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, D are characteristic velocity and length scales, and N is the buoyancy frequency) is examined. The maximum value of Re and the range of Fr values considered allow extrapolation of the results to geophysical and naval applications.
At higher Re, the NEQ regime, where three-dimensional turbulence adjusts towards a quasi-two-dimensional, buoyancy-dominated flow, lasts significantly longer than at lower Re. At Re = 5 × 103, vertical fluid motions are rapidly suppressed, but at Re = 105, secondary Kelvin–Helmholtz instabilities and ensuing turbulence are clearly observed up to Nt ≈ 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 on Re/Fr2 and suggest that, in the field, the NEQ regime may last up to Nt ≈ 1000. At a given high Re value, during the NEQ regime, the scale separation between Ozmidov and Kolmogorov scale is independent of Fr. 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.