On the applicability of the Hasselmann kinetic equation to the Phillips spectrum

We investigate applicability of the Hasselmann kinetic equation to the spectrum of surface gravity waves at different levels of nonlinearity in the system, which is measured as average steepness. It is shown that even in the case of relatively high average steepness, when Phillips spectrum is present in the system, the spectral lines are still very narrow, at least in the region of direct cascade spectrum. It allows us to state that even in the case of Phillips spectrum the kinetic equation can be applied to the description of the ensembles of ocean waves.Comment: 9 pages, 24 figure

Numerical simulation of surface waves instability on a discrete grid

We perform full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid. We show that the instability development leads to chaotization and formation of wave turbulence. We study instability both of propagating and standing waves. We studied separately pure capillary wave unstable due to three-wave interactions and pure gravity waves unstable due to four-wave interactions. The theoretical description of instabilities in all cases is included into the article. The numerical algorithm used in these and many other previous simulations performed by authors is described in details.Comment: 47 pages, 40 figure

Branch cuts of Stokes wave on deep water. Part I: Numerical solution and Pad\'e approximation

Complex analytical structure of Stokes wave for two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth is analyzed. Stokes wave is the fully nonlinear periodic gravity wave propagating with the constant velocity. Simulations with the quadruple and variable precisions are performed to find Stokes wave with high accuracy and study the Stokes wave approaching its limiting form with $2\pi/3$ radians angle on the crest. A conformal map is used which maps a free fluid surface of Stokes wave into the real line with fluid domain mapped into the lower complex half-plane. The Stokes wave is fully characterized by the complex singularities in the upper complex half-plane. These singularities are addressed by rational (Pad\'e) interpolation of Stokes wave in the complex plane. Convergence of Pad\'e approximation to the density of complex poles with the increase of the numerical precision and subsequent increase of the number of approximating poles reveals that the only singularities of Stokes wave are branch points connected by branch cuts. The converging densities are the jumps across the branch cuts. There is one branch cut per horizontal spatial period $\lambda$ of Stokes wave. Each branch cut extends strictly vertically above the corresponding crest of Stokes wave up to complex infinity. The lower end of branch cut is the square-root branch point located at the distance $v_c$ from the real line corresponding to the fluid surface in conformal variables. The limiting Stokes wave emerges as the singularity reaches the fluid surface. Tables of Pad\'e approximation for Stokes waves of different heights are provided. These tables allow to recover the Stokes wave with the relative accuracy of at least $10^{-26}$. The tables use from several poles to about hundred poles for highly nonlinear Stokes wave with $v_c/\lambda\sim 10^{-6}.$Comment: 38 pages, 9 figures, 4 tables, supplementary material

Beyond the random phase approximation: Stimulated Brillouin backscatter for finite laser coherence times

We develop a statistical theory of stimulated Brillouin backscatter (BSBS) of a spatially and temporally partially incoherent laser beam for laser fusion relevant plasma. We find a new collective regime of BSBS (CBSBS) with intensity threshold controlled by diffraction, an insensitive function of the laser coherence time, $T_c$, once light travel time during $T_c$ exceeds a laser speckle length. The BSBS spatial gain rate is approximately the sum of that due to CBSBS, and a part which is independent of diffraction and varies linearly with $T_c$. We find that the bandwidth of KrF-laser-based fusion systems would be large enough to allow additional suppression of BSBS.Comment: 8 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1105.209