A shallow water model with eddy viscosity for basins with varying bottom topography

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Published 18 September 2001 • Published under licence by IOP Publishing Ltd
, , Citation C David Levermore and Marco Sammartino 2001 Nonlinearity 14 1493 DOI 10.1088/0951-7715/14/6/305

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Author affiliations

1 Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA

2 Dipartimento di Matematica, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy

3 Current address: Department of Mathematics, University of Maryland, College Park, MD 20742, USA.

Dates

  1. Received 24 July 2000
  2. Published

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0951-7715/14/6/1493

Abstract

The motion of an incompressible fluid confined to a shallow basin with a varying bottom topography is considered. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model to derive a two-dimensional shallow water model. The global regularity of the resulting model is proved. The anisotropic form of the stress tensor in our three-dimensional eddy viscosity model plays a critical role in ensuring that the resulting shallow water model dissipates energy.

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10.1088/0951-7715/14/6/305