Theoretical framework for the response of barotropic shelf current to along-shelf bathymetric perturbations

Abstract The mechanism underlying the response of barotropic shelf current to along-shelf bathymetric perturbations is rationalized by a one-dimensional vorticity equation. Fourier analysis of the equation in the wavenumber domain suggests that bathymetric features with relatively short length scales in the alongshore direction drive steady cross-shelf velocity undulations when the shelf circulation is against the direction of Kelvin wave propagation (upwelling regime). In contrast, much weaker and non-oscillatory cross-shelf velocity is expected when the shelf circulation is in alignment with propagating Kelvin waves (downwelling regime). The velocity undulations in the upwelling regime result from a positive feedback mechanism associated with potential vorticity (PV) advection; however, the presence of bottom friction restricts such undulations within a few wavelengths. The characteristic wavelength of undulations is determined by when the normalized drag coefficient , where u is the along-shelf mean flow speed, H s is shelf depth, α s is the bottom slope, f is the Coriolis parameter, and r is the linear drag coefficient. Using this formula, a scale of the cross-shelf displacement distance Y t is proposed, aligning with one-layer barotropic simulations over a large parameter space. The study provides a framework for investigating barotropic cross-shelf exchange caused by shelf circulation over irregular bottom bathymetries.