Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Scarred and Striated Signature of a Vortex Pair on the Free Surface
Scarred and Striated Signature of a Vortex Pair on the Free Surface
Pages 503-520
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From page 503... ...
, are investigated through the use of an infra-red camera, flow visualization, an image analysis system, and the vortex-element method. The results have shown that the striations are a consequence of the short wavelength instability, inherent to the vortex pair itself, and the whirls result from the interaction of striations with the surface vorticity Dice = 2qK, twice the tangential velocity times the curvature of the intersection of the free surface with the plane normal to it)
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From page 504... ...
For small Froude numbers Fr (= VO/~O, where VO is the initial mutual induction velocity of the vortex pair) , the vortices follow the simple path described by Lamb's potential-flow solution, the free surface remains fairly flat, and each scar front Fig.
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From page 505... ...
6 Sample vortex-center paths Fig. 7 Sample scar cross sections viscous- or inviscid-flow numerical models, the results are not likely to lead to the understanding of the physics of the dark narrow images.
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From page 506... ...
The wave number ,B for the short wavelength instability varies from about 4 to 17, corresponding to wavelengths of ~ = 0.37bo to 1~57bo. It is in view of the foregoing that it was decided to generate nearly two-dimensional vortex pairs at relatively large Froude numbers, rather than inclined trailing vortices at relatively small Froude numbers, and to construct a numerical model of the threedimensional surface structures.
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From page 507... ...
The initial separation ho of the vortex pair was chosen as the reference length; the mutual-induction velocity VO of the vortex pair as the reference velocity; bo/Vo as the reference time, and the initial strength F0 of a vortex as the reference vortex strength. The equations describing the motion were non-dimensionalized through the use of the characteristic parameters ho, VO, bo/Vo' and IN where VO = F0 /~2~bol.
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From page 508... ...
, 2 ~amalgamation distance, etc., have shown that the fundamental nature of the randomly dis tributed vortices within a narrow band is to self-limit the amalgamation process and to reduce the effect of the imposed perturba tions (for sensitivity analysis) on the result ing characteristics of the scar band.
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From page 509... ...
Several plots were created at regular intervals during the execution of the numerical simulation, carried out to times corresponding to the disappearance of the surface structures, in order to compare the predicted results with those obtained experimentally. DISCUSSION OF RESULTS Physical Experiments A careful frame-by-frame analysis of the video recordings of literally hundreds of test runs has shown that the sloping of the vortex pair relative to the free surface or the generation of vortices by a lifting surface is not necessary for the creation of scars and striations.
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From page 510... ...
12-15) , i.e., the striations (nearly uniform corrugations, at least at their inception} are a manifestation of the short wavelength instability of the vortex pair.
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From page 511... ...
The histograms of the striation wavelength have shown that \/bo varies from about 0.75 to 1.25, depending primarily on the initial rollup of the vortex sheets as dictated by the Froude number. As far as a vortex pair in an infinite homogeneous medium is concerned, the striational instability corresponds to the short wavelength instability (see Fig.
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From page 512... ...
Figure 20 shows the evolution of a whirl and its neighborhood during a time interval of 0.25 seconds. It is clear that neither a trailing vortex pair nor a nearly two-dimensional Kelvin oval, neither a contaminated free surface nor a Reynolds ridge is necessary to create scars and striations.
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From page 513... ...
It will be interesting to discover as to how the scar band, comprised of whirls, tend to increase the radar return in order to provide bright lines in the SAR images. Numerical Experiments Figures 21a through 21c show at So/bo = 1.6 (where time is taken to be ~ = 0 I, the position of the whirls, the streamlines (with respect to a coordinate system moving with the scars)
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From page 514... ...
However, the amalgamation process does lead to a set of larger whirls. The increase of the number of large structures slows down or stops after a short time period.
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From page 515... ...
The sloping of the vortex pair (as in the case of trailing vortices) is not necessary to produce surface signatures or footprints of vortex wakes in the form of scars and stri s~s
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From page 516... ...
3. The short-wavelength instability has a wavelength in the order of unity, compared with the initial spacing of the main vortex pair.
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From page 517... ...
7. Among the numerous mechanisms proposed to explain the physics of the SAR images, the hypothesis of the interaction of a vortex pair with the free surface emerges as the most viable one in view of the observations and measurements made and the conclusions arrived at in this investigation.
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From page 518... ...
E., Jr., "Free Surface Scars due to a Vortex Pair," M.S. Thesis, Naval Postgraduate School, Monterey, CA., March 1988.
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From page 519... ...
Can you comment upon the possible importance of the vortex-free surface interactions discussed in your paper as they might apply to the remotely sensed surface ship wake? AUTHORS' REPLY As I have noted in the Introduction of the written version of the paper, "Just a narrow patch of darkness, bounded by two bright lines, provides the impetus for this investigation partly because it is seen in the synthetic aperture radar (SAR)
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