382 research outputs found
Direct numerical experiment on measuring of dispersion relation for gravity waves in the presence of condensate
During previous numerical experiments on isotropic turbulence of surface
gravity waves we observed formation of the long wave background (condensate).
It was shown (Korotkevich, Phys. Rev. Lett. vol. 101 (7), 074504 (2008)), that
presence of the condensate changes a spectrum of direct cascade, corresponding
to the flux of energy to the small scales from pumping region (large scales).
Recent experiments show that the inverse cascade spectrum is also affected by
the condensate. In this case mechanism proposed as a cause for the change of
direct cascade spectrum cannot work. But inverse cascade is directly influenced
by the linear dispersion relation for waves, as a result direct measurement of
the dispersion relation in the presence of condensate is necessary. We
performed the measurement of this dispersion relation from the direct numerical
experiment. The results demonstrate that in the region of inverse cascade
influence of the condensate cannot be neglected.Comment: 5 pages, 3 figure
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
Tracking water molecules and carboxylate ions in confinement using advanced vibrational spectroscopy
Tracking water molecules and carboxylate ions in confinement using advanced vibrational spectroscopy
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 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 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 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 . The tables use from several poles to about
hundred poles for highly nonlinear Stokes wave with Comment: 38 pages, 9 figures, 4 tables, supplementary material
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