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A Weak Formulation of the Shallow-Water Equations for a Rotating Basin

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  • 1 Instituto di Geofisico dell'Università di Bologna, Via Irnerio 46, 40126 Bologna, Italy
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Abstract

A weak formulation of the equation for the elevation field arising from the shallow-water equations for a rotating inviscid fluid has been developed.

The difficulties of this problem, which are due chiefly to the fact that the normal velocity along the contour is given by a linear combination of normal and tangential derivatives of the elevation field, are overcome. As a result, many problems, until now treated using the elevation and velocity component variables, might be solved dealing only with the elevation.

Abstract

A weak formulation of the equation for the elevation field arising from the shallow-water equations for a rotating inviscid fluid has been developed.

The difficulties of this problem, which are due chiefly to the fact that the normal velocity along the contour is given by a linear combination of normal and tangential derivatives of the elevation field, are overcome. As a result, many problems, until now treated using the elevation and velocity component variables, might be solved dealing only with the elevation.

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