Submesoscale contribution to subduction: Tracer and momentum fluxes

An important component of the carbon-cycle is subduction, for example of dissolved carbon, from the surface layers to depths of (10²-10³)m. Recently, attention has been focused on the contribution by small-scale, mesoscale M, and submesoscale SM eddies. In the Southern Ocean, the M contribution to subduction was found to be negative and of an order of magnitude smaller than the positive one by vertical diffusion. Since there is now observational evidence that SM export organic carbon but they have not yet been included in subduction studies, the goal of this work is to derive the following results needed to carry out such studies: (a) OGCMs used in C-cycle studies solve the equations for the mean temperature, mean salinity, and mean concentration. We derive the forms of the 3-D arbitrary tracer fluxes in terms of resolved fields. (b) The same OGCMs also solve the mean momentum equation. We derive the form of the SM momentum fluxes (Reynolds Stresses) also in terms of resolved fields. (c) It is shown that whether there is subduction or obduction depends on the ratio h/H, where h is depth of the SM regime and H is the mixed-layer depth. We show that in the ACC the ratio depends on the specific location and that both subduction and obduction occur but with a topology different than that of mesoscales.