2,076 research outputs found
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
Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation
By performing two parallel numerical experiments -- solving the dynamical
Hamiltonian equations and solving the Hasselmann kinetic equation -- we
examined the applicability of the theory of weak turbulence to the description
of the time evolution of an ensemble of free surface waves (a swell) on deep
water. We observed qualitative coincidence of the results.
To achieve quantitative coincidence, we augmented the kinetic equation by an
empirical dissipation term modelling the strongly nonlinear process of
white-capping. Fitting the two experiments, we determined the dissipation
function due to wave breaking and found that it depends very sharply on the
parameter of nonlinearity (the surface steepness). The onset of white-capping
can be compared to a second-order phase transition. This result corroborates
with experimental observations by Banner, Babanin, Young.Comment: 5 pages, 5 figures, Submitted in Phys. Rev. Letter
Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves
We study the long-time evolution of gravity waves on deep water exited by the
stochastic external force concentrated in moderately small wave numbers. We
numerically implement the primitive Euler equations for the potential flow of
an ideal fluid with free surface written in canonical variables, using
expansion of the Hamiltonian in powers of nonlinearity of up to fourth order
terms.
We show that due to nonlinear interaction processes a stationary energy
spectrum close to is formed. The observed spectrum can be
interpreted as a weak-turbulent Kolmogorov spectrum for a direct cascade of
energy.Comment: 4 pages, 5 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
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