期刊名称：Tellus A: Dynamic Meteorology and Oceanography
电子版ISSN：1600-0870
出版年度：2001
卷号：53
期号：2
页码：129-145
DOI：10.3402/tellusa.v53i2.12182
摘要：Previous work on the classical problem of shocks in a 2-layer density-stratified fluid used eithera parameterized momentum exchange or an assumed Bernoulli loss. We propose a new theorybased on a set of viscous model equations. We define an idealized shock in two-layer densitystratified flow under a rigid lid as a jump or drop of the interface in which (1) the force balanceremains nearly hydrostatic in the shock, (2) there is no exchange of momentum between thetwo layers except by pressure forces on the sloping interface, and (3) dissipative processes canbe treated with a constant viscosity. We proceed in two steps. First, we derive a necessarycondition for shock existence based on a requirement for wave steepening. Second, we formulateand solve a set of viscous model equations. Some results are the following: Shocks requirestrong layer asymmetry; one layer must be much faster and/or shallower than the other layer.The linearized equations describing the shock tails provide boundary conditions and a proofof shock uniqueness. It is possible to derive an analytical solution for weak shocks if thesteepening condition is met. The weak shock solutions provide closed form expressions for theBernoulli loss in each layer. Bernoulli losses are strongly concentrated in the expanding layeras the relative layer depth change is much larger in that layer. Bernoulli losses are independentof layer viscosity. A sudden cessation of shock existence is found for strong shocks when thepossible end state migrates into the supercritical regime. Surprisingly, the new ideal shocktheory compares well with a 2-D, time-dependent shallow water model (SWM) with a fluxformulation, but with no viscous formulation. Both the Bernoulli drop and shock cessationcondition agree quantitatively.
