The Bolus Velocity in the Stochastic Theory of Ocean Turbulent Tracer Transport

Abstract

A stochastic theory of tracer transport in compressible turbulence has recently been developed and then applied to the ocean case because stratified flow in isopycnal coordinates is analogous to compressible flow with the isopycnal layer thickness playing the role of density. The results generalize the parameterization of Gent and McWilliams in the sense that the eddy-induced transport velocity (i.e., the bolus velocity, which is directly related to the thickness?velocity correlation) is given by downgradient Fickian diffusion of thickness with a general mixing tensor K. This result is however dependent on an imprecise postulate relating the Lagrangian to the Eulerian mean velocities. In this paper the authors show that this postulate is unnecessary in a certain flow regime. This regime exists whenever the effect of thickness?velocity correlations dominates over the effect of relative vorticity?velocity correlations. The primary example is planetary geostrophic turbulence, but it may also exist in homogeneous quasigeostrophic turbulence. The bolus velocity is modified and becomes equivalent to upgradient diffusion of potential vorticity along isopycnals with the same mixing tensor K. This changes the conceptual basis of the bolus velocity parameterization of Gent and McWilliams at least in this regime, but practically, the effective change is of rather small magnitude.