Abstract In coastal seas and straits, the interaction of barotropic tidal currents with the continental shelf, seamounts or sills is often observed to generate large-amplitude, horizontally propagating internal solitary waves. Typically these waves occur in regions of variable bottom topography, with the consequence that they are often modeled by nonlinear evolution equations of the Korteweg-de...

The influence of gas bubbles on the properties of internal waves in a continuously stratified fluid is studied in the framework of a two-dimensional model of a diluted monodisperse mixture of an incompressible fluid with gas bubbles. The model takes into account surface tension on the walls of the bubbles and an effective viscosity. The dispersion relation is obtained for linear waves in the Bo...

Laboratory experiments were conducted to determine the steady state internal wave response of a periodically forced long and narrow lake. The system is two-layer stratified and is subjected to periodic forcing over a wide frequency range. The ratio of the forcing frequency (f) to horizontal mode-one (H1) internal seiche frequency (fH1) governs the system response. For f ≥ 2fH1, highermode inter...

In both the ocean and the atmosphere, the interaction of a density stratified flow with topography can generate large-amplitude, horizontally propagating internal solitary waves. Often these waves are observed in regions where the waveguide properties vary in the direction of propagation. In this article we consider nonlinear evolution equations of the Kortewegde Vries type, with variable coeff...

Submitted for the DFD05 Meeting of The American Physical Society Progressive internal waves of permanent form JOHN MCHUGH, University of New Hampshire — Progressive internal waves of permanent form in a semi-infinite layer of stratified fluid are considered. Such waves were previously considered in a layer of finite depth by Thorpe (1968) and Yih (1974). Both of these previous studies have diff...

Observations of internal solitary waves over an antarctic ice shelf (Rees and Rottman, 1994) demonstrate that even large amplitude disturbances have wavelengths that are bounded by simple heuristic arguments following from the Scorer parameter based on linear theory for wave trapping. Classical weak nonlinear theories that have been applied to stable stratifications all begin with perturbations...

The generation and evolution of solitary waves by intrusive gravity currents in an approximate two-layer fluid with equal upperand lower-layer depths is examined in a cylindrical geometry by way of theory and numerical simulations. The study is limited to vertically symmetric cases in which the density of the intruding fluid is equal to the average density of the ambient. We show that even thou...

The extended KdV equation ut + uux + αuux + uxxx = 0 is widely used as a model describing internal waves in ideal fluids. The equation admits a family of negative and positive solitary waves c. These solitary waves exhibit the typical broadening effect seen in internal waves. It is shown here that all solitary-wave solutions of the extended KdV equation are orbitally stable. The proof of stabil...

In a fluid system in which two immiscible layers are separated by a sharp free interface, there can be strong coupling between large amplitude nonlinear waves on the interface and waves in the overlying free surface. We study the regime where long waves propagate in the interfacial mode, which are coupled to a modulational regime for the freesurface mode. This is a system of Boussinesq equation...

Internal gravity waves are a key process linking the large-scale mechanical forcing of the oceans to small-scale turbulence and mixing. In this review, we focus on internal waves generated by barotropic tidal flow over topography. We review progress made in the past decade toward understanding the different processes that can lead to turbulence during the generation, propagation, and reflection...