Barotropic instability of coastal flows as a boundary-value problem: linear and non-linear theory

Willmott, Andrew J.; Cushman-Roisin, Benoit. 2009 Barotropic instability of coastal flows as a boundary-value problem: linear and non-linear theory. Geophysical and Astrophysical Fluid Dynamics, 103 (4). 279-292. https://doi.org/10.1080/03091920802604648

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Abstract/Summary

The barotropic instability is traditionally viewed as an initial-value problem wherein wave perturbations of a laterally sheared flow in a homogeneous uniformly rotating fluid that temporally grows into vortices. The vortices are capable of mixing fluid on the continental shelf with fluid above the continental slope and adjacent deep-sea region. However, the instability can also be viewed as a boundary-value problem. For example, a laterally sheared coastal flow is perturbed at some location, creating perturbations that grow spatially downstream. This process leads to a time periodic flow that exhibits instability in space. This article first examines the linear barotropic instability problem with real frequency and complex wavenumber. It is shown that there exists a frequency band within which a spatially growing wave is present. It is then postulated that far downstream the spatially unstable flow emerges into a chain of identically axisymmetric vortices. Conservation of mass, momentum and energy fluxes are applied to determine the diameter, spacing and the speed of translation of the vortices

Item Type:	Publication - Article
Digital Object Identifier (DOI):	https://doi.org/10.1080/03091920802604648
ISSN:	0309-1929
Additional Keywords:	VORTICES; CONTINENTAL SHELF; COASTAL FLOW; BAROTROPIC INSTABILITY; ROTATING FLUIDS; BOUNDARY VALUE PROBLEM;
NORA Subject Terms:	Marine Sciences
Date made live:	21 Nov 2011 11:11 +0 (UTC)
URI:	https://nora.nerc.ac.uk/id/eprint/15936

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