Shock Waves in Currents and Outflows

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Abstract
Shock waves are discontinuities (in the physical properties of a fluid) which behave in an organized manner. The possibility that such waves may occur in oceanic boundary currents is examined with a nonlinear two-layer analytical model. Attention is focused on separated boundary currents (i.e., light currents whose lower interface strikes the free surface or heavy currents whose upper interface intersects the floor) with zero potential vorticity. The shocks result from an increase in the upstream transport; they correspond to abrupt and violent changes in depth and velocity accompanied by a local energy loss. Nonlinear solutions for steadily translating shocks are constructed analytically by connecting the upstream and downstream fields without solving for the complicated region in the immediate vicinity of the shock. It is found that, while stationary shocks are impossible, steadily propagating shocks can always occur. There are no special requirements on the boundary currents in question and th... Abstract Shock waves are discontinuities (in the physical properties of a fluid) which behave in an organized manner. The possibility that such waves may occur in oceanic boundary currents is examined with a nonlinear two-layer analytical model. Attention is focused on separated boundary currents (i.e., light currents whose lower interface strikes the free surface or heavy currents whose upper interface intersects the floor) with zero potential vorticity. The shocks result from an increase in the upstream transport; they correspond to abrupt and violent changes in depth and velocity accompanied by a local energy loss. Nonlinear solutions for steadily translating shocks are constructed analytically by connecting the upstream and downstream fields without solving for the complicated region in the immediate vicinity of the shock. It is found that, while stationary shocks are impossible, steadily propagating shocks can always occur. There are no special requirements on the boundary currents in question and th...

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