The Role of Physical Scale in Shear-Stratified Turbulence

The generation of turbulence in pure shear-stratified environments is known to be driven by interfacial instabilities within the stratified shear layer, typically resulting in coherent overturning structures such as Kelvin-Helmholz billows (particularly for near-critical values of the gradient Richardson number) that subsequently decay to turbulence. Efforts to scale these processes using bulk flow variables have resulted in a variety of approaches, where non-dimensional forms of turbulent intensity, including the entrainment ratio, E, and a non-dimensional turbulent buoyancy flux, ξ, are typically assumed to be functions of a local bulk Richardson number, Ri_B. Little dynamic relevance has been attributed to the Reynolds number, Re, which provides a relative measure of physical scale, beyond a minimum critical value of Re necessary for the generation of turbulence, perhaps because most studies have focused on single environments, either at the laboratory scale or geophysical scales, where values of Reare relatively constant. However, recent comparisons of laboratory data with data collected from the coastal ocean, including several supercritical river plume environments, indicates that geophysical turbulence (expressed either as E or ξ) falls several orders of magnitude below similarly generated laboratory turbulence at consistent values of Ri_B, suggesting a strong dependence on physical scale. Simple scaling analyses suggest that ξ may be a function of Re^-2/3 for constant Ri_B, which is roughly consistent with the observed gap between laboratory and geophysical data. An enhanced understanding of the role of physical scale in the generation of shear-stratified turbulence will facilitate the use of laboratory data or direct numerical simulation (DNS) output to inform dynamics at geophysical scales, and may improve turbulence closure schemes for ocean models.