A theoretical study of the transformation of large amplitude internal solitary waves (ISW) of permanent form over a slope-shelf topography is considered using as basis the Reynolds equations. The vertical fluid stratification, amplitudes of the propagating ISWs, and the bottom parameters were taken close to those observed in the Andaman and Sulu Seas. The problem was solved numerically. It was found that, when an intense ISW of depression propagates from a deep part of a basin onto the shelf with water depth H s , a breaking event will arise whenever the wave amplitude a m is larger than 0.4(H s Ϫ H m), where H m is the undisturbed depth of the isopycnal of maximum depression. The cumulative effect of nonlinearity in a propagating ISW leads to a steepening and overturning of a rear wave face over the inclined bottom. Immediately before breaking the horizontal orbital velocity at the site of instability exceeds the phase speed of the ISW. So, the strong breaking is caused by a kinematic instability of the propagating wave. At the latest stages of the evolution the overturned hydraulic jump transforms into a horizontal density intrusion (turbulent pulsating wall jet) propagating onto the shelf. The breaking criterion of the ISW over the slope was found. Over the range of examined parameters (0.52Њ Ͻ ␥ Ͻ 21.8Њ, where ␥ is the slope angle) the breaking event arises at the position with depth H b , when the nondimensional wave amplitude ϭ a m /(H b Ϫ H m) satisfies the condition ഡ 0.8Њ/␥ ϩ 0.4. If the water depth a a H s on a shelf is less than H b , a solitary wave breaks down before it penetrates into a shallow water zone; otherwise (at H s Ͼ H b) it passes as a dispersive wave tail onto the shelf without breaking.

Internal solitary waves commonly observed in the coastal ocean are often modeled by a nonlinear evolution equation of the Korteweg-de Vries type. Because these waves often propagate for long distances over several inertial periods, the effect of Earth's background rotation is potentially significant. The relevant extension of the Kortweg-de Vries is then the Ostrovsky equation, which for internal waves does not support a steady solitary wave solution. Recent studies using a combination of asymptotic theory, numerical simulations, and laboratory experiments have shown that the long time effect of rotation is the destruction of the initial internal solitary wave by the radiation of small-amplitude inertia-gravity waves, and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. However, in the ocean, internal solitary waves are often propagating over variable topography, and this alone can cause quite dramatic deformation and transformation of an internal solitary wave. Hence, the combined effects of background rotation and variable topography are examined. Then the Ostrovsky equation is replaced by a variable coefficient Ostrovsky equation whose coefficients depend explicitly on the spatial coordinate. Some numerical simulations of this equation, together with analogous simulations using the Massachusetts Institute of Technology General Circulation Model (MITgcm), for a certain cross section of the South China Sea are presented. These demonstrate that the combined effect of shoaling and rotation is to induce a secondary trailing wave packet, induced by enhanced radiation from the leading wave.

Abstract. The modelling of baroclinic tides generated in the northern South China Sea is studied using a fully-nonlinear non-hydrostatic numerical model. The focus of the modelling efforts was on the vertical structure of internal waves in the vicinity of the Luzon Strait.The barotropic tidal flow interacting with a two-ridge bottom topography in the area of the Luzon Strait produces a complex baroclinic tidal signal. A multimodal baroclinic bore with counter-phase displacement of isopycnals generated over the ridges and propagating westward disintegrates into a series of large-amplitude solitary internal waves. The leading first-mode solitary wave of depression is followed by a second mode solitary wave coupled with a packet of shortscale internal waves riding it. Scrutiny of the characteristics of the both wave forms, i.e. the carrier second-mode solitary wave and the packet of short waves, revealed that the shortscale waves are basically concentrated in the upper 500 m layer and attenuate exponentially below it. The short waves exist only thanks to a specific structure of horizontal velocity produced by the second-mode solitary wave. Having equal phase speeds and propagating together for a long distance, this coupled system produces quite a remarkable signal at the free surface, which can be detected by means of remote sensing technique.It was found in a series of sensitivity experiments that the eastern ridge is responsible for the generation of progressive first-mode tidal waves disintegrated into packets of first-mode ISWs. The western ridge produces quite a strong higher-mode signal. The waves generated over the eastern and western ridges interfere in the near-field, and their nonlinear superposition enhances the multimodal signal in the whole domain.

This book was first published in 2005. When an oceanic tidal wave that is primarily active on the water surface passes an ocean shelf or a region with a seamount, it is split into a less energetic surface wave and other internal modes with different wavelengths and propagation speeds. This cascading process, from the barotropic tides to the baroclinic components, leads to the transformation of tidal energy into turbulence and heat, an important process for the dynamics of the lower ocean. Baroclinic Tides demonstrates the analytical and numerical methods used to study the generation and evolution of baroclinic tides and, by comparison with experiments and observational data, shows how to distinguish and interpret internal waves. Strongly non-linear solitary internal waves, which are generated by internal tidal waves at the final stage of their evolution, are investigated in detail. This book is intended for researchers and graduate students of physical oceanography, geophysical fluid dynamics and hydroacoustics.

Globally, the Celtic Sea shelf break is ranked highest as an energetic ''hot spot'' of tidal energy conversion, therefore making it the most significant contributor to global internal tidal energy flux. In this paper, the three-dimensional dynamics of baroclinic tides in the shelf-slope area of the Celtic Sea was investigated numerically and using observational data collected on the 376th cruise of the RV ''RRS Discovery'' in June 2012. The time series recorded at a shelf break mooring showed that semidiurnal internal waves were accompanied by packets of internal solitary waves with maximum amplitudes up to 105 m, the largest internal waves ever recorded in the Celtic Sea, and ranking among the largest observed in the global ocean. The observed baroclinic wavefields were replicated numerically using the Massachusetts Institute of Technology general circulation model. A fine-resolution grid with 115 m horizontal and 10 m vertical steps allowed the identification of two classes of short-scale internal waves. The first classification was generated over headlands and resembles spiral-type internal waves that are typical for isolated underwater banks. The second classification, generated within an area of several canyons, revealed properties of quasi-planar internal wave packets. The observed in situ intensification of tidal bottom currents at the shelf break mooring is explained in terms of a tidal beam that was formed over supercritical bottom topography at the mooring location.