Hyperviscosity, Galerkin truncation and bottlenecks in turbulence

Abstract

It is shown that the use of a high power $α$ of the Laplacian in the dissipative term of hydrodynamical equations leads asymptotically to truncated inviscid \textit{conservative} dynamics with a finite range of spatial Fourier modes. Those at large wavenumbers thermalize, whereas modes at small wavenumbers obey ordinary viscous dynamics [C. Cichowlas et al. Phys. Rev. Lett. 95, 264502 (2005)]. The energy bottleneck observed for finite $α$ may be interpreted as incomplete thermalization. Artifacts arising from models with $α> 1$ are discussed.

4 pages, 2 figures, Phys. Rev. Lett. in press