An analytical and experimental study of boundary gravity currents propagating through a two-layer stratified ambient of finite vertical extent is presented. The theoretical discussion considers slumping, supercritical gravity currents, i.e. those that generate an interfacial disturbance whose speed of propagation matches the front speed, U and follows from the classical analysis of Benjamin [J. Fluid Mech. 31, pp. 209-248, 1968]. In contrast to previous investigations, the amplitude of the interfacial disturbance is parameterized so that it can be determined straightforwardly from ambient layer depths. The theoretical model, which is applicable to the special case where the depth, D, of the gravity current fluid at the initial instant spans the channel depth, H, shows good agreement with experimental measurements and also analogue numerical simulations performed in conjunction with the present investigation. Unfortunately, it is difficult to extend our theoretical results to the more general case where D < H. Reasons for this difficulty will be discussed. From experimental and numerical observations, the interface thickness is observed to negligibly affect the speed of supercritical gravity currents even in the limit where the interface spans the channel depth so that the ambient fluid is linearly stratified over the whole of its depth. Conversely, subcritical gravity currents show a mild upward trend of U on the interface thickness. Finally, the effects of densities, ambient depths, interface thickness and D on the horizontal position, X where deceleration first begins are considered. In contrast to the uniform ambient configuration, the gravity current can propagate without decelerating beyond 12 lock lengths and decelerate as early as 1 lock length. / Thermo Fluids

Internal waves include soliton of period 10-20 minutes and tidal frequency waves. Large internal solitons with amplitude over 100 m were observed frequently in the South China Sea (SCS). There were convergence zones of 500-1000 m wide in the wave front of solitons which can be detected by satellite from the space. The hypothesis of this study is the internal wave signal can be extracted from the sea surface anomalies of satellite altimetry. Data analyzed include TOPEX/Poseidon altimeter from August 2002 to October 2005 in the northern SCS and Kuroshio regions. Methods applied include (1) standard deviation analysis, (2) harmonic analysis and (3) wavenumber spectrum analysis. The results show that¡]1¡^there is an annual variation in the sea surface height, which is explained due to water temperature changes in different seasons. (2) The results of harmonic analysis show that the amplitude of M2 aliasing is only a few centimeters on the sea surface. The different is small between internal active region and that of without. (3) The absolute values of slope, of internal wave energy and wavenumber spectrum, are 2-3 in the wave active region. This suggests that there are wave motions of scale 100 km or larger, which matches with the length scale of internal waves in the northern SCS.

Laboratory experiments were conducted to investigate the propagation of internal solitary waves on a uniform slope in a two-layered free surface fluid system. The laboratory facilities employed in this study is the first in Taiwan, which include a stainless steel wave flume (dimensions: 12 meters long with cross-section 0.5 m wide and 0.7m deep) and experimental apparatus for generating and measuring internal waves. The flume incorporates a movable vertical gate at one end for generating internal solitary waves, and a uniform slope (either £c = 30o, 50o, 60o, 90o, 120o or 130o) at the other end. The upper layer had fresh water with density £l1 (999kg/m3), to a depth H1; the lower layer was saline brine density £l2 (1030 kg/m3), which was slowly filled into the flume to a depth of H2 by gravity through several openings at the bottom of the flume, Boussinesq parameter . A mini pump was used to remove a small quantity of fresh water from one side of the vertical gate to another side. By creating a prescribed difference £bo in the interface levels on either side of the gate beforehand, internal solitary wave was generated by the mechanism of overturning the brine and fresh water behind the movable gate. Five ultrasonic probes at equidistant distance recorded the interface fluctuations, one density probe measured the change of density at the interface, while two electrical capacitance gauges for the free surface displacements likely to occur. Digital cameras were also used to record the motions of internal wave in the flume and on the slope for further analysis. Laboratory test on internal solitary wave were arranged from one of the combinations using different layer thickness ratios H1/H2, interface differences £bo, density ratios £l1/£l2, and bottom slopes £c. In addition to internal solitary wave reflection from a uniform slope, laboratory investigations included internal wave propagation on a rigid impermeable bottom and evolution on a uniform slope. Keeping the total water depth in the flume at H = 40cm, an increase in the depth parameter |H2-H1|/H produced large internal wave amplitude, reduced phase velocity, and enhanced soliton feature. From the experimental result analyzed, it suggests that the Korteweg-de Vries (KdV) theory fits solitary waves of small amplitude, and the modified KdV is suitable for large amplituded waves. Considering wave motion in an inviscid fluid, the dissipation of internal solitary waves propagating in a flume may occur through bottom friction and wave breaking. Subjected to bottom friction alone, the amplitude of most internal solitary waves in the experiments decayed approximate by 10% over a journey of 6 meters. Two types of wave breaking mechanism were found to produce strong mixing and local vortex in the fluid, causing significant energy losses. For internal solitary waves of large amplitudes, reflection coefficient for wave amplitude or energy decreased, as amplitude or energy increased. Under this condition, however, the reflection coefficient due to bottom friction may be assumed as constant. Using the experimental results obtained, empirical equation is now proposed to account for wave dissipation due to for non-breaking internal waves. The equation indicates that decrease in reflection coefficient as wave amplitude or energy increases may be expressed using a second order polynomial. Overall, experimental results suggest that good agreement can be found between experimental data and the empirical equation so derived. Upon assuming the wave reflection coefficient is solely dependent on the incoming wave amplitude or energy, prediction for reflection coefficient can be calculated in a straight forward manner. Either large-scale, high-frequency internal wave motion or internal solitary waves have been observed in natural lakes. The observed rapid decay of internal wave energy after severe breaking events seemed to be mostly due to dissipation on various sloping boundaries in a lake. From the basic laboratory experiments on internal wave reflection from various single slopes, the results many benefit provide researchers to promote further research on practical applications related to limnology.

