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 k_d,. 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.