Kinetic energy dynamics in forced, homogeneous, and axisymmetric stably stratified turbulence

Direct numerical simulations with up to 4096 x 4096 x 2048 grid points are used to study the dynamics of kinetic energy in forced, homogeneous, and axisymmetric stably stratified flow with unit Prandtl number. No mean shear or internal waves are introduced into the flows, forcing represents persistent large horizontal motions with a small amount of noise, and turbulence develops in response. Three different stratification levels result in buoyancy Reynolds numbers ranging from 11 to 230, and multiple cross-checks for consistency in various dimensionless ratios show that the flows are consistent with theory for strong stratification. The balance equations for the horizontal and vertical contributions to kinetic energy are examined in terms of two-dimensional spectra. Downscale cascades of horizontal energy are evident at both the horizontal and the vertical, as is upscale transfer of energy at large horizontal scales but small vertical scales. Vertical energy also cascades down scale in both directions, so the dissipation rate of vertical energy relative to that of horizontal energy is the same as for unstratified isotropic turbulence. The horizontal and vertical length scales responsible for dissipation rate and the relative importance of dissipation rate compared with the energy transfer rate depend on the strength of the stratification. Both three-dimensional turbulence at scales smaller than the Ozmidov length scale and stratified turbulence at scales between the Ozmidov and the buoyancy scale produce power law scaling of kappa(-5/3)(1) in one-dimensional spectra. A sharper power law is observed at scales larger than the buoyancy scale. The second-order longitudinal structure functions, while exhibiting power law over the same scaling range, do not corroborate the Kolmogorov-Obukhov-Corrsin scaling.