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The evolution of the Kolmogorov-Zakharov (K-Z) spectrum of weak turbulence is studied in the limit of strongly local interactions where the usual kinetic equation, describing the time evolution of the spectral wave-action density, can be…
The kinetic wave equation arises in wave turbulence to describe the Fourier spectrum of solutions to the cubic Schroedinger equation. The equation has two Kolmogorov-Zakharov steady states corresponding to out-of-equilibrium cascades…
The way in which kinetic energy is distributed over the multiplicity of inertial (intermediate) scales is a fundamental feature of turbulence. According to Kolmogorov's 1941 theory, on the basis of a dimensional analysis, the form of the…
In weak turbulence theory, the Kolmogorov-Zakharov spectra is a class of time-independent solutions to the kinetic wave equations. In this paper, we construct a new class of time-dependent isotropic solutions to the decaying turbulence…
The Kolmogorov-Zakharov spectrum predicted by the Weak Turbulence Theory remains elusive for wave turbulence of flexural waves at the surface of an thin elastic plate. We report a direct measurement of the nonlinear timescale $T_{NL}$…
We investigate the self-similar evolution of the transient energy spectrum which precedes the establishment of the Kolmogorov spectrum in homogeneous isotropic turbulence in three dimensions using the EDQNM closure model. The transient…
Fast magnetosonic waves are among the fundamental oscillation modes of astrophysical plasmas. To study their dynamics, we carry out numerical simulations of the wave turbulence kinetic equation, which describes the evolution of the energy…
An analytical theory of wave turbulence is developed for pure compressible magnetohydrodynamics in the small $\beta$ limit. In contrast to previous works where the multiple scale method was not mentioned and slow magneto-acoustic waves were…
We introduce and study a random matrix model of Kolmogorov-Zakharov turbulence in a nonlinear purely dynamical finite size system with many degrees of freedom. For the case of a direct cascade the energy and norm pumping takes place at low…
Using the theory of wave turbulence for rapidly rotating incompressible fluids derived by Galtier (2003), we find the locality conditions that the solutions of the kinetic equation must satisfy. We show that the exact anisotropic…
Recent numerical work on the fate of plasma instabilities in weakly-coupled non-Abelian gauge theory has shown the development of a cascade of energy from long to short wavelengths. This cascade has a steady-state spectrum, analogous to the…
Rotating turbulence is commonly known for being dominated by geostrophic vortices that are invariant along the rotation axis and undergo inverse cascade. Yet, it has recently been shown to sustain fully three-dimensional states with a…
We develop a continuous Wilsonian renormalized-flow theory of weak wave turbulence directly in spectral frequency space, for finite cascades in experimentally driven Newtonian fluids. The central quantity is a scale-dependent effective…
We study the long-time evolution of waves of a thin elastic plate in the limit of small deformation so that modes of oscillations interact weakly. According to the theory of weak turbulence a nonlinear wave system evolves in long-time…
We numerically simulate, in both the forced and decay regimes, a fourth-order nonlinear diffusion equation derived from the kinetic equation of gravitational wave turbulence in the limit of strongly local quartic interactions. When a…
We simulate the Gross-Pitaevskii equation to model the development of turbulence in a quantum fluid confined by a cuboid box potential, and forced by shaking along one axis. We observe the development of isotropic turbulence from…
According to the celebrated Bolgiano--Obukhov \citep{Bolgiano_1959,Obukhov_1959} phenomenology for moderately stably stratified turbulence, the energy spectrum in the inertial range shows a dual scaling; the kinetic energy follows (i) $\sim…
A dynamical model is proposed for isotropic turbulence driven by steady forcing that yields a viscosity independent dynamics for the small-scale (inertial) regime. This reproduces the Kolmogorov spectrum for the two-point velocity…
In the study of weakly turbulent wave systems possessing incomplete self-similarity it is possible to use dimensional arguments to derive the scaling exponents of the Kolmogorov-Zakharov spectra, provided the order of the resonant wave…
We study the saturation of three-dimensional unstable perturbations on a fast rotating turbulent flow using direct numerical simulations (DNSs). Under the effect of Kolmogorov forcing, a transition between states dominated by coherent…