Rotating stratified turbulence and the slow manifold

Abstract

Abstract Numerical simulations of decaying rotating stratified turbulence were performed from balanced initial conditions using the Baer–Tribbia initialisation scheme as an approximate projection onto the slow manifold of the non-hydrostatic Boussinesq equations. Starting with the low Rossby and Froude numbers characterising the quasigeostrophic limit, these were increased somewhat until small-scale balance appeared to break down. Following a previous paper by the authors, this occurred in conjunction with the emergence of a shallow range in the energy spectrum. The goal here is to work towards identifying the mechanism and characteristic scales of the resulting spontaneous imbalance. It is found that it originates at relatively large scales near the low-wave number end of the shallow spectral range. Unbalanced energy then cascades to small scales where it is efficiently dissipated in the decay case. The predominant interaction over the shallow range was seen to be a downscale cascade of unbalanced energy with little interaction with the balanced flow. At even smaller scales the decomposition loses its meaning and the spectrum remains shallow.