We apply the Hilbert transform to the physics of internal waves in two-dimensional fluids. Using this demodulation technique, we can discriminate internal waves propagating in different directions: This is very helpful in answering several fundamental questions in the context of internal waves. We focus more precisely in this paper on phenomena associated with dissipation, diffraction, and refl...

A vortex sheet formulation of irrotational, incompressible Euler flow is used to compute periodic traveling waves at the interface between two constant-density, two-dimensional fluids, including waves with overturned crests. Branches of traveling waves are computed via numerical continuation, which are jointly continuous in the physical parameters: Bond number, Atwood number and mean shear. Glo...

A series of experiments is presented that model the generation of internal gravity waves in the ocean by the forcing of turbulent eddies in the surface mixed layer.The experimental setup consists of a shallowmixed upper layer and a deep continuously stratified lower layer. A source of turbulence is dragged through the upper layer. Internal waves can freely propagate in the lower layer. The inte...

A variety of waves can be generated in the region between two fluids of different densities. These so called internal waves are dispersive and nonlinear even for modest amplitudes. This paper provides an review of various models (from weakly to fully nonlinear) of internal waves in the density-stratified flows. The properties of these waves as well as the processes of generation, interaction an...

Diapycnal mixing is an integral factor in the meridional overturning circulation of the ocean. The slow upwelling in the ocean interior across density surfaces requires counteracting diapycnal diffusion. Diapycnal diffusion in a stably stratified fluid requires mechanical energy and the availability of this energy might well be the controlling factor in setting the strength of the overturning c...

Recent laboratory methods developed to generate and to analyze internal waves have revealed important insights that sometimes guide and sometimes challenge theoretical predictions and the results of numerical simulations. Here we focus upon observations of internal waves generated by oscillatory or uniform flow over a solid boundary in a continuously stratified fluid. In the laboratory such flo...

Yuri S. Kivshar,1 Dmitry E. Pelinovsky,1,2 Thierry Cretegny,3 and Michel Peyrard3 1Optical Sciences Center, Australian National University, Canberra ACT 0200, Australia 2Department of Applied Mathematics, University of Cape Town, Rondeboch 7701, Western Cape, South Africa 3Laboratoire de Physique de l’Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69364 Lyon Cedex 07, France (Received 26 ...

The objectives are to use a combination of theoretical and numerical models to study the evolution of the internal tide and its possible disintegration into internal solitary waves. A central aspect of this work is to explore the role of rotation in the process. Rotation permits the presence of periodic, nonlinear inertia-gravity waves (i.e., the tide) that can act as attractors and arrest the ...