141 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
Double scaling in the relaxation time in the -FPUT model
We consider the original -Fermi-Pasta-Ulam-Tsingou (-FPUT)
system; numerical simulations and theoretical arguments suggest that, for a
finite number of masses, a statistical equilibrium state is reached
independently of the initial energy of the system. Using ensemble averages over
initial conditions characterized by different Fourier random phases, we
numerically estimate the time scale of equipartition and we find that for very
small nonlinearity it matches the prediction based on exact wave-wave resonant
interactions theory. We derive a simple formula for the nonlinear frequency
broadening and show that when the phenomenon of overlap of frequencies takes
place, a different scaling for the thermalization time scale is observed. Our
result supports the idea that Chirikov overlap criterium { identifies} a
transition region between two different relaxation time scaling.Comment: 5 page
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