Oscillatory spatially periodic weakly nonlinear gravity waves on deep water

Modulated periodic stokes waves in deep water

Modulated deep-water 1D Stokes waves are considered experimentally and theoretically. Wave trains are modulated in a controlled fashion and their evolution is recorded. Data from repeated laboratory experiments are reproducible near the wave maker, but diverge away from the wave maker. Numerical integration of a perturbed nonlinear Schrodinger equation and an associated linear spectral problem ...

Weakly nonlinear analysis of wind-driven gravity waves

We study the weakly nonlinear development of shear-driven gravity waves induced by the physical mechanism first proposed by Miles, and furthermore investigate the mixing properties of the finite-amplitude solutions. Linear theory predicts that gravity waves are amplified by an influx of energy through the critical layer, where the velocity of the wind equals the wave phase velocity. As the wave...

Long wavelength bifurcation of gravity waves on deep water

Conditions are found for the appearance of non-uniform progressive waves of permanent form from a long-wave modulation of a finite-amplitude Stokes wave on deep water. The waveheight at which the modulated waves can occur is a very slowly decreasing function of the modulation wavelength for values up to 150 times the original wavelength. Some qualitative remarks are made about the problem of de...

On Nonlinear Water Waves in a Channel

Quasi-periodic standing wave solutions of gravity-capillary water waves

We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension.