Related papers: Numerical Solutions of the Isotropic 3-Wave Kineti…
Based on the Karman-Howarth equation in 3D incompressible fluid, a new isotropic turbulence scale evolution equation and its related theory progress. The present results indicate that the energy cascading process has remarkable similarities…
This technical note addresses the challenge of accurate turbulence characterization using robust, bandwidth-limited sensors which fail to resolve the high-wavenumber dissipation range. To correct the resulting underestimation of turbulent…
We study the stability of steady-state solutions of the Wave-Kinetic Equations for acoustic waves. Combining theoretical analysis and numerical simulations, we characterise the time evolution of small isotropic perturbations for both 2D and…
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…
A numerical method is proposed for computing time-periodic and relative time-periodic solutions in dissipative wave systems. In such solutions, the temporal period, and possibly other additional internal parameters such as the propagation…
Strong discontinuities in solutions of the gas dynamic equations under isentropic conditions, i.e., with continuity of entropy at the discontinuity, are examined. Solutions for a standard shock wave with continuity of energy at the…
We study a self-similar solution of the kinetic equation describing weak wave turbulence in Bose-Einstein condensates. This solution presumably corresponds to an asymptotic behavior of a spectrum evolving from a broad class of initial data,…
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…
This work presents Direct Numerical Simulations of capillary wave turbulence solving the full 3D Navier Stokes equations of a two-phase flow. When the interface is locally forced at large scales, a statistical stationary state appears after…
This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\mathbb{R}^3$ with fractional damping of the form $(-\Delta_x+1)^\frac{1}{2}\partial_t u$. The work extends previously known…
The theory of isotropic capillary turbulence was developed in the late 1960s by Zakharov and Filonenko. To date, the analytical solution of the kinetic equation describing the stationary transfer of energy to small scales due to three-wave…
We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the…
A novel model of wave turbulence is presented which allows to explain in the same frame various nonlinear wave phenomena: intermittency, form and direction of the energy cascades, formation of a zero-frequency band with non-zero energy,…
The wave-kinetic description of weak kinetic-Alfv\'{e}nic turbulence based on the gyrokinetic theoretical framework is proposed. The wave kinetic equation describing kinetic Alfv\'{e}n wave spectral cascading via resonant three-wave…
We present results of large-scale three-dimensional simulations of supersonic Euler turbulence with the piecewise parabolic method and multiple grid resolutions up to 2048^3 points. Our numerical experiments describe non-magnetized driven…
Wave Kinetic Equations (WKEs) are often used to describe the evolution of ensemble averaged wave amplitudes for nonlinear wave systems. In the present manuscript we describe a new approach to direct numerical simulation of solutions to…
The piece-wise parabolic method (PPM) is applied to simulations of forced isotropic turbulence with Mach numbers $\sim 0.1... 1$. The equation of state is dominated by the Fermi pressure of an electron-degenerate fluid. The dissipation in…
We study wave turbulence in systems with two special properties: a large number of fields (large $N$) and a nonlinear interaction that is strongly local in momentum space. The first property allows us to find the kinetic equation at all…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonmagnetic, linearly polarized, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the…
This paper aims to quantitatively relate the energy dissipated at a shock wave in a nonlinearly elastic bar to the energy in the oscillations in two related dissipationless, dispersive systems. In contrast to a phase boundary, there is no…