# 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.
10.1080/03091920802604648

## 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 |
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Digital Object Identifier (DOI): | 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 |

URI: | http://nora.nerc.ac.uk/id/eprint/15936 |

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