Intermittency and Thermalization in Turbulence

A dissipation rate, which grows faster than any power of the wave number in Fourier space, may be scaled to lead a hydrodynamic system to actually or potentially converge to its Galerkin truncation. Actual convergence here means 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 μcosh (κ/κ_c)-1that behaves as k² (newtonian) and expκ/κ_cfor small and large κ/κ_c respectively. Competing physics of cascade, thermalization and dissipation are discussed for numerical Navier-Stokes turbulence, emphasizing the intermittency growth issue.