Numerical study of the decay of enstrophy in a two-dimensional Navier–Stokes fluid in the limit of very small viscosities

Abstract

The rate of enstrophy decay in two-dimensional Navier–Stokes turbulence is explored numerically with high resolution pseudospectral simulations. Initial conditions and all other physical parameters are held fixed while viscosity is decreased through about three orders of magnitude, while increasing the numerical resolution as required to resolve the smallest scales that develop. The attempt is to discern whether or not a regime is being approached in which the behavior of the vorticity decay could be approximated as ideal and nondissipative. Although the enstrophy decay shows a (logarithmic) tendency to go to zero as the viscosity is decreased, at fixed times, the extrapolated values of viscosity to approach a zero enstrophy decay regime lie many orders of magnitude out of our currently available numerical resolution.