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On Stratified Shear Flow in Sea Straits of Arbitrary Cross Section

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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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1111/1467-9590.t01-1-00040 DOIUNSPECIFIED
http://onlinelibrary.wiley.com/doi/10.1111/1467-9590.t01-1-00040/abstractPublisherUNSPECIFIED
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.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-01-1-0167
Office of Naval Research (ONR)N00014-92-J-1481
Record Number:CaltechAUTHORS:20111005-095550575
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20111005-095550575
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.
ID Code:26591
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Oct 2011 21:34
Last Modified:05 Oct 2011 21:34

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