Many problems in shallow water acoustics require accurate predictions of the acoustic field in space and time. The accuracy of the predicted acoustic field depends heavily on the accuracy of the inputs to the propagation model. Oceanographic internal waves are known to introduce considerable temporo-spatial variability to the water column, subsequently affecting the propagation of acoustic waves. As a result, when internal waves are present, errors in model inputs can significantly degrade the accuracy of the predicted acoustic field. Accurate temporo-spatial predictions of the acoustic field in the presence of internal waves therefore depend largely on one's ability to accurately prescribe the water column properties for the acoustic model. This work introduces a data-driven oceanographic model, named the evolutionary propagated thermistor string (EPTS) model, that captures the temporo-spatial evolution of the internal wave field along a fixed track, thereby permitting prediction of temporal fluctuations in the acoustic field. Simultaneously-measured oceanographic and acoustic data from the Office of Naval Research Shallow Water 2006 experiment are utilized in this work. Thermistor measurements, recorded on four oceanographic moorings spaced along the continental shelf, provide the data from which the EPTS model constructs the internal wave field over a 30 km track. The acoustic data were acquired from propagation measurements over a co-located path between a moored source and a vertical line array. Acoustic quantities computed in the model space, such as received level, depth-integrated intensity, and scintillation index are directly compared to measured acoustic quantities to evaluate the fidelity of the oceanographic model. In addition, a strong correlation is observed between the amplitude of the internal wave field and acoustic intensity statistics at a distant receiving array. It is found that the EPTS model possessed sufficient fidelity to permit the prediction of acoustic intensity distributions in the presence of nonlinear internal waves. / text

No description available.

Les ondes internes de gravité jouent un rôle essentiel dans la dynamique océanique. La relation de dispersion anisotrope de ces ondes conduit à des lois de réflexion qui sont différentes de celles dont nous avons l'habitude avec les ondes acoustiques ou les rayons lumineux. Dans cette thèse de doctorat, nous nous intéressons aux structures créées par ces ondes en deux dimensions puis en trois dimensions. Dans la plupart des géométries 2D, le parcours des ondes va converger vers un attracteur. Nous étudions d'abord expérimentalement, dans une géométrie trapézoïdale, l'aspect énergétique d'un de ces attracteurs d'ondes. Nous examinons ensuite expérimentalement la transformation de ces attracteurs dans des géométries tridimensionnelles. Dans certaines géométries, la réflexion des ondes conduit à un phénomène de piégeage dans un plan 2D. Ce phénomène, d'abord étudié à l'aide de tracés de rayons, a été reproduit dans une géométrie trapézoïdale ainsi que dans une géométrie de canal. Cette mise en évidence expérimentale du piégeage pourrait expliquer certaines mesures in-situ réalisées dans l'estuaire du Saint Laurent où la propagation des ondes internes est encore mal comprise. Cette thèse est enrichie par deux études expérimentales portant sur la propagation et la réflexion d'un faisceau d'ondes interne : d'une part, l'instabilité créant un courant moyen dans le cas d'un faisceau se propageant dans une géométrie tridimensionnelle et d'autre part la génération d'ondes rétro-réfléchies lors de la réflexion sur des surfaces courbes. / Internal waves play a critical rôle in the ocean dynamics. The anisotropic dispersion relation of these waves leads to reflexion law which are different from what we are used to with acoustic waves or light rays. In the PhD thesis, we are interested in structures generated by these waves, in two dimensions then in three dimensions. In most of the 2D geometries, wave path will converge onto an attractor. We firstly study experimentally, in a trapezoidal geometry, the energy aspect of one of these attractors. Then, we survey experimentally the future of these attractors in tridimensional geometries. In some of them, reflexion leads to a trapping event in a 2D plan. This phenomenon was firstly studied by means of ray tracing, and was reproduced in both a trapezoidal and a canal geometry. The experimental obtainment of trapping could explain some in-situ measurements done in the Saint Laurent estuary, where internal wave propagation is still under scrutiny. This thesis is enhanced by two experimental studies on propagation and reflexion of an internal wave beam. Firstly, the instability generating a mean flow from a beam propagating in a three-dimensional geometry. Secondly, the generation of back-reflected waves from beam reflexion on a curved surface.

