scholarly journals Instability of the Rayleigh-Jeans spectrum in weak wave turbulence theory

2009 ◽  
Vol 79 (6) ◽  
Author(s):  
Miguel Escobedo ◽  
Manuel A. Valle
Keyword(s):  
Turbulence Theory ◽  
Wave Turbulence ◽  
Weak Wave

scholarly journals Numerical Simulation of Feller’s Diffusion Equation

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1067
Author(s):  
Denys Dutykh
Keyword(s):  
Numerical Simulation ◽  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Fluid Mechanics ◽  
Open Source ◽  
Stability Condition ◽  
Numerical Scheme ◽  
Turbulence Theory ◽  
Wave Turbulence ◽  
Matlab Code

This article is devoted to Feller’s diffusion equation, which arises naturally in probability and physics (e.g., wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties, we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation, and the corresponding Matlab code is provided with this article under an open source license.

scholarly journals Rogue waves, rational solitons and wave turbulence theory

2011 ◽  
Vol 375 (35) ◽  
pp. 3149-3155 ◽  
Author(s):  
Bertrand Kibler ◽  
Kamal Hammani ◽  
Claire Michel ◽  
Christophe Finot ◽  
Antonio Picozzi
Keyword(s):  
Rogue Waves ◽  
Turbulence Theory ◽  
Wave Turbulence

scholarly journals Energy partition, scale by scale, in magnetic Archimedes Coriolis weak wave turbulence

2017 ◽  
Vol 95 (2) ◽  
Author(s):  
A. Salhi ◽  
F. S. Baklouti ◽  
F. Godeferd ◽  
T. Lehner ◽  
C. Cambon
Keyword(s):  
Wave Turbulence ◽  
Energy Partition ◽  
Weak Wave

scholarly journals On the Wave Turbulence Theory for the Nonlinear Schrödinger Equation with Random Potentials

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 823
Author(s):  
Sergey Nazarenko ◽  
Avy Soffer ◽  
Minh-Binh Tran
Keyword(s):  
Porous Medium ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Porous Medium Equation ◽  
Nonlinear Schrodinger Equation ◽  
Turbulence Theory ◽  
Wave Turbulence ◽  
Random Potentials ◽  
Nonlinear Schrödinger

We derive new kinetic and a porous medium equations from the nonlinear Schrödinger equation with random potentials. The kinetic equation has a very similar form compared to the four-wave turbulence kinetic equation in the wave turbulence theory. Moreover, we construct a class of self-similar solutions for the porous medium equation. These solutions spread with time, and this fact answers the “weak turbulence” question for the nonlinear Schrödinger equation with random potentials. We also derive Ohm’s law for the porous medium equation.

On waves in incompressible Hall magnetohydrodynamics

2007 ◽  
Vol 73 (5) ◽  
pp. 723-730 ◽  
Author(s):  
FOUAD SAHRAOUI ◽  
SÉBASTIEN GALTIER ◽  
GÉRARD BELMONT
Keyword(s):  
Plasma Physics ◽  
Spatial Scales ◽  
Skin Depth ◽  
Turbulence Theory ◽  
Wave Turbulence ◽  
Incompressible Limit ◽  
Fluid Approximation ◽  
Closure Equation ◽  
Validity Range ◽  
Mhd System

AbstractHall magnetohydrodynamics (HMHD) is a mono-fluid approximation extending the validity domain of the ordinary MHD system to spatial scales down to a fraction of the ion skin depth or frequencies comparable to the ion gyrofrequency. In the paper by Galtier (2006 J. Plasma Physics), an incompressible limit of the HMHD system is used for developing a wave turbulence theory. Nevertheless, the possibility and the consequences of such an approximation are different in HMHD and in MHD. Here, we analyse these differences by investigating the properties of the HMHD equations in the incompressible limit: the existence of linear modes, their dispersion relations and polarizations. We discuss the possibility of replacing the fluid closure equation of a complete HMHD system by an incompressibility hypothesis and determine the validity range.

scholarly journals HIGH RESOLUTION WAVE FORECASTING MODELS AND WAVE TURBULENCE THEORY

2019 ◽  
Vol 47 (1) ◽  
pp. 15-17
Author(s):  
S. I. Badulin ◽  
V. G. Grigorieva ◽  
L. Aouf ◽  
A. Dalphinet
Keyword(s):  
High Resolution ◽  
Spatial Resolution ◽  
Turbulence Theory ◽  
Wave Turbulence ◽  
Weak Turbulence ◽  
Wave Modeling ◽  
State Assignment ◽  
Forecasting Models ◽  
Wave Forecasting ◽  
Sea Wave

Results of high resolution sea wave modeling are treated within the theory of wave (weak) turbulence. Spatial resolution 1 km is shown likely to be excessive and lead to appearance of artificial structures in fields of wave periods and steepness. The research was supported by the state assignment of IO RAS, theme 0149-2019-0002.

scholarly journals Statistics of surface gravity wave turbulence in the space and time domains

2009 ◽  
Vol 642 ◽  
pp. 395-420 ◽  
Author(s):  
SERGEY NAZARENKO ◽  
SERGEI LUKASCHUK ◽  
STUART McLELLAND ◽  
PETR DENISSENKO
Keyword(s):  
Gravity Wave ◽  
Coherent Structures ◽  
Turbulence Theory ◽  
Wave Turbulence ◽  
Random Waves ◽  
Surface Gravity Wave ◽  
Frequency Spectra ◽  
Time Domains ◽  
Weak Turbulence Theory ◽  
Singular Wave

We present experimental results on simultaneous space–time measurements for the gravity wave turbulence in a large laboratory flume. We compare these results with predictions of the weak turbulence theory (WTT) based on random waves, as well as with predictions based on the coherent singular wave crests. We see that the both wavenumber and frequency spectra are not universal and dependent on the wave strength, with some evidence in favour of the WTT at larger wave intensities when the finite-flume effects are minimal. We present further theoretical analysis of the role of the random and coherent waves in the wave probability density function (p.d.f.) and the structure functions (SFs). Analysing our experimental data we found that the random waves and the coherent structures/breaks coexist: the former show themselves in a quasi-Gaussian p.d.f. core and the low-order SFs and the latter in the p.d.f. tails and the high-order SFs. It appears that the x-space signal is more intermittent than the t-space signal, and the x-space SFs capture more singular coherent structures than the t-space SFs do. We outline an approach treating the interactions of these random and coherent components as a turbulence cycle characterized by the turbulence fluxes in both the wavenumber and the amplitude spaces.

Stationary Spectra of Weak Wave Turbulence

1992 ◽  
pp. 83-143 ◽  
Author(s):  
Vladimir E. Zakharov ◽  
Victor S. L’vov ◽  
Gregory Falkovich
Keyword(s):  
Wave Turbulence ◽  
Weak Wave
Sign in / Sign up

Export Citation Format

Share Document