Self-similarity in decaying two-dimensional stably stratified adjustment

The evolution of large-scale density perturbations is studied in a stably stratified, two-dimensional flow governed by the Boussinesq equations. As is known, initially smooth density (or temperature) profiles develop into fronts in the very early stages of evolution. This results in a frontally dominated k−1 potential energy spectrum. The fronts, initially characterized by a relatively simple geometry, spontaneously develop into severely distorted sheets that possess structure at very fine scales, and thus there is a transfer of energy from large to small scales. It is shown here that this process culminates in the establishment of a k−5∕3 kinetic energy spectrum, although its scaling extends over a shorter range as compared to the k−1 scaling of the potential energy spectrum. The establishment of the kinetic energy scaling signals the onset of enstrophy decay, which proceeds in a mildly modulated exponential manner and possesses a novel self-similarity. Specifically, the self-similarity is seen in the ti...