Nonlinear dynamics of time-variable slope circulation

Abstract. Bottom topography strongly constrains ocean circulation in the Arctic, and both theory and numerical modeling suggest that nonlinear flow–topography interactions influence slope-following currents. Yet, how such interactions modify the circulation response to time-variable surface forcing remains poorly understood. Using idealized shallow-water simulations of flow over a corrugated slope in a re-entrant channel, we investigate how nonlinear features arise and evolve under oscillatory forcing. We observe both a persistent prograde flow bias (aligned with topographic Rossby wave propagation) relative to linear estimates, and an asymmetry in the circulation response, with retrograde flow (opposing wave propagation) exhibiting a saturation of flow strength once the flow reaches sufficiently strong velocities. To identify the mechanisms responsible for these behaviors, we evaluate integrated momentum budgets. Which terms appear as dynamically relevant, in addition to linear surface and bottom stresses, depends on the choice of integration path: when integrated along constant-depth contours, the nonlinear dynamics appear as a cross-slope relative vorticity flux, whereas integration along straight transects instead highlights momentum flux convergence and topographic form stress. These perspectives can be unified under quasi-geostrophic scaling as describing a flux of potential vorticity (PV). This PV flux is strongest during retrograde flow and predominantly down-slope, explaining the prograde bias. When retrograde velocities approach the arrest speed of topographic Rossby waves with wavelengths comparable to the corrugation scale, the flux increases sharply, halting further acceleration and producing the observed asymmetry. These results show how flow–topography interactions shape time-variable slope circulation, biasing the flow toward prograde states and limiting retrograde flow strength. Such effects are likely underrepresented in coarse-resolution numerical simulations, and highlight the need for improved representations of unresolved topographic interactions.