Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Generation Mechanisms and Sources of Vorticity Within a Spilling Breaking Wave
Generation Mechanisms and Sources of Vorticity Within a Spilling Breaking Wave
Pages 520-533
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From page 520... ...
, berg the fast Furthermore, a thin free surface fluid layer is found to to experimentally study the spilling breaking wave, pride wave breaking that moves et a fester speed with showed~at there exists a turbulent wake behead Me respect to the fluid directly beneath it and to the fluid spilling breaker which extended downstream beyond Me bulk. For the second case, also based on the wave breaker, even though the flow remans highly l~min~r height,the Reynolds and Frouden~berswerelSOO and and steady prior tobreaking.Peregr~ne and Svendson(4)
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From page 521... ...
The water tunnel has a contraction ratio of 4:1, with a 15.2 x 15.2 x 61 cm3 test section. Previous approaches for generating spilling breaking waves have been to situate a hydrofoil located at some distance below the water level a water tunnel.
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From page 522... ...
Therefore a second set of experiments were done at lower Reynolds and Froude numbers to produce larger capillary waves, in order to determine their role in He vorticity flux. 3.1 Case 1: Higher Froude & Reynolds numbers For this case, the incoming velocity into the grid is 24.6 cm/s.
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From page 523... ...
For the vorticity plots, positive vorticity are shown by solid lines while negative vorticity are shown by Mashed lines. The capillaries preceding spilling wave breaking are <1 mm in wavelength, and were too small to produce results that clearly determine the role of the capillaries in vorticity production.
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From page 524... ...
surface and upstream of the positive vorticity layer are also evident. Also, the negative vorticity layer which was shown to exist beneath the Me surface highervelocity layer in section 1 still continues filer downstream beneath Me positive vorticity layer.
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From page 525... ...
Upon comparison of the flow of figures 9 and 11, it is seen that We positive vorticity shear layer origin has been displaced by 0.5 cm in the x-direction. In fact, after examining several minutes of the flow in detail, it became evident that this "breathing" effect is quite persistent yet erratic in amplitude, with an oscillation ,.
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From page 526... ...
Therefore, the dominant terms contributing to the vorticity flux are the gravity term and the deceleration term. Equation (1)
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From page 527... ...
Marker "b" at 4.4 cm shows the stagnation point of the flee surface fluid, and marker "c"at 4.35 cm shows initiation of wave breaking observed visually. For bow these cases, even [bough the vorticity flux peaks fluctuate back and forth with respect to breaking, the stagnation points are consistently within 0.1 cm of breaking, Bus verifying the observations of Banner and Phillips.
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From page 528... ...
... _ / the origin of the shear layer evident in figures 9, 1 l, mxl 0.
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From page 529... ...
Therefore, the vorticity must be fluxed deeper into the fluid, beyond the stagnation region, so that it can be convected downstream Trough the shear layer. A good check of the above analysis is to first calculate the net vorticity flux from the free surface into the fluid bunk by integrating We fluid deceleration at the fine surface; second, calculate the convected vorticity flux by integrating the vorticity flux in the y-direction for each x-location; and finally show Mat the vorticity fluxed into the flow is equal to the vorticity being convected through the flow.
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From page 530... ...
The vectors within Be velocity fields show Be magnitude and direction of the velocity vectors throughout each of the three sections. For the vorticity plots, positive vorticity are shown by solid lines while negative vorticity are shown by dashed lines.
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From page 531... ...
The vorticity field from this section concurs that Me positive shear layer seen within Me gravity wave does not separate from Me free surface, but follows its contour. Also, it is seen that 531 vorticity located beneath the trough of to ~ _ 12.8 12.6 12.4 ~ 1 2.2 .: IN 11.8 11.6 11.4 1.4 1.6 1.8 2 v c-> 'I x - ~ (cm)
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From page 532... ...
The integrated viscous vorticity flux shows that after the last trough, the final value achieved is ~200 cm2/s2 at x=2.2 cm, while that achieved by the integrated vorticity flux due to the gravity term at that point is ~0 cm2/s2. Thus, the capillaries do not contribute to the generation of positive vorticity.
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From page 533... ...
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 Bee surface, does not flux into the flow from the free surface.
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