Cross-Shelf Exchange Driven by Oscillatory Barotropic Currents at an Idealized Coastal Canyon

Abstract

Numerical simulations are used to study on-shelf transport of dense water by oscillatory barotropic currents incident upon an isolated coastal canyon. The physical system is a laboratory-scale annulus in which forcing is provided by an oscillatory modulation in the rotation rate and for which the external nondimensional parameters match those from an appropriate oceanic analog. The numerical simulations were conducted for comparison with a companion set of laboratory experiments, and these prior studies have shown good qualitative and quantitative agreement between the two. Here the numerical simulations are examined in further detail to determine the three-dimensional structure of the time-mean currents and density field on the shelf, to quantify the resulting onshore transport of dense water, and to expose the underlying nondimensional parameter dependencies. The incident barotropic currents produce, in equilibrium, an extensive pool of anomalously dense fluid on the shelf surrounding the canyon. This dense pool is maintained on the shelf by a combination of cross-shelf mean and eddy density fluxes. The associated time-mean pools of dense water on the shelf have considerable spatial structure, most prominently a vertically thick lens of anomalously dense water along the upstream limb of the canyon, accompanied by strong anticyclonic residual currents. The dense pool occupies an area and volume that are large when compared with that of the canyon itself. Several bulk measures of on-shelf exchange of dense water are devised to facilitate comparison across the simulations performed. This comparison of bulk measures indicates that net on-shelf transport of dense water varies linearly with forcing period (inverse temporal Rossby number) and quadratically with forcing strength (Rossby number). Variations in on-shelf pumping with Burger number are found to be weak. A simple dynamical scaling argument is consistent with the observed dependencies.