An idealized shock in two-layer density stratified flow is a jump or drop of the interface in which the force balance remains nearly hydrostatic in the shock and there is no exchange of momentum between the two layers except by pressure forces on the sloping interface. Previous work on this classical problem using an arbitrary average pressure, an assumed Bernoulli loss, or an end-state entropy principle is shown to be unphysical. A new theory of shocks is proposed based on two principles: wave steepening and a viscous computation of Bernoulli loss. Shocks described in this way satisfy the entropy principle in both layers and are pseudo-inviscid, but have a layer partitioned Bernoulli loss which depends on internal processes. Bernoulli losses tend to be concentrated in the expanding layer. The results of a momentum-conserving two-dimensional, two-layer numerical model are shown to agree qualitatively with the new theory.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics