arXiv subjects

Yuri V Lvov

Publications and source records attributed to Yuri V Lvov.

5 recordsLinked to original sources

arXiv2023

A One-Dimensional Model for Investigating Scale-separated Approaches to the Interaction of Oceanic Internal Waves

High-frequency wave propagation in near-inertial wave shear has been considered fundamental in setting the spectral character of the oceanic internal wave continuum and for transporting energy to wave-breaking. We compare idealized ray tracing numerical results with metrics derived using a wave turbulence derivation for the kinetic equation and a path integral to study such scale-separated interactions. At small inertial wave amplitudes, all three provide consistent descriptions for the mean drift of wavepackets in the spectral domain and dispersion about that mean drift. Extrapolating our results to the background internal wavefield over-predicts downscale energy transports by an order of magnitude. At oceanic amplitudes, however, the numerics support diminished transport and dispersion that coincide with the mean drift time scale becoming similar to the lagged correlation time scale. Despite this decrease, numerical estimates of downscale energy transfer are still significantly larger than oceanic derived metrics. Our results support replacing the long standing interpretive paradigm of extreme scale-separated interactions with a more nuanced slate of 'local' interactions in the kinetic equation.

physics.ao-ph↗

arXiv2023

Generalized Transport Characterizations for Short Oceanic Internal Waves in a Sea of Long Waves

Internal waves in the ocean interact in triads. Early work emphasized the importance of extreme-scale separated interactions in which two large wavenumber waves interact with one small wavenumber wave. More recent efforts have called this early paradigm into question. We use wave turbulence kinetic equation and the ray-tracing WKB technique to derive two versions of the corresponding Fokker-Planck (generalized diffusion) equation. We then use these Fokker-Planck equations to estimate the spectral energy flux towards dissipation (high wave numbers) we obtain different results: spectral transport of the kinetic equation Fokker-Planck equation is an order of magnitude larger than either observations or reported ray tracing estimates. This apparent contradiction stems from the difference between Eulerian and ray-path descriptions of these scale-separated interactions.

physics.flu-dyn↗

arXiv2020

Anomalous correlators, "ghost" waves and nonlinear standing waves in the $β$-FPUT system

We show that Hamiltonian nonlinear dispersive wave systems with cubic nonlinearity and random initial data develop, during their evolution, anomalous correlators. These are responsible for the appearance of "ghost" excitations, i.e. those characterized by negative frequencies, in addition to the positive ones predicted by the linear dispersion relation. We use generalization of the Wick's decomposition and the wave turbulence theory to explain theoretically the existence of anomalous correlators. We test our theory on the celebrated $β$-Fermi-Pasta-Ulam-Tsingou chain and show that numerically measured values of the anomalous correlators agree, in the weakly nonlinear regime, with our analytical predictions. We also predict that similar phenomena will occur in other nonlinear systems dominated by nonlinear interactions, including surface gravity waves. Our results pave the road to study phase correlations in the Fourier space for weakly nonlinear dispersive wave systems.

nlin.CD↗

arXiv2019

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.

physics.flu-dyn↗

arXiv2018

Double scaling in the relaxation time in the $β$-FPUT model

We consider the original $β$-Fermi-Pasta-Ulam-Tsingou ($β$-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.

nlin.CD↗