Numerical Simulations of Upstream Bores and Solitons in a Two-Layer Flow past an Obstacle

Abstract

Numerical simulations of upstream propagating disturbances generated through the interaction of an inviscid, nearly two-layer flow past a two-dimensional obstacle are discussed. The experimental configuration is an appropriate one for flow past ice keels?the inverted ridges of submerged ice found in frozen seas. In the first series of simulations, a steady inflow is specified and properties of upstream propagating bores are compared with the predictions of hydrostatic theory. While the comparison shows a generally good agreement with theory, a dependence of the response an the height-to-width aspect ratio of the obstacle is identified. For obstacles with relatively large aspect ratios, bore amplitudes and propagation speed are overestimated by the theory as the Froude number becomes large. Conversely, bore amplitudes are slightly underestimated for obstacles with small aspect ratios. In a second series of simulations, flow past the obstacle is modulated at the M2 frequency over one-half tidal cycle. In these cases, the response is characterized by the generation of an upstream propagating bore, which evolves into a packet of rank-ordered solitons as the tidal flow slackens. The results suggest ice keels as possible generation sites for internal solitons over Arctic shelves.