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An analytic solution for barotropic flow along a variable slope topography
Author(s) -
Kuehl Joseph J.
Publication year - 2014
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/2014gl061188
Subject(s) - barotropic fluid , canyon , geology , flow (mathematics) , plume , variable (mathematics) , similarity (geometry) , dissipation , geometry , geophysics , geomorphology , mathematical analysis , thermodynamics , physics , mathematics , oceanography , artificial intelligence , computer science , image (mathematics)
An analytic solution is derived for the generic oceanographic situation of a barotropic current flowing along sloping topography. It is shown that the shallow water equations can be reduced to a heat‐like equation in which β effect is balanced by Ekman dissipation. For constant topography, the system is found to admit a well‐known similarity solution and this solution is generalized to the case of variable topography. Several properties of the solution are explored, and an example is given for flow along the northern Gulf of Mexico slope, between the De Soto Canyon and the Mississippi Canyon. This “Topographic β ‐plume” solution may serve as a model for further research concerning the influence exerted by geophysical boundary layers on the interior flow via their structure and stability.