5 This paper deals with the dead-water phenomenon, which occurs when a ship sails in a stratified fluid, and experiences an important drag due to waves below the surface. More generally, we study the generation of internal waves by a disturbance moving at constant speed on top of two layers of fluids of different densities. Starting from the full Euler equations, we present several nonlinear as...

[1] The nonlinearity of Tropical InstabilityWaves (TIWs) is studied using shallow-water equations with various mean states from the equatorial Pacific Ocean. In the early linear stage, unstable TIWs, centered near 5 N with a wavelength about 1000 km and a period about one month, dominate the whole domain. However neutral Yanai waves with periods about 15–22 days emerge near the equator when the...

A generalization of the Woodward's theorem is applied to the case of random signals jointly modulated in amplitude and frequency. This yields the signal spectrum and a rather robust estimate of the bispectrum. Furthermore, higher order statistics that quantify the amount of energy in the signal due to nonlinearities, e.g., wave–wave interaction in the case of water waves, can be inferred. Consi...

Consider a uniform train of surface waves with a two-dimensional, bi-periodic surface pattern, propagating on deep water. One approximate model of the evolution of these waves is a pair of coupled nonlinear Schrödinger equations, which neglects any dissipation of the waves. We show that in this model, such a wave train is linearly unstable to small perturbations in the initial data, because of ...

The propagation of wave disturbances in water of uniform depth is discussed, accounting for both gravity and compressibility effects. In the linear theory, free-surface (gravity) waves are virtually decoupled from acoustic (compression) waves, as the sound speed in water far exceeds the maximum gravity wave phase speed. However, these two types of wave motion could exchange energy via resonant ...

The influence of localized water currents on the nonlinear dynamics and stability of large amplitude, statistically distributed gravity waves is investigated theoretically and numerically by means of an evolution equation for a Wigner function governing the spectrum of waves. It is shown that water waves propagating in the opposite direction of a localized current channel can be trapped in the ...

In this contribution we discuss Higher Order Perturbation of Surfaces (HOPS) methods with particular application to traveling water waves. The Transformed Field Expansion method (TFE) is discussed as a method for handling the unknown fluid domain. The procedures for computing Stokes waves and Wilton Ripples are compared. The Lyapunov-Schmidt procedure for the Wilton Ripple is presented explicit...

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We study the generation of surface waves on water as a bifurcation phenomenon. For a critical wind-speed there appear traveling wave solutions. While linear waves do not transport mass (in the mean), nonlinear effects create a shear-flow and result in a net mass transport in the direction of the wind. We derive an asymptotic formula for the average tangential velocity along the free surface. Nu...

The influence of localized water currents on the nonlinear dynamics and stability of large amplitude, statistically distributed gravity waves is investigated theoretically and numerically by means of an evolution equation for a Wigner function governing the spectrum of waves. It is shown that water waves propagating in the opposite direction of a localized current channel can be trapped in the ...