Jian-Zhou Zhu
Theoretical Division, Los Alamos National Laboratory
in collaboration with Uriel Frisch, Walter Paul, Susan Kurien

Turbulence Thermalization and Spectral Bottleneck

For many equations of hydrodynamical type, including the three-dimensional Navier-Stokes equations, the Burgers equation and various models of turbulence, the use of hyperviscous dissipation with a high power α (dissipativity) of the Laplacian and suitable rescaling of the hyperviscosity becomes asymptotically equivalent to using a Galerkin truncation with zero dissipation and suppression of all Fourier modes whose wavenumber exceeds a cutoff kd,. The Galerkin-truncated Euler system will develop a thermalized range at high wave numbers as presented by Cichowlas et al [Phys. Rev. Lett. 95 (2005) 264502]. It is therefore proposed to interpret the phenomenon of bottleneck, which becomes stronger with increasing α, as an aborted thermalization. Helicity effects on the aborted thermalization/ bottleneck are also discussed along with numerical verifications.