THE EFFECT OF SMALL-SCALE FORCING ON LARGE-SCALE STRUCTURES IN 2-DIMENSIONAL FLOWS

The effect of small-scale forcing on large-scale structures in beta-pl ane two-dimensional (2D) turbulence is studied using long-term direct numerical simulations (DNS). We find that nonlinear effects remain str ong at all times and for all scales and establish an inverse energy ca scade that extends to the largest scales available in the system. The large-scale flow develops strong spectral anisotropy: k(-5/3) Kolmogor ov scaling holds for almost all phi, phi = arctan(ky(/)k(x)), except i n the small vicinity of k(x) = 0, where Rhines's k(-5) scaling prevail s. Due to the k(-5) scaling, the spectral evolution of beta-plane turb ulence becomes extremely slow which, perhaps, explains why this scalin g law has never before been observed in DNS. Simulations with differen t values of beta indicate that the beta-effect diminishes at small sca les where the flow is nearly isotropic. Thus, for simulations of beta- plane turbulence forced at small scales sufficiently removed from the scales where beta-effect is strong, large eddy simulation (LES) can be used. A subgrid scale (SGS) parameterization for such LES must accoun t for the small-scale forcing that is not explicitly resolved and corr ectly accommodate two inviscid conservation laws, viz. energy and enst rophy. This requirement gives rise to a new anisotropic stabilized neg ative viscosity (SNV) SGS representation which is discussed in the con text of LES of isotropic 2D turbulence.