684 research outputs found
Excitation of interfacial waves via near---resonant surface---interfacial wave interactions
We consider interactions between surface and interfacial waves in the two
layer system. Our approach is based on the Hamiltonian structure of the
equations of motion, and includes the general procedure for diagonalization of
the quadratic part of the Hamiltonian. Such diagonalization allows us to derive
the interaction crossection between surface and interfacial waves and to derive
the coupled kinetic equations describing spectral energy transfers in this
system. Our kinetic equation allows resonant and near resonant interactions. We
find that the energy transfers are dominated by the class III resonances of
\cite{Alam}. We apply our formalism to calculate the rate of growth for
interfacial waves for different values of the wind velocity. Using our kinetic
equation, we also consider the energy transfer from the wind generated surface
waves to interfacial waves for the case when the spectrum of the surface waves
is given by the JONSWAP spectrum and interfacial waves are initially absent. We
find that such energy transfer can occur along a timescale of hours; there is a
range of wind speeds for the most effective energy transfer at approximately
the wind speed corresponding to white capping of the sea. Furthermore,
interfacial waves oblique to the direction of the wind are also generated
Anomalous probability of large amplitudes in wave turbulence
Time evolution equation for the Probability Distribution Function (PDF) is
derived for system of weakly interacting waves. It is shown that a steady state
for such system may correspond to strong intermittency
Joint statistics of amplitudes and phases in Wave Turbulence
Random Phase Approximation (RPA) provides a very convenient tool to study the
ensembles of weakly interacting waves, commonly called Wave Turbulence. In its
traditional formulation, RPA assumes that phases of interacting waves are
random quantities but it usually ignores randomness of their amplitudes.
Recently, RPA was generalised in a way that takes into account the amplitude
randomness and it was applied to study of the higher momenta and probability
densities of wave amplitudes. However, to have a meaningful description of wave
turbulence the RPA properties assumed for the initial fields must be proven to
survive over the nonlinear evolution time, and such a proof is the main goal of
the present paper. We derive an evolution equation for the full probability
density function which contains the complete information about the joint
statistics of all wave amplitudes and phases. We show that, for any initial
statistics of the amplitudes, the phase factors remain statistically
independent uniformly distributed variables. If in addition the initial
amplitudes are also independent variables (but with arbitrary distributions)
they will remain independent when considered in small sets which are much less
than the total number of modes. However, if the size of a set is of order of
the total number of modes then the joint probability density for this set is
not factorisable into the product of one-mode probabilities. In the other
words, the modes in such a set are involved in a ``collective'' (correlated)
motion. We also study new type of correlators describing the phase statistics.Comment: 27 pages, uses feynmf packag
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