Thermalization and Turbulence Bottleneck

It is conjectured that 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 $\alpha$ (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 wavenumbers as presented by Cichowlas et al [{\it Phys. Rev. Lett.} {\bf 95} (2005) 264502]. It is therefore proposed to interpret the phenomenon of bottleneck, which becomes stronger with increasing $\alpha$, as an aborted thermalization. Numerical verification of these ideas are discussed, along with various artefacts which can appear when using hyperviscosity.