Intermittency and Thermalization in Turbulence

TL;DR

This paper investigates how different dissipation rates influence the convergence and thermalization in turbulence, highlighting the role of intermittency and the competition between cascade, thermalization, and dissipation through numerical Navier-Stokes simulations.

Contribution

It introduces a dissipation rate model that can lead to both actual and potential convergence in turbulence, and analyzes the interplay of cascade, thermalization, and intermittency.

Findings

Dissipation rate models can induce convergence in turbulence simulations.

Thermalization and intermittency growth are influenced by dissipation physics.

Numerical results demonstrate the competition between cascade, thermalization, and dissipation.

Abstract

A dissipation rate, which grows faster than any power of the wave number in Fourier space, may be scaled to lead a hydrodynamic system {\it actually} or {\it potentially} converge to its Galerkin truncation. Actual convergence we name for the asymptotic truncation at a finite wavenumber $k_G$ above which modes have no dynamics; and, we define potential convergence for the truncation at $k_G$ which, however, grows without bound. Both types of convergence can be obtained with the dissipation rate $\mu[cosh(k/k_c)-1]$ who behaves as $k^2$ (newtonian) and $\exp\{k/k_c\}$ for small and large $k/k_c$ respectively. Competition physics of cascade, thermalization and dissipation are discussed with numerical Navier-Stokes turbulence, emphasizing on the intermittency growth.