Nonlinear dynamics of time-variable slope circulation

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 prograde flow bias (aligned in the direction of topographic Rossby wave propagation) relative to linear estimates, and retrograde flow (opposing wave propagation) exhibiting flow strength saturation 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 frictional stresses, depends on the choice of integration path: when integrated along isobaths, 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 predominantly down-slope and strongest during retrograde phases, resulting in the prograde bias. When retrograde velocities approach the arrest speed of topographic Rossby waves with wavelengths comparable to the corrugation wavelength, the flux increases sharply, halting further acceleration and producing the observed asymmetry. The interplay between forcing timescale and frictional timescale shapes how these nonlinear effects manifest: when the forcing period is comparable to the dampening timescale, the response is strongly low-pass filtered, whereas for much longer forcing periods the flow has time to adjust toward distinct prograde and retrograde states. 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 under-represented in coarse-resolution numerical simulations, and highlight the need for improved representations of unresolved topographic interactions.