相关论文: Numerical Solutions of the Isotropic 3-Wave Kineti…

There is a formal correspondence between the isotropic 3-wave kinetic equation and the rate equations for a non-linear fragmentation--aggregation process. We exploit this correspondence to study analytically the time evolution of the wave…

We introduce a finite volume scheme to solve a special case of isotropic 3-wave kinetic equations. We test our numerical solution against theoretical results concerning the long time behavior of the energy and observe that our solutions…

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…

Wave turbulence is the study of the long-time statistical behaviour of equations describing a set of weakly non-linear interacting waves. Such a theory, which has a natural asymptotic closure, allows us to probe the nature of turbulence…

The isotropic 4-wave kinetic equation is considered in its weak formulation using model (simplified) homogeneous kernels. Existence and uniqueness of solutions is proven in a particular setting where the kernels have a rate of growth at…

This article introduces a novel numerical approach, based on Finite Volume Techniques, for studying fully nonlinear coagulation-fragmentation models, where both the coagulation and fragmentation components of the collision operator are…

Model of laminated wave turbulence allows to study statistical and discrete layers of turbulence in the frame of the same model. Statistical layer is described by Zakharov-Kolmogorov energy spectra in the case of irrational enough…

Starting from the stochastic Zakharov-Kuznetsov equation, a multidimensional KdV type equation on a hypercubic lattice, we provide a derivation of the 3-wave kinetic equation. We show that the two point correlation function can be…

In our previous work, numerical schemes for a simplified version of 3-wave kinetic equations, in which only the simple forward-cascade terms of the collision operators are kept, have been successfully designed, especially to capture the…

A phenomenological turbulence model in which the energy spectrum obeys a nonlinear diffusion equation is presented. This equation respects the scaling properties of the original Navier-Stokes equations and it has the Kolmogorov -5/3 cascade…

We consider an extension of the kinetic equation developed by Newell & Zakharov (A.C. Newell and V.E. Zakharov. The role of the generalized Phillips' spectrum in wave turbulence. Phys.Lett.A, 372:4230-4233, 2008). The new equation takes…

Several numerical schemes for 3-wave kinetic equations have been proposed in recent work and shown to be accurate and computationally efficient [8,33,34,35]. However, their rigorous numerical analysis remains open. This paper aims to close…

Wave turbulence is by nature a multiple time scale problem for which there is a natural asymptotic closure. The main result of this analytical theory is the kinetic equation that describes the long-time statistical behaviour of such…

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…

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…

This work presents a review of previous articles dealing with an original turbulence theory proposed by the author, and provides new theoretical insights into some related issues. The new theoretical procedures and methodological approaches…

We present a deep learning approximation, stochastic optimization based, method for wave kinetic equations. To build confidence in our approach, we apply the method to a Smoluchowski coagulation equation with multiplicative kernel for which…

A parallel pseudospectral code for the direct numerical simulation (DNS) of isotropic turbulence has been developed. The code has been extensively benchmarked using established results from literature. The code has been used to conduct a…

We consider turbulence of waves that interact weakly via four-wave scattering (sea waves, plasma waves, spin waves, and many others). In the first non-vanishing order in the interaction, the occupation number of waves satisfy a closed…

Starting from a stochastic Zakharov-Kuznetsov (ZK) equation on a lattice, the previous work [ST21] by the last two authors gave a derivation of the homogeneous 3-wave kinetic equation at the kinetic limit under very general assumptions: the…