Near-resonant triad interactions and wave generation theory are investigated for continuously stratified fluids. Interaction equations are derived for spatially-varying wave trains under the inviscid Boussinesq approximation. Rotational effects are included, and properties of the underlying eigenvalue problem are explored. To facilitate a numerical study of the near-resonant interactions, numerical methods are developed and an analysis of wave generation on a periodic domain is performed. Numerical experiments using laboratory and ocean-scale parameters are conducted, and the simulations confirm the validity of the wave forcing theory. Interaction experiments demonstrate a strong tendency for waves to exhibit nonlinear behaviour. While resonant interactions are observed in the laboratory scale simulations, nonlinear steepening effects and the formation of solitary-like waves dominate the ocean-scale experiments. The results suggest that the weakly-nonlinear interaction theory is only appropriate in a limited parameter regime. The problem of analyzing forced wave equations on an infinite domain is also considered. Motivated by the results obtained on a periodic domain, asymptotic analysis is applied to three important wave equations. The method of steepest descents is used to determine the large-time behaviour for the linearized Korteweg-de Vries, Benjamin-Bona-Mahony, and internal gravity wave equations. The asymptotic results are compared with numerical experiments and found to agree to high precision.

Sea surface temperature (SST) is an important oceanic parameter which can be accessed easily and vastly by satellite remote sensing. Recent hydrographic observations suggested that the water temperature near Dongsha Atoll were affected by internal waves of South China Sea (SCS). This study hypothesizes that the SST variations near Dongsha Atoll and continental shelf cab be observed by satellite data. To test the hypothesis, MODIS SST data during January 2005 to December 2009 were collected and analyzed using harmonic and EOF analyses. The results show that there can be a 1 ¢XC temperature drop, near Dongsha Atoll during the passage of internal waves, based on a longitudinal section cut for a typical SST image. The SST patterns in northern SCS are distributed lower in the east and higher in the west. The temperature showed an average of 0.5¢XC lower near Dongsha Atoll. Especially, the pattern of lower temperature near Dongsha is significant during neap tide in summer season. EOF analysis showed that the spatial distribution of SST aligned well with the bottom topography of the continental shelf. This result suggests that internal tide may be important to the vertical mixing in this region. The total variation of mode 1 in EOF accounted for 97.7% and is dominated by seasonal changes. For the long term and large area SST statistics, the internal wave induced variation is insignificant, as comparing the Dongsha region with shelf region and Kuroshio region.

This dissertation includes two fluid dynamics studies that involve fluid flows on vastly different scales, and therefore vastly different physics. The first study is of bacterial swimming using a flagellum for propulsive motion. Because bacteria are only about 10 [micrometers] in length, they swim in a very low Reynolds number (10⁻⁴) world, which is described by the linear set of governing equations known as the Stokes equations, that are a simplified version of the Navier-Stokes equations. The second study is of harmonic generation from nonlinear effects in internal, ocean-like wave beams that reflect from boundaries in a density stratified fluid. Internal wave reflection is an important oceanic process and may help sustain ocean circulation and affect global weather patterns. Such ocean processes have typical Reynold's numbers of 10¹⁰ or more and are only described by the full, nonlinear Navier-Stokes equations. In the low Reynolds number study, I examine theories by Gray et al.(1956) and Lighthill (1975) that describe swimming microorganisms using a helical flagellum for propulsive motion. I determine the resistance matrix, which can fully describe the dynamics of a flagellum, for flagella with different geometries, defined by: filament radius a, helical radius R, helical pitch [lambda], and axial length L. I use laboratory experiments and numerical simulations conducted in collaboration with Dr. Hepeng Zhang. The experiments, conducted with assistance from a fellow graduate student Chih-Hung Chen, use macroscopic scale models of bacterial flagella in a bath of highly viscous silicone oil. Numerical simulations use the Regularized Stokeslet method, which approximates the Stokeslet representation of an immersed body in a low Reynolds number flow. My study covers a biologically relevant parameter regime: 1/10R < a < 1/25R, R < [lambda] < 20R, and 2R< L <40R. I determine the three elements of the resistance matrix by measuring propulsive force and torque generated by a rotating, non-translating flagellum, and the drag force on a translating, non-rotating flagellum. I investigate the dependences of the resistance matrix elements on both the flagellum's axial length and its wavelength. The experimental and numerical results are in excellent agreement, but they compare poorly with the predictions of resistive force theory. The theory's neglect of hydrodynamic interactions is the source of the discrepancies in both the length dependence and wavelength dependence studies. I show that the experimental and simulation data scale as L/ln(L/r), a scaling analytically derived from slender body theory by my other collaborator Dr. Bin Liu. This logarithmic scaling is new and missing from the widely used resistive force theory. Dr. Zhang's work also includes a new parameterized version of resistive force theory. The second part of the dissertation is a study of harmonic generation by internal waves reflected from boundaries. I conduct laboratory experiments and two-dimensional numerical simulations of the Navier-Stokes equations to determine the value of the topographic slope that gives the most intense generation of second harmonic waves in the reflection process. The results from my experiments and simulations agree well but differ markedly from theoretical predictions by Thorpe (1987) and by Tabaei et al. (2005), except for nearly inviscid, weakly nonlinear flow. However, even for weakly nonlinear flow (where the dimensionless Dauxois-Young amplitude parameter value is only 0.01), I find that the ratio of the reflected wavenumber to the incoming wavenumber is very different from the prediction of weakly nonlinear theory. Further, I observe that for incident beams with a wide range of angles, frequencies, and intensities, the second harmonic beam produced in reflection has a maximum intensity when its width is the same as the width of the incident beam. This observation yields a prediction for the angle corresponding to the maximum in second harmonic intensity that is in excellent accord with my results from experiments and numerical simulations. / text

