We study the original $\alpha$-Fermi-Pasta-Ulam (FPU) system with $N=16,32$ and $64$ masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave-wave interaction theory, i.e. we assume that, in weakly regime (the one which Fermi was originally interested), large time dynamics ruled exact resonances. After detailed analysis of $\alpha$-FPU equation motion, find that first non trivial resonances correspond to six-wave interactions. Those are precisely interactions...

Many major oceanographic internal wave observational programs of the last 4 decades are reanalyzed in order to characterize variability deep ocean wavefield. The observations discussed context universal spectral model proposed by Garrett and Munk. Munk is a good description wintertime conditions at Site-D on continental rise north Gulf Stream. Elsewhere other times, significant deviations terms amplitude, separability 2-D vertical wavenumber - frequency spectrum, departure from model's...

We consider the original β-Fermi-Pasta-Ulam-Tsingou system; numerical simulations and theoretical arguments suggest that, for a finite number of masses, statistical equilibrium state is reached independently initial energy system. Using ensemble averages over conditions characterized by different Fourier random phases, we numerically estimate time scale equipartition find that very small nonlinearity it matches prediction based on exact wave-wave resonant interaction theory. derive simple...

Wave turbulence formalism for long internal waves in a stratified fluid is developed, based on natural Hamiltonian description. A kinetic equation appropriate the description of spectral energy transfer derived, and its self-similar stationary solution corresponding to direct cascade toward short scales found. This very close high wavenumber limit Garrett-Munk spectrum ocean. In fact, small modification includes consistent with one predicted by wave turbulence.

Abstract The spectral energy density of the internal waves in open ocean is considered. Garrett and Munk spectrum resonant kinetic equation are used as main tools study. Evaluations a that suggest slow time evolution not fact reported. Instead, nonlinear transfers lead to scales smaller than one wave period at high vertical wavenumber. Such values transfer rates inconsistent with viewpoint expressed papers by C. H. McComas P. Müller, Müller et al., which regards an approximate stationary...

The high-frequency limit of the Garrett and Munk spectrum internal waves in ocean observed deviations from it are shown to form a pattern consistent with predictions wave turbulence theory. In particular, constitutes an exact steady-state solution corresponding kinetic equation.

Abstract Steady scale-invariant solutions of a kinetic equation describing the statistics oceanic internal gravity waves based on wave turbulence theory are investigated. It is shown in nonrotating limit that collision integral diverges for almost all spectral power-law exponents. These divergences come from resonant interactions with smallest horizontal wavenumbers and/or largest extreme scale separations. A small domain identified which converges and numerically find convergent solution....

Assuming that resonances play a major role in the transfer of energy among Fourier modes, we apply Wave Turbulence theory to describe dynamics on nonlinear one-dimensional chains. We consider <i>α</i> and <i>β</i> Fermi-Pasta-Ulam-Tsingou (FPUT) systems, discrete Klein-Gordon chain. both thermodynamic limit regime conjecture all systems thermalize for large times, equipartition time scales as power-law strength nonlinearity, at least range values parameter. perform state art numerical...

Across the stable density stratification of abyssal ocean, deep dense water is slowly propelled upward by sustained, though irregular, turbulent mixing. The resulting mean upwelling determines large-scale oceanic circulation properties like heat and carbon transport. In ocean interior, this mixing caused mainly breaking internal waves: generated predominantly winds tides, these waves interact nonlinearly, transferring energy downscale, finally become unstable, break mix column. This...

We demonstrate via numerical simulation that in the strongly nonlinear limit Beta-Fermi-Pasta-Ulam (Beta-FPU) system thermal equilibrium behaves surprisingly like weakly waves properly renormalized normal variables. This arises because collective effect of interactions effectively renormalizes linear dispersion frequency and leads to weak interaction among these waves. Furthermore, we show dynamical scenario for thermalized Beta-FPU chains is spatially highly localized discrete breathers...

We study the $k$-space fluctuations of wave action about its mean spectrum in turbulence dispersive waves. use a minimal model based on random phase approximation (RPA) and derive evolution equations for arbitrary-order one-point moments intensity wave-number space. The first equation this series is familiar kinetic wave-action spectrum, whereas second higher describe spectrum. exhibit nontrivial dynamics if some long coordinate-space correlations are present system, as it case typical...

A theory of nonlinear response the channel a field effect transistor subjected to two terahertz beams (measured signal and local oscillator) with close frequencies has been developed. It is shown that electric current flowing in drastically increases heterodyne efficiency. Also, it demonstrated such detector capable operating effectively very high intermediate up 10÷100 GHz.

The dispersive interacting waves in Fermi-Pasta-Ulam (FPU) chains of particles thermal equilibrium are studied from both statistical and wave resonance perspectives. It is shown that, even a strongly nonlinear regime, the chain can be effectively described by system weakly renormalized that possess (i) Rayleigh-Jeans distribution (ii) zero correlations between waves, just as noninteracting free would. This renormalization achieved through set canonical transformations. linear dispersion...

Abstract

Abstract We provide a first-principles analysis of the energy fluxes in oceanic internal wave field. The resulting formula is remarkably similar to renowned phenomenological for turbulent dissipation rate ocean, which known as finescale parameterization. prediction based on turbulence theory gravity waves and new methodology devised computation associated fluxes. In standard spectral representation density, two-dimensional vertical wavenumber–frequency ( m – ω ) domain, with steady state are...