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arXiv · 0803.4269

Hyperviscosity, Galerkin truncation and bottlenecks in turbulence

Uriel Frisch·Susan Kurien·Rahul Pandit·Walter Pauls·Samriddhi Sankar Ray·Achim Wirth·Jian-Zhou Zhu
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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.

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Uriel Frisch, Susan Kurien, Rahul Pandit, Walter Pauls, Samriddhi Sankar Ray, Achim Wirth, Jian-Zhou Zhu. 2008-09-03. Hyperviscosity, Galerkin truncation and bottlenecks in turbulence. https://doi.org/10.1103/physrevlett.101.144501

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