Willert, Christian E. and Gharib, Morteza (1997) The interaction of spatially modulated vortex pairs with free surfaces. Journal of Fluid Mechanics, 345 . pp. 227-250. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20120125-134914989
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Spatially modulated vortex pairs were generated below a free surface by two counter-rotating flaps whose edges approximate a sinusoid. The surface interactions of the vertically approaching vortex pairs were visualized by the shadowgraph technique. Two limiting cases were investigated in detail: the interaction with a surfactant-rich (contaminated) surface and with a surfactant-poor (‘clean’) surface. In the latter case shadowgraph images showed that the underlying vortex core formed a line of circular surface depressions. Subsequent measurements of the temporally evolving velocity fields using digital particle image velocimetry (DPIV) of the vortex pair cross-sections and the subsurface plane confirmed the connection process of the main vortex core with the surface. As a result of the connection the initially modulated vortex tube was broken into a line of U-vortices. In the presence of surfactants this connection could not be observed; rather a Reynolds ridge (or stagnation line) was formed and a very weak connection of the secondary separation vortex could be seen in the shadowgraphs as well as measured with the time-resolved DPIV technique. A prerequisite for connection of the vortex with the surface is that the flow's kinematics force the vortex core, that is, regions of concentrated vorticity, toward the surface. The ensuing locally concentrated viscous flux of surface-parallel vorticity through the surface is balanced by a local surface deceleration. Surface-normal vorticity appears on each side of the decelerated region whose gradually increasing circulation is directly balanced by the loss of circulation of the surface-parallel vortex. However, the shear forces caused by small amounts of surface contamination and its associated subsurface boundary layer inhibit the connection process by preventing the essential viscous flux of parallel vorticity through the surface. Instead, the subsurface boundary layer is associated with a flux of parallel vorticity into the surface which then concentrates into the observable secondary separation vortex.
|Additional Information:||© 1997 Cambridge University Press. Received 19 September 1995 and in revised form 18 April 1997. Published online: 08 September 2000. This work was sponsored by the Office of Naval Research under a URI Grant (N00014-92-J-1610).|
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|Deposited By:||Tony Diaz|
|Deposited On:||28 Feb 2012 19:09|
|Last Modified:||30 Sep 2016 17:35|
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