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 β\beta-FPUT model

We consider the original $\beta$-Fermi-Pasta-Ulam-Tsingou ($\beta$-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