XLI. On deep water waves

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 ...

low-vorticity waves in deep water

Stability of plane waves on deep water with dissipation

The Benjamin-Feir modulational instability effects the evolution of perturbed planewave solutions of the cubic nonlinear Schrödinger equation (NLS), the modified NLS, and the band-modified NLS. Recent work demonstrates that the BenjaminFeir instability in NLS is “stabilized” when a linear term representing dissipation is added. In this paper, we add a linear term representing dissipation to the...

On a fourth-order envelope equation for deep-water waves

The ordinary nonlinear Schrodinger equation for deep-water waves (found by a perturbation analysis to 0(€3 ) in the wave steepness €) compares unfavourably with the exact calculations of Longuet-Higgins (1978) for € > 0·10. Dysthe (1979) showed that a significant improvement is found by taking the perturbation analysis one step further to 0(€ ). One of the dominant new effects is the wave-induc...

Transverse instabilities of deep-water solitary waves

The dynamics of a one-dimensional slowly modulated, nearly monochromatic localized wave train in deep water is described by a one-dimensional soliton solution of a twodimensional nonlinear Schrödinger (NLS) equation. In this paper, the instability of such a wave train with respect to transverse perturbations is examined numerically in the context of the NLS equation, using Hill’s method. A vari...