameterise vertical mixing in coarse-grid numerical models of lakes and reservoirs. However, any effort to incorporate such parameterisations becomes meaningless without measures to reduce numerical diffusion, which often dominates over parameterised physical mixing. As a third part of the research, an explicit filtering tool was developed to negate numerical diffusion in a threedimensional hydrodynamic model. The adaptive filter ensured that temperature gradients in the metalimnion remained within bounds of the measured values and so the computation preserved the spectrum of internal wave motions that trigger diapycnal mixing events in the deeper reaches of a lake. The results showed that the ratio of physical to numerical diffusion is dictated by the character of the dominant internal wave motions.

Density stratification is one of the essential underlying physical mechanisms for atmospheric and oceanic flow. As a first step to investigating the mechanisms of stratified turbulence, linear stability plays a critical role in determining under what conditions a flow remains stable or unstable. In the study of transition to stratified turbulence, a common vortex model, known as the Lamb-Chaplygin dipole, is used to investigate the conditions under which stratified flow transitions to turbulence. Numerous investigations have determined that a critical length scale, known as the buoyancy length, plays a key role in the breakdown and transition to stratified turbulence. At this buoyancy length scale, an instability unique to stratified flow, the zigzag instability, emerges. However investigations into sub-buoyancy length scales have remained unexplored. In this thesis we discover and investigate a new instability of the Lamb-Chaplyin dipole that exists at the sub-buoyancy scale. Through numerical linear stability analysis we show that this short-wave instability exhibits growth rates similar to that of the zigzag instability. We conclude with nonlinear studies of this short-wave instability and demonstrate this new instability saturates at a level proportional to the cube of the aspect ratio.

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.

A numerical model has been developed for the study of stratified tidal circulation in Indian Arm - a representative inlet on the southern coast of British Columbia. Equations for horizontal velocity, salt conservation, continuity, density (calculated as a linear function of salinity), and the hydrostatic approximation govern the dynamics. All equations have been laterally integrated under the assumption of negligible cross-inlet variability. The model is time dependent and includes nonlinear advective terms, horizontal and vertical turbulent diffusion of salt and momentum, and variations in width and depth. Provisions for surface wind stress and a flux of fresh water are also included, although neither was utilized in this study. An explicit finite difference scheme centred in both time and space was used to solve for the horizontal and vertical velocity components, salinity, and surface elevation on a staggered rectangular grid. A backward Euler scheme was used to suppress the computational mode. Tests using a semi-implicit scheme to solve the finite difference equations over realistic topography led to numerical instabilities at modest values of the time step - in spite of the unconditional stability criteria - suggesting that linear stability analysis may give misleading results for strongly nonlinear systems. Surface elevations calculated from tidal harmonic analysis and salinity timeseries derived from linearly interpolated CTD casts were prescribed at the open boundary. Initial and boundary conditions based on observations in Burrard Inlet and Indian Arm during the winter of 1974-75 were used to study the inlet's response to tidal forcing and to simulate the deep-water renewal that occurred during this period. Coefficients for the horizontal turbulent diffusion of momentum and salt were set equal to 10⁶ cm² s⁻¹. Reducing this value by a factor of two was found to have little impact on the solution. A further reduction to 10³ cm² s⁻¹ led to numerical instabilities under conditions of dense water inflow. The side friction term in the momentum balance was tuned to match calculated and observed dissipation rates in Burrard Inlet; leading to good agreement between the observed and calculated barotropic tide. Contour plots of tidal amplitudes and phases for model currents and salinities revealed a standing wave pattern for the K₁ and M₂ internal tides in Indian Arm; thus allowing for the possibility of resonance. A comparison of model results with vertical amplitude and phase profiles from harmonic analysis of Cyclesonde current meter timeseries at two locations in Indian Arm was consistent with this result. A least-squares fit was made of the vertical modal structure in the model to the complex tidal amplitudes. This led to calculations of the kinetic energy contained in each of the modes along the model inlet for the M₂ and K₁ constituents. Most of the energy was found to be contained in the barotropic and first baroclinic modes, with the latter dominating in the deep basin, and the former dominating near the sill. Second mode energy was significant for the K₁ constituent at some locations in Indian Arm. There are clear indications in the model of barotropic tidal energy being radiated into the inlet basin via the internal tide. Simulations of the influx of dense water into Indian Arm yielded exchange rates that are consistent with observed values and suggest the possibility of fine-tuning the model coefficients to allow prediction of future overturning events. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

Internal waves are generated in stratified fluids, like the ocean, where density increases with depth. Tides are one of the major generation mechanisms of internal waves. As the tides move water back and forth over underwater topography, internal waves can be generated. Topography slope and amplitude are major factors in the behavior of the generated internal wave field. In order to further understand the effects topographic shape plays, the effect of asymmetry on internal waves is investigated. This research investigates internal waves generated by dual-ridge topographies. Four cases of symmetric topographies, T, M, W, and W2, with three different peak spacings are compared to their singular ridge counter parts at three oscillation frequencies, ω = 0.6N, ω = 0.75N, and ω = 0.9N. Both subcritical and supercritical symmetric ridges were investigated. Experiments were also performed for subcritical, asymmetric dual ridges at the middle oscillation frequency. The internal wave fields were captured with synthetic schlieren and analyzed with the Hilbert transform and sum of kinetic energy in wavenumber space. It is found that for wave fields from substantially separated ridges, mixing and wave interference occurs that decreases total kinetic energy of the system.