If is a general material surface in a flow in the space, we show the relationship between the three components of the vorticity field on and the curvatures of the streamlines of the tangential component of the velocity field (geodesic torsion, normal curvature, and geodesic curvature); and we show the relationship for the case of a general free surface. We present geometric formulae relating vorticity flux, from , and curvatures of (Gaussian curvature, mean curvature, curvatures of the streamlines of the tangential component of the velocity field); and we show the formulae for the case of a general free surface.
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2010
American Institute of Physics
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