Hyperviscosity, Galerkin truncation, and bottlenecks in turbulence.
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 conservative dynamics with a finite range of spatial Fourier modes. Those at large wave numbers thermalize, whereas modes at small wave numbers obey ordinary viscous dynamics [C. Cichowlas et al., Phys. Rev. Lett. 95, 264502 (2005)10.1103/Phys. Rev. Lett. 95.264502]. The energy bottleneck observed for finite alpha may be interpreted as incomplete thermalization. Artifacts arising from models with alpha>1 are discussed.
Laboratoire Cassiopée, OCA, UNS, CNRS, BP 4229, 06304 Nice cedex 4, France.
Uriel
U
Frisch
Susan
S
Kurien
Rahul
R
Pandit
Walter
W
Pauls
Samriddhi Sankar
SS
Ray
Achim
A
Wirth
Jian-Zhou
JZ
Zhu