Similarity scaling and vorticity structure in high-Reynolds-number stably stratified turbulent wakes

Abstract

The mean velocity profile scaling and the vorticity structure of a stably stratified, initially turbulent wake of a towed sphere are studied numerically using a high-accuracy spectral multi-domain penalty method model. A detailed initialization procedure allows a smooth, minimum-transient transition into the non-equilibrium (NEQ) regime of wake evolution. A broad range of Reynolds numbers,Re= UD/ν ∈ [5 × 10³, 10⁵] and internal Froude numbers,Fr= 2U/(ND) ∈ [4, 64] (U,Dare characteristic velocity and length scales, andNis the buoyancy frequency) is examined. The maximum value ofReand the range ofFrvalues considered allow extrapolation of the results to geophysical and naval applications.At higherRe, the NEQ regime, where three-dimensional turbulence adjusts towards a quasi-two-dimensional, buoyancy-dominated flow, lasts significantly longer than at lowerRe. AtRe= 5 × 10³, vertical fluid motions are rapidly suppressed, but atRe= 10⁵, secondary Kelvin–Helmholtz instabilities and ensuing turbulence are clearly observed up toNt≈ 100. The secondary motions intensify with increasing stratification strength and have significant vertical kinetic energy.These results agree with existing scaling of buoyancy-driven shear onRe/Fr²and suggest that, in the field, the NEQ regime may last up toNt≈ 1000. At a given highRevalue, during the NEQ regime, the scale separation between Ozmidov and Kolmogorov scale is independent ofFr. This first systematic numerical investigation of stratified turbulence (as defined by Lilly,J. Atmos. Sci.vol. 40, 1983, p. 749), in a controlled localized flow with turbulent initial conditions suggests that a reconsideration of the commonly perceived life cycle of a stratified turbulent event may be in order for the correct turbulence parametrizations of such flows in both geophysical and operational contexts.