This thesis investigates the effects of the earth's rotation on internal waves from two perspectives of nonlinear internal wave theory: near-resonant triads and weakly nonlinear models. We apply perturbation theory (multiple scale analysis) to the governing equations of internal waves and develop a near-resonant internal wave triad theory. This theory explains a resonant-like phenomenon in the numerical results obtained from simulating internal waves generated by tide topography interaction. Furthermore, we find that the inclusion of the earth's rotation (nonzero $f$) in the numerical runs leads to a very special type of resonance: parametric subharmonic instability. Through using perturbation expansion to solve separable solutions to the governing equations of internal waves, we derive a new rotation modified KdV equation (RMKdV). Of particular interest, the dispersion relation of the new equation obeys the exact dispersion relation for internal waves for both small and moderate wavenumbers ($k$). Thus this new RMKdV is able to model wea kly nonlinear internal waves with various wavenumbers ($k$), better than the Ostrovsky equation which fails at describing waves of small $k$.

This thesis investigates the effects of the earth's rotation on internal waves from two perspectives of nonlinear internal wave theory: near-resonant triads and weakly nonlinear models. We apply perturbation theory (multiple scale analysis) to the governing equations of internal waves and develop a near-resonant internal wave triad theory. This theory explains a resonant-like phenomenon in the numerical results obtained from simulating internal waves generated by tide topography interaction. Furthermore, we find that the inclusion of the earth's rotation (nonzero $f$) in the numerical runs leads to a very special type of resonance: parametric subharmonic instability. Through using perturbation expansion to solve separable solutions to the governing equations of internal waves, we derive a new rotation modified KdV equation (RMKdV). Of particular interest, the dispersion relation of the new equation obeys the exact dispersion relation for internal waves for both small and moderate wavenumbers ($k$). Thus this new RMKdV is able to model wea kly nonlinear internal waves with various wavenumbers ($k$), better than the Ostrovsky equation which fails at describing waves of small $k$.

The main topic of this research is the simulation of internal wave interaction by a two-dimensional numerical model developed by Lynett & Liu (2002) of Cornell University, then modified by Cheng et al. (2005). The governing equation includes two-dimensional momentum and continuity equation. The model uses constant upper and lower layer densities; hence, these factors as well as the upper layer thickness. Should be determined before the simulation. This study discusses the interface depth and the density according to the buoyancy frequency distribution, the EOF, and the eigen-value based on the measured density profile. Besides, a method based on the two-layer KdV equation and the KdV of continuously-stratified fluid. By minimize the difference of linear celeriy, nonlinear and dispersion terms, the upper layer thicknes can also be determined. However, the interface will be much deeper than the depth of max temperature drop in the KdV method if the total water depth is bigger than 500 meters. Thus, the idealization buoyancy frequency formula proposed by Vlasenko et al. (2005) or Xie et al. (2010) are used to modify the buoyancy frequency. The internal wave in the Luzon Strait and the South China Sea are famous and deserves detailed study. We use the KdV method to find the parameters in the two fluid model to speed up the simulation of internal wave phenomena found in the satellite image.

The wave–seabed interaction issue is of great importance for the design of foundation around marine infrastructures. Most previous investigations for such a problem have been limited to uncoupled or one-way coupled methods connecting two separated wave and seabed sub models with the continuity of pressures at the seabed surface. In this study, a strongly coupled model was proposed to realize both wave and seabed processes in a same program and to calculate the wave fields and seabed response simultaneously. The information between wave fields and seabed fields were strongly shared and thus results in a more profound investigation of the mechanism of the wave–seabed interaction. In this letter, the wave and seabed models were validated with previous experimental tests. Then, a set of application of present model were discussed in prediction of the wave-induced seabed response. Numerical results show the wave-induced liquefaction area of coupled model is smaller than that of uncoupled model. / Yes