The majority of internal gravity wave energy in the ocean is produced by tidal flow over bottom topography. Regions of critical topography, where the topographic slope is equal to the slope of the internal gravity waves, is often believed to contribute most significantly to the radiated internal gravity wave power. Here, we present 2D computational studies of internal gravity wave generation by tidal flow over several types of topographic ridges. We vary the criticality parameter [epsilon], which is the ratio of the topographic slope to the wave beam slope, by independently changing the tidal frequency, stratification and topographic slope, which allows to study subcritical ([epsilon] < 1), critical ([epsilon] = 1), and supercritical ([epsilon] > 1) topography. This parameter variation allows us to explore a large range of criticality parameter, namely 0.1< [epsilon] < 10, as well as beam slope S, 0.05< S < 10. As in prior work [Zhang et al., Phys. Rev. Lett. (2008)], we observe resonant boundary currents for [epsilon] = 1. However, we find that the normalized radiated power monotonically increases with internal wave beam slope. We show that an appropriate normalization condition leads to a universal scaling of the radiated power that is proportional to the inverse of the beam slope 1/S and the tidal intensity I[subscript tide], except near [epsilon] = 1 where the behavior undergoes a transition. We characterize this transition and the overall scaling with the criticality parameter f([epsilon]), which is weak compared to the scalings mentioned before and only varies by a factor of two over the entire range of criticality parameter that we explored. Our results therefore suggest that estimates of the ocean energy budget must account for the strong scaling with the local beam slope, which dominates the conversion of tidal motions to internal wave energy. Thus we argue that detailed characterization of the stratification in the ocean is more important for global ocean models than high-resolution bathymetry to determine the criticality parameter. / text

The shoaling of horizontally propagating internal waves may provide an important source of mixing and transport in estuaries and coastal seas. Parameterizing such effects in numerical models demands better understanding of several aspects of wave energetics, especially relating to horizontal energy flux and turbulence generation. Observations are needed to build this understanding. To address some of these issues in the estuarine context, an intensive field program was undertaken in Summer 2008 in the St. Lawrence Estuary, involving shore-based photogrammetry, ship-based surveys, and moorings that held conventional and turbulence-resolving sensors. The measurements reveal that waves generally arrived during the rising phase of the M2 tide. Shoreward of the 40m isobath, waves traversed the field site perpendicular to bathymetry, a pattern that continued as the waves transformed nonlinearly. A tight temperature-salinity relationship permits the estimation of the time-varying density field from a moored chain of temperature-depth recorders. A new method for inferring the heaved internal wave density field is developed, using a relaxation solver to determine the wave streamfunction. The method is applied to discrete events measured with acoustic Doppler profilers to estimate the kinetic and available potential energy, as well as the nonlinear horizontal energy flux. Acoustic Doppler velocimeters were used to infer near-bottom turbulent energetics, revealing two main features. First, a period of wave incidence had turbulence dissipation rates that exceeded values associated with tidal shear by an order of magnitude. Second, the evolving spectral signatures associated with a particular wave-shoaling event indicate that the turbulence is at least partly locally generated. A simple model for wave-induced turbulence is proposed based on the energy flux measurements. Generally, the results suggest that during the rising phase of the tide, energy input from shoaling waves is required to explain the observed levels of dissipation. Estimates of vertical diffusivity during times of wave shoaling are on average 3 times larger than values predicted by tidal shear alone.

