Hyperviscosity, Galerkin truncation and bottlenecks in turbulence

Details Hyperviscosity, Galerkin truncation and bottlenecks in turbulence Hyperviscosity, Galerkin truncation and bottlenecks in turbulence

2008-03-29

arxiv.org/abs/0803.4269v3

Nonlinear Sciences

Chaotic Dynamics

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

Scientific paper

10.1103/PhysRevLett.101.144501

It is shown that the use of a high power $\alpha$ 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 $\alpha$ may be interpreted as incomplete thermalization. Artifacts arising from models with $\alpha > 1$ are discussed.

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