Threshold behavior of local gradient Richardson number in strongly stratified nonequilibrium turbulence

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American Physical Society
In this paper we examine the possible self-organization of strongly stratified turbulence around a local critical state by analyzing a data set of a numerically simulated stratified turbulent wake. To facilitate the analysis, the turbulent flow field is decomposed into a“large-scale” flow of horizontal scales greater than the Ozmidov scale, and a “small-scale” flow of scales below O. A local gradient Richardson number, Ri, characterizing the large-scale flow is calculated and then utilized to produce conditional sampling of various turbulence statistics relevant to the local dynamics. While the bulk turbulence is observed to decay by approximately one order of magnitude in terms of the dissipation rate, the median Ri has remained nearly constant due to the self-organization of flow structures under strong stratification; the subsampled Ri distribution peaks around 1/4 for regions in the upper quartile of local dissipation. Regions of small Ri are found to be associated with large dissipation and large net transfer of energy to the small scales. Regions of “back-scatter”of kinetic energy to large scales, where the local eddy viscosity,νe, takes a negative value,are also observed. Occurrence of a large magnitude of both positive and negative νe appears to be most frequent around the critical value of Ri∼1/4, indicating an intense two-way exchange of kinetic energy between the large and small scales around the local critical state. The threshold behavior of Ri underscores the dynamical significance of the critical Ri of 1/4 for locally self-sustained turbulence in a strongly stratified configuration and bears some resemblance to the celebrated self-organized criticality dynamics [Baket al.,Phys.Rev.Lett.59, 381 (1987)].
Zhou, Q. (2022) Threshold behavior of local gradient Richardson number in strongly stratified nonequilibrium turbulence. Physical Review Fluids, 7(10).