Scale-dependent anisotropy in forced stratified turbulence

The author has the right to post and update the article on a free-access e-print server using files prepared and formatted by the author. Any such posting made or updated after acceptance of the article for publication by APS should include a link to the online APS journal article abstract. In all cases, the appropriate bibliographic citation and notice of the APS copyright must be included.In stratified turbulence, buoyancy forces inhibit vertical motion and lead to anisotropy over a wide range of length scales, which is characterized by layerwise pancake vortices, thin regions of strong shear, and patches of small-scale turbulence. It has long been known that stratified turbulence becomes increasingly isotropic as one moves to smaller length scales, as the eddy timescale decreases towards and below the buoyancy period. This paper investigates the anisotropy of stratified turbulence across scales and the transition towards isotropy at small scales, using a variety of techniques. Direct numerical simulations of strongly stratified turbulence, with buoyancy Reynolds numbers Reb up to 50, are analyzed. We examine the relative contributions of different components of the strain rate tensor to the kinetic energy dissipation, the invariants of the isotropy tensor, directional kinetic energy spectra, and the subfilter energy flux across different length scales. At small scales, the degree of isotropy is determined by Reb, while at the Ozmidov and larger scales, the anisotropy also depends on the Froude number. The change in the anisotropy with scale and with the parameters is examined in detail. Interestingly, Ozmidov-scale eddies are found to become increasingly isotropic as Reb increases, as characterized by the isotropy tensor invariants and the subfilter energy flux. At larger scales, the energy spectra for near-vertical wave vectors have a spectral slope around −3, which shallow towards −1 for near-horizontal wave vectors. These spectra converge beyond the Ozmidov scale, increasingly so for large Reb. These results suggest that Reb > 500 would be necessary to obtain the same degree of small-scale isotropy that is found in similarly sized simulations of unstratified turbulence.Shared Hierarchical Academic Research Computing Network (SHARCNET) || Compute/Calcul Canada || Natural Sciences and Engineering Research Council of Canada, Grant No. RGPIN-386456-2015 || Canadian Foundation for Innovation