EDDY VISCOSITY IN TWO AND THREE DIMENSIONS.

Abstract

The test-field model for isotropic turbulence is used to examine the effective eddy viscosity acting on wavenumbers less than k//m due to interactions with subgrid-scale wavenumbers, defined as wavenumbers greater than k//m. In both two and three dimensions, the effective eddy viscosity for k much less than k//m is independent of k and of local spectrum shape. In two dimensions, this asymptotic eddy viscosity is negative. The physical mechanism responsible for the negative eddy viscosity is the interaction of large-spatial-scale straining fields with the secondary flow associated with small-spatial-scale vorticity fluctuations. This process is examined without appeal to turbulence approximations. For k//m - k much less than k//m, the effective eddy viscosity rises sharply to a cusp at k equals k//m if k//m lies in a long energy-transferring inertial range in either two or three dimensions or in a long enstrophy-transferring inertial range in two dimensions.