Is the Eddy-driven Velocity Different for Different Tracers?

Following Andrews et al (1987), the eddy flux of a tracer can be decomposed into components parallel and perpendicular to the tracer gradient. The divergence of the component perpendicular to the tracer gradient can be shown to be identical to an advection of the tracer. This advection velocity, also referred to as the eddy-driven velocity, is described by a streamfunction B that is a function of the eddy flux of the tracer considered and the distribution of this tracer (Olbers et al. 2012). Since the distribution of tracer A generally differs from the distribution of tracer B, the eddy-driven velocity of tracer A is expected to be different from that of tracer B, even when the eddy fluxes of both tracers are parallel to each other. Using a 0.1° simulation performed with the May-Planck Institute Ocean Model, we address the question of whether the eddy-driven velocity is different for different tracers. Three tracers, temperature, salinity, and density, are considered. For each tracer, the eddy-driven velocity is diagnosed from the respective eddy flux and the spatial distribution of the tracer. We found that the eddy-driven velocity for temperature is significantly different from the eddy-driven velocity of salinity. Both have amplitudes larger than that of density. The result implies that in a non-eddy resolving model, the eddy-induced transport has to be parameterized differently for different tracers, rather than described by the same advection velocity as it is the case in the state-of-the-art ocean models with the Gent-McWilliams parameterization.