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.