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Hamiltonian Structure and a Variational Principle for Grounded Abyssal Flow on a Sloping Bottom in a Mid‐Latitude β‐Plane.

Authors :
Swaters, Gordon E.
Source :
Studies in Applied Mathematics. Aug2018, Vol. 141 Issue 2, p247-263. 17p. 1 Diagram, 1 Graph.
Publication Year :
2018

Abstract

Abstract: Observations, numerical simulations, and theoretical scaling arguments suggest that in mid‐latitudes, away from the high‐latitude source regions and the equator, the meridional transport of abyssal water masses along a continental slope correspond to geostrophic flows that are gravity or density driven and topographically steered. These dynamics are examined using a nonlinear reduced‐gravity geostrophic model that describes grounded abyssal meridional flow over sloping topography that crosses the planetary vorticity gradient. It is shown that this model possesses a noncanonical Hamiltonian formulation. General nonlinear steady solutions to the model can be obtained for arbitrary bottom topography. These solutions correspond to nonparallel shear flows that flow across the planetary vorticity gradient. If the in‐flow current along the poleward boundary is strictly equatorward, then no shock can form in the solution in the mid‐latitude domain. It is also shown that the steady solutions satisfy the first‐order necessary conditions for an extremal to a suitably constrained potential energy functional. Sufficient conditions for the definiteness of the second variation of the constrained energy functional are examined. The theory is illustrated with a nonlinear steady solution corresponding to an abyssal flow with upslope and down slope groundings in the height field. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00222526
Volume :
141
Issue :
2
Database :
Academic Search Index
Journal :
Studies in Applied Mathematics
Publication Type :
Academic Journal
Accession number :
131052032
Full Text :
https://doi.org/10.1111/sapm.12224