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.

High-order discontinuous element-based schemes for the inviscid shallow water equations: Spectral multidomain penalty and discontinuous Galerkin methods

“…SMPM have been successfully applied to high Re incompressible stratified flow process studies in vertically non-periodic domains such as internal solitary wave-induced bottom boundary layers, turbulent wakes and propagating internal wave packets [28,29,30]. DGM have been effectively used in the simulation of the shallow water equations (SWE) both on the sphere and on planar but fully unstructured domains [20,21,23,25,24] and for compressible atmospheric models [22,26].…”

The internal wavefield generated by a towed sphere at low Froude number

“…Gourlay et al 2001;Brucker & Sarkar 2010;Diamessis, Spedding & Domaradzki 2011) and on the turbulent wake-generated internal wavefield (e.g. Meng Abdilghanie & Diamessis 2013), using smooth self-similar initial velocity and density profiles at a short distance downstream of the body.…”

The turbulent wake of a towed grid in a stratified fluid

“…As DNS can extend to higher Re b , the possibility has been raised that energetic secondary instabilities of the developing shear layers in strongly stratified turbulence (Riley & de Bruyn Kops 2003;Hebert & de Bruyn Kops 2006a;Diamessis, Spedding & Domaradzki 2011) provide a further barrier to extrapolating laboratory experiments to higher Re, and so it is interesting to consider experimental devices that may eventually reach high-Re b regimes (Augier et al 2014). The different initial conditions can also be compared in similar frameworks, experimental or computational (e.g.…”

“…The strong vertical shear is thought to be an important mechanism for triggering secondary turbulence (Lilly 1983;Hebert & de Bruyn Kops 2006a), even in strongly stratified flows (Riley & de Bruyn Kops 2003;Diamessis et al 2011), and therefore has received significant attention in the literature. The averaged mean-squared vertical shear S 2 is…”