Ageostrophic Velocities of Curved Ocean Fronts

Abstract

Ageostrophic velocities at ocean fronts play a key role in ventilating the upper ocean. The overturning circulation driven by cross‐front ageostrophic flow is widely recognized as the major mechanism of vertical transport, but the role of along‐front ageostrophic velocities remains underrepresented in existing theory. Here, we recast the quasigeostrophic (QG) momentum equations in a reference frame that follows the local geostrophic flow (a front‐following coordinate system) and show that the along‐front and cross‐front ageostrophic flows originate from distinct underlying dynamics. To maintain the leading‐order geostrophic balance of the front, the next‐order Coriolis force acting on supplies the tangential acceleration of the geostrophic flow in the along‐front direction. In the cross‐front momentum balance, by contrast, the Coriolis force acting on acts as the centripetal acceleration of , yielding , where the curvature number Cu is defined by the local radius of curvature and the Coriolis frequency . For curved fronts where Cu varies rapidly, adjustments of generate horizontal divergence and drive overturning circulations along the frontal axis. Idealized simulations of curved fronts confirm that ageostrophic motions can be successfully reconstructed from geostrophic fields. These results suggest an underappreciated role of front curvature in modulating vertical velocity at ocean fronts, with implications for identifying curvature‐induced hotspots of vertical transport from satellite sea surface height observations.