Deng, Jian and Pratt, Larry and Howard, Lou and Jones, Chris (2003) On Stratified Shear Flow in Sea Straits of Arbitrary Cross Section. Studies in Applied Mathematics, 111 (4). pp. 409-434. ISSN 0022-2526 http://resolver.caltech.edu/CaltechAUTHORS:20111005-095550575
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Equations and theorems governing the flow of an inviscid, incompressible, continuously-stratified fluid in a gradually varying channel with an arbitrary cross section are developed. The stratification and longitudinal velocity are assumed to be uniform in the transverse direction, an assumption that is supported under the assumption of gradual topographic variations. Extended forms of Long's model and the Taylor–Goldstein equation are developed. Interestingly, the presence of topographic variation does not alter the necessary condition for instability (Richardson number < 1/4) nor the bounds on unstable eigenvalues (the semi-circle theorem). The former can be proved using a new technique introduced herein. For the special case of homogeneous shear flow, generalized versions of the theorems of Rayleigh and Fjørtoft do depend on the form of the topography, though no general tendency toward stabilization or destabilization is apparent. Previous results on the bounds and enumeration of neutral modes are also extended. The results should be of use in the hydraulic interpretation of exchange flow in sea straits.
|Additional Information:||© 2003 Massachusetts Institute of Technology. Received November 5, 2002. Article first published online: 23 Sep. 2003. L. P. was supported by ONR grant N00014-01-1-0167, and C. J. was supported by ONR grant N00014-92-J-1481.|
|Official Citation:||Deng, J., Pratt, L., Howard, L. and Jones, C. (2003), On Stratified Shear Flow in Sea Straits of Arbitrary Cross Section. Studies in Applied Mathematics, 111: 409–434. doi: 10.1111/1467-9590.t01-1-00040|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||05 Oct 2011 21:34|
|Last Modified:||05 Oct 2011 21:34|
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