A mechanism for layer formation in stratified geophysical flows

Abstract

Abstract.We discuss the possibility that steplike structures are formed in subcritical regions of vertically stratified shear flow. The mechanism we propose essentially consists of localized intense mixing in highly stratified and sheared flows, probably following frontogenesis. Its main assumption is that the vertical density flux increases monotonically with decreasing gradient Richardson numbers, which corresponds to enhanced stratification and/or diapycnal shear. This differs from Phillips' [1972] mechanism, which we argue may not apply to vertically stratified shear flow. An essential condition for the formation of constant density steps is the incorporation of a Langevin type equation which takes into account that turbulence must last for some finite characteristic time. We present numerical computations for the case of approximately constant diapycnal shear which lead to the formation of a staircase depth-density structure. The Phillips MechanismPhillips [1972] suggested that small perturbations in an initially well stratified density profile will grow with time if a local increase in the vertical density gradient is accompanied by an even larger decrease of the (turbulent) vertical density diffusivity K. In this case, the vertical density flux will become smaller (larger) with increasing (decreasing) stratification, leading to vertical density divergence (convergence) where the density perturbation is negative (positive). The density perturbations will turn into progressively better defined steps, until the turbulent density flux becomes equal in the well-stratified and well-mixed portions of the staircase. He further parameterized K in terms of some local Richardson number, to show that the density layers will form when the turbulent density diffusivity is a large enough inverse function of this local Richardson tions the numerical solution of the density, momentum, and eddy diffusivity equations leads to the formation of evolving staircase type structures. The key assumption for Phillips' mechanism is the dependence of F on density stratification. This mechanism requires F to be small both for well-mixed and highly stratified conditions, with a maximum at some critical stratification value. The physical justification is that for low stratification p' decreases while for high stratification w' is inhibited; additionally, under high stratification the correlation p'w' is reduced as the nature of the flow changes, with internal wave motions becoming more dominant [Ivey and Imberger, 1991]. Linden [1979, 1980] reviewed and did many laboratory experiments on grid-generated mixing across density interfaces and found that in all of them, independent of the stirring rate, the dependence was similar to that required by Phillips' mechanism. Linden [1980] 10, beyond which it became uniform, but they could not accurately confirm that the density flux decreased for values below 1. They further observed that the steps reached an equilibrium state which corresponded to a uniform density flux in the layered regi...

Distribution of water masses and diapycnal mixing in the Cape Verde Frontal Zone

“…A full description of the method can be found in the work of Rodríguez‐Santana et al [1999]. The scales of the instabilities induced by vertical shear are on the order of 1–10 m [ Pelegrí and Sangrá , 1998] implying that the depth interval used in the calculation of Ri , should be greater than these values. The use of relatively large vertical intervals produces a smoothing effect on Ri , and consequently on K s , that has been analyzed by Miller and Evans [1985].…”

Turbulent layering beneath the pycnocline in a strongly stratified pit lake

“…It is possible that the observations are manifestations of the natural evolution of layering evolving as a consequence of basinscale shear and stratification. Pelegrí and Sangrà (1998) consider diffusion of density and the formation of steps in the density structure. These are not seen here, although as the mixing is not produced everywhere, potentially the stratification adjusts sufficiently rapidly that these regions are only observed as the weak perturbations of Fig.…”

Turbulence as a driver for vertical plankton distribution in the subsurface upper ocean

“…In particular, Pelegrí and Sangrà (1998) have shown how the formation of layers with vertically homogeneous properties depends on the temporal memory of the turbulence, i.e. K v remaining high for some temporal characteristic scale even after the mechanism that led to the turbulence has ceased.…”