The role of surface potential vorticity in the vertical structure of mesoscale eddies in wind-driven ocean circulations

The vertical structure of ocean eddies is generally surface-intensified, commonly attributed to the dominant baroclinic modes arising from boundary conditions (BCs).Conventional BC consideration mostly focuses on either flat-or rough-bottom conditions.The impact of surface buoyancy anomaly-often represented by surface potential vorticity (PV) anomaly-has not been fully explored.Here, we study the role of the surface PV in setting the vertical distribution of eddy kinetic energy (EKE) in an idealized adiabatic ocean model.The simulated EKE profile in the extra-tropical ocean tends to peak at the surface and have an 𝑒-folding depth typically smaller than half of the ocean depth.This vertical structure can be reasonably represented by a single surface quasi-geostrophic (SQG) mode at the energy-containing scale resulting from surface-trapped baroclinic instability and inverse energy cascades.The surface meridional PV gradient-key to oceanic baroclinic instability-induces surface-trapped unstable modes that decay faster with depth for smaller horizontal scales.Subsequently, through an inverse energy cascade from scales close to or smaller than the deformation radius to the energy-containing scale, the vertical structure grows deeper while remaining surface-trapped.These results indicate that the vertical EKE distribution depends on the horizontal scale since smaller eddies tend to be shallower.Guided by this interpretation, an SQG-based scale-aware parameterization of the EKE profile is proposed here.Preliminary offline diagnosis of a high-resolution simulation shows the proposed scheme successfully reproducing the dependence of the vertical structure of EKE on the horizontal grid resolution.