No description available.

This thesis investigates several aspects of stratified flow over isolated topography in ocean, lake, and atmospheric settings. Three major sub-topics are addressed: steady, inviscid internal waves trapped over topography in a pycnocline stratification, topographically generated internal waves and their interaction with the viscous bottom boundary layer, and flow over large-scale crater topography in the atmosphere. The first topic examines the conditions that lead to very large internal waves trapped over topography in a fluid with a pycnocline stratification. This type of stratification is connected to ocean or lake settings. The steady-state Euler equations of motion are used to derive a single partial differential equation for the isopycnal displacement in supercritical flows under two conditions: a vertically varying background current under the Boussinesq approximation and a constant background current under non-Boussinesq conditions. A numerical method is developed to solve these equations for an efficient exploration of parameter space. Very large waves are found over depression topography when the background flow speed is close to a limiting value. Variations in the background current are examined, as well as comparisons between Boussinesq and non-Boussinesq results. The second topic aims to extend the above subject by considering unsteady, viscous flows. Once again, supercritical flow over topography in a pycnocline stratification generates internal waves. These internal waves interact with the viscous bottom boundary layer to produce bottom boundary instabilities. The three-dimensional aspects of these instabilities are studied under changes in viscosity. The boundary layer instabilities have important implications for sediment transport in the coastal oceans or lakes. Lastly, the final topic is motivated by the connection between dust streaks on the Martian surface and crater topography. Flow over a large 100-km diameter crater is examined with numerical simulations conducted using the Weather Research and Forecasting model. Modifications to the stratification and topography are applied. It is found that a large hydraulic structure of amplitude comparable to the crater depth forms in many cases. This structure may have important implications for dust transport in the atmosphere. In addition, Martian atmospheric parameters are used to study the flow properties under Mars-like conditions.

Near-resonant triad interactions and wave generation theory are investigated for continuously stratified fluids. Interaction equations are derived for spatially-varying wave trains under the inviscid Boussinesq approximation. Rotational effects are included, and properties of the underlying eigenvalue problem are explored. To facilitate a numerical study of the near-resonant interactions, numerical methods are developed and an analysis of wave generation on a periodic domain is performed. Numerical experiments using laboratory and ocean-scale parameters are conducted, and the simulations confirm the validity of the wave forcing theory. Interaction experiments demonstrate a strong tendency for waves to exhibit nonlinear behaviour. While resonant interactions are observed in the laboratory scale simulations, nonlinear steepening effects and the formation of solitary-like waves dominate the ocean-scale experiments. The results suggest that the weakly-nonlinear interaction theory is only appropriate in a limited parameter regime. The problem of analyzing forced wave equations on an infinite domain is also considered. Motivated by the results obtained on a periodic domain, asymptotic analysis is applied to three important wave equations. The method of steepest descents is used to determine the large-time behaviour for the linearized Korteweg-de Vries, Benjamin-Bona-Mahony, and internal gravity wave equations. The asymptotic results are compared with numerical experiments and found to agree to high precision.

The generation and evolution of internal solitary waves by intrusive gravity currents and river plumes are examined in an axisymmetric geometry by way of theory, experiments and numerical simulations. Full depth lock-release experiments and simulations demonstrate that vertically symmetric intrusions propagating into a two-layer fluid with an interface of finite thickness can launch a mode-2 double humped solitary wave. The wave then surrounds the intrusion head and carries it outwards at a constant speed. The properties of the wave's speed and shape are shown to agree well with a Korteweg-de Vries theory that is derived heuristically on the basis of energy conservation. The numerical code is also adapted to oceanographic scales in an attempt to simulate the interaction between the ocean and a river plume emanating from the mouth of the Columbia River. Despite several approximations, the fundamental dynamics of the wave generation process are captured by the model.

Thesis (Ph.D.)--University of Western Australia, 2007.