Contribution of sub-mesoscales to the vertical velocity: The ω-equation

Abstract

The ocean's ability to regulate carbon dioxide depends on biogeochemical processes that are influenced strongly by eddies. Eddy-resolving simulations have shown that sub-mesoscales (SM) (1–10km) generate the highest magnitude vertical velocity and that mesoscales (M) also enhance their contribution to the vertical velocity but to a lesser extent. In this study, we consider the question: can analogous results be obtained using the less numerically demanding ω-equation? Previously, this question has not been answered because of two reasons: 1) the canonical Hoskins’ form of the ω-equation does not include the buoyancy vertical fluxes caused by M and SM; and 2) Giordani et al. (2016) showed how to include an arbitrary vertical buoyancy flux, but no parameterizations were available for the M and SM vertical fluxes. However, the latter are now available together with their assessments, so we consider SM because they make the largest contribution to the vertical velocity. The resulting vertical velocity depends on the extent of the SM regime, the horizontal buoyancy gradient (representing baroclinic instabilities), and the SM eddy kinetic energy. The vertical velocity depends in a linear manner on the wind stress and it may exhibit seasonal variations. The wind stress has two effects on the ω-equation: indirectly via its contribution to the sub-mesoscale buoyancy flux and directly through the wind stress itself. The results of our sensitivity analysis highlight the range of SM-induced vertical velocities obtained using different input data.