Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Measurement and Computations of Vortex Pair Interaction with a Clean or Contaminated Free Surface
Measurement and Computations of Vortex Pair Interaction with a Clean or Contaminated Free Surface
Pages 521-532
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From page 521... ...
New vorticity produced on either side of the vortex pair when the surface is contaminated initially forms a Reynolds ridge, (the surface signature at the leading edge of a subsurface boundary layer) , and then the new vorticity beneath the contaminated surface rolls up to form secondary vortices outboard of the original vortices and with opposite sign.
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From page 522... ...
A steady state boundary layer is formed as a result of a balance between viscous shear forces in the viscous flow beneath the surface and the force produced by gradients in the surface tension which are a result of surface active agent concentration gradients in the blocked film of surface active agent. At the leading edge of the contaminated surface, where the surface tension begins to decrease, there is a rapid variation in height of the surface which appears as an easily observable ridge.
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From page 523... ...
, are for an initially clean free surface with 1.06 x 10-7 (cm3/cm2) of oleyl alcohol spread on the surface before the vortex pairs were generated.
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From page 524... ...
The case without oleyl alcohol shows no sign of secondary vorticity formation or rebounding of the primary vortices. Free Surface Secondary Vortices V , ,_ ,~-' ~` \.\ 1 1 1 -- Free Surface - no surfactant added - " w/ Oleyl alcohol, ~0.3 - 1.1 1 ..
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From page 525... ...
The trajectories plotted in Figure 4 show that when oleyl alcohol is present on the free surface, the trajectory of the primary vortex departs from the trajectory for the case with no surfactant. From these trajectories it is apparent that the greater the surface pressure, the greater the amount of rebounding of the primary vortex from the free surface.
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From page 526... ...
on the contaminated side of the Reynolds ridge. The surface deformations on the ~ight side of the same vortex pair formed when a small amount of oleyl alcohol, surface pressure of 0.3 (dynes/cm)
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From page 527... ...
as the previous two figures but with a higher concentration of oleyl alcohol. For this case, enough oleyl alcohol was spread on the surface to saturate it so that the surface pressure was equal to the saturation pressure which for oleyl alcohol is approximately 31.5 (dynes/cm)
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From page 528... ...
A slight boundary layer (not visible at the initial time, t = tip is formed beneath the contaminated surface an instant after the motion begins. In the second frame the upward motion of the vortex has ended, and, due to the image vortieity above the free surface, it is now moving outward.
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From page 529... ...
Except for the completely stress free boundary a secondary vortex is formed and the primary vortex rebounds, even though in some cases a clean region is formed, and in others the contaminant distribution is hardly changed at all. The only difference in the vorticity distribution is that the boundary layer at the top starts further away from the center when a clean region is formed.
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From page 530... ...
To efficiently display the similarities and differences in the flow fields caused by the surface boundary condition and/or Reynolds number, we plot in Figure 12 (a) , the path of the primary vortices and secondary vortices, at Re = 2000, for the no-stress case, for a contaminated surface with C = 2 and for the rigid boundary case.
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From page 531... ...
, an exact comparison between the vortex pair flow and the actual ship wake is not possible and in fact is not intended. The vortex pair offers a simple flow which can be studied in order to provide insight into the nonlinear ship wake problem.
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