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distinction between these regions, shows that the surface discontinuous point does not serve as a source of vorticity, but rather as point from which the vorticity separates into a shear layer.

Case 2, the lower Reynolds and Froude number case, shows that the capillary curvature provides a negligible contribution of the gravity term to the vorticity flux, and that the contribution is dominated by the deceleration term as the flow passes through the capillaries. The net flux of vorticity into the flow is shown to be one order of magnitude smaller than that seen in case 1, which would also serve as an indication of the separating shear layer in case 2. Also, the vorticity seen beneath the capillaries is due to the free surface curvature, and while remaining at the free surface, does not flux into the flow from the free surface. The vorticity is thus confined to a region within a thickness of the order of the capillary amplitude.

ACKNOWLEDGMENTS

This work is supported by URI research grant number N00014–92-J-1618 by the office of Naval Research. We gratefully acknowledge the insightful discussions with Dr. Longuet-Higgins, Dr. Doug Dommermuth, and Dr. Edwin Rood that lead to our insight into this topic.

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