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：146-167
DOI：10.3402/tellusa.v53i2.12183
摘要：In this second part of the study, ideal shock theory in two-layer stratified flow is extended toinclude a third passive layer (i.e., a two and a half layer system). With the presence of a passivelayer, two linear wave modes and ‘‘viscous tail modes’’ exist, complicating the solubility conditionsand uniqueness proofs for two layer shocks. It is found however, that shocks can beunambiguously classified as external or internal based on the states of criticality that theyconnect. The steepening condition, while still necessary, provides a less restrictive constraintthan it did with a rigid lid. Thus, we have to rely more on solutions to the full viscous shockequations to establish shock existence. The detailed structure, momentum exchange, andBernoulli loss in a viscous shock are examined using an analytical weak shock solution and aset of numerical solutions for shocks with finite amplitudes. A shock regime diagram (F 1 by F 2 )is constructed based on the numerical integration of the full viscous shock equations. For strongexternal jumps, a cusp region (i.e., in the sense of catastrophe theory) is identified on the regimediagram. For pre-shock states within the cusp, three end states are possible and two of theseare realizable. The cusp has several physical implications. It indicates that an equal distributionof dissipation between the two layers in shocks is mathematically possible but physically inaccessible.It also allows hysteresis in time varying flows, and promotes the occurrence of doubleshocks (i.e., closely spaced shocks of different character). The results are compared with classicalshock solutions and a set of time dependent numerical experiments.
