Exploring the Relationship between Eddy-Induced Transport Velocity, Vertical Momentum Transfer, and the Isopycnal Flux of Potential Vorticity

Gent et al. have emphasized the role of the eddy-induced transport (or bolus) velocity as a mechanism for redistributing tracers in the ocean. By writing the momentum equations in terms of the isopycnal flux of potential vorticity, the author shows that any parameterization of the eddy-induced transport velocity must be consistent with the conservation equation for potential vorticity. This places a constraint on possible parameterizations, a constraint that is satisfied by the Gent and McWilliams parameterization only if restrictions are placed on the diffusivity coefficient. A new parameterization is suggested that is the simplest extension of Gent and McWilliams based on the potential vorticity formulation. The new parameterization parameterizes part of the time-mean flow driven by the Reynolds stress terms in addition to the eddy-induced transport velocity. It is also shown that the eddy-induced transport velocity can always be written as the Ekman velocity associated with the vertical derivative of a horizontally directed eddy stress. The author shows how the eddy stress is related to the “inviscid pressure drag” or “form drag” associated with the eddies, although the correspondence is not exact.