The Temporal-Residual-Mean Velocity. Part II: Isopycnal Interpretation and the Tracer and Momentum Equations

Abstract

Abstract Mesoscale eddies mix fluid parcels in a way that is highly constrained by the stratified nature of the fluid. The temporal-residual-mean (TRM) theory provides the link between the different views that are apparent from temporally averaging these turbulent flow fields in height coordinates and in density coordinates. Here the original TRM theory is modified so that it applies to unsteady flows. This requires a modification not only to the streamfunction (and hence the velocity vector) but also a specific interpretation of the density field; it is not the Eulerian-mean density. The TRM theory reduces the problem of parameterizing the eddy flux from three dimensions to two dimensions. The three-dimensional TRM velocity is shown to be the same as is obtained by averaging with respect to instantaneous density surfaces and the averaged conservation equations in height coordinates and in density coordinates are the same except for a nondivergent flux that is identified and explained. The TRM theory demo...