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Monday, March 10, 2008
3:00 PM - 4:00 PM
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Hyperviscosity, Galerkin truncation and bottlenecks

Uriel Frisch
Observatoire de la Cote d'Azur

It is shown that the replacement in hydrodynamical equations of the usual dissipation by a high power $\alpha$ of the Laplacian leads asymptotically to truncating the dynamics to a a finite number of Fourier modes. When this number is large, a range of thermalized modes appear through the mechanism discovered by Cichowlas et al. [PRL 95, 264502, 2005]. The dynamics at small and intermediate wavenumbers is governed by the ordinary Navier-Stokes equations but a huge bottleneck in thermal equilibrium with Gaussian statistics is present at large wavenumbers. The usual ($\alpha=1$) bottleneck can be viewed as an aborted thermalization. Practical implications for turbulence modelling are discussed. This material is based on work in collaboration with Susan Kurien and Jian-Zhou Zhu.

Host: Susan Kurien, T-7