Numerical experiments in forced stably stratified turbulence

Abstract

We present results of numerical simulations of stably stratified, randomly forced turbulence. The selection of forcing and damping are designed to give insight into the question of whether cascade of energy to large scales is possible for strongly stratified three-dimensional turbulence in a manner similar to two-dimensional turbulence. We consider narrow-band wavenumber forcing, whose angular distribution ranges from two-dimensional to three-dimensional isotropic. Our principal results are as follows; for two-dimensional forcing, and for sufficiently small Froude number, the statistically steady state is characterized by a weakly inverse-cascading horizontal-velocity variance field. The vertical variability of the horizontal-velocity field is pronounced, but seems to approach a limit independent of the Brunt–Väisälä frequency N, as N → ∞. If, on the other hand, the Froude number exceeds a critical value, the vertical variability is weak, and the statistics of the scales larger than the forcing scale is near that predicted by inviscid equipartitioning. For all forcing functions considered the vertical motion and temperature field (w, T), centred at smaller scales, are more three-dimensionally isotropic, with no large-scale organization. At large N, (small Froude number) the w-field scales as 1/N, with horizontal motion field nearly independent of N. Furthermore, at large N and for horizontal forcing, the horizontal motion field is consistent with the condition that a substantial fraction of the total dissipation is attributable to an effective drag acting upon all horizontal scales of motion, which in turn flattens the slope of the energy spectrum in the inverse-cascade range, and increases it in the enstrophy-cascade range.