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Vorticity and curvature at a free surface

Published online by Cambridge University Press:  10 February 1998

MICHAEL S. LONGUET-HIGGINS
MICHAEL S. LONGUET-HIGGINS
Affiliation:
Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093-0402, USA
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Abstract

For two-dimensional flow there is a simple relation between the vorticity at a stress-free surface and the surface curvature. In this note the relation is generalized to flow in three dimensions. It is shown that in addition to a component of vorticity perpendicular to the flow there is also a component parallel to the direction of flow. The latter vanishes only at an umbilical point or when the flow is in one of the two principal directions of curvature.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 356 , 10 February 1998 , pp. 149 - 153
Copyright
© 1998 Cambridge University Press

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