Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Steep and Breaking Faraday Waves
Steep and Breaking Faraday Waves
Pages 812-826
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At larger forcing amplitude, we have observed experimentally a steep waveform with a double-peaked crest, while simulation of the same forcing condition results in a sharper crest (Jiang et al., 1996~. Increasing wave steepness leads first to a double-plunging breaker at the dimpled crest, then to more violent breaking in three recurrent modes (period tripling)
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(1996) is that for larger wave steepness, unexpected flat and dimpled crests appear in the physical experiments while the numerical simulation presents a wave with much sharper crest.
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By comparing with images taken by an 8 mm camera without dye present, we verified that the small change in surface tension does not cause a change in the wave profiles For the time history of surface elevation, we used a capacitance-type wave probe with an outside diameter of 1.6 mm positioned at the horizontal center of the tank. The measurement error is less than 1% of the wave height.
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In both situations, flat and dimpled crests appear in the forced standing waves when the wave steepness H/) exceeds 0.15.
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As shown in the analysis of the dimpled waveform, when the second harmonic has relatively large amplitude, different phase angles between the second harmonic and the fundamental mode introduce different wave forms: a zero phase difference produces waveforms similar to that of Penney & Price (1952~; a wave with a dimpled crest has a positive phase difference 82 - 28: between 90° and 180°; a sharp-crested waveform has a negative phase angle 82 - 28: ~—40° in the numerical experiments. Therefore, the three modes in the breaking events are strongly connected with the interaction between the first and second harmonics.
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Increasing the forcing amplitude or decreasing the forcing frequency causes the wave with dimpled crest to become unstable. It leads to period tripling with three breaking modes: mode A: sharp crest forms, the upward jet or the large plunger to each side impinges on the ware surface, creating bubbles and a strong rebounding jet; mode B: the waveform has a flat or dimpled crest, two outward plungers forms to each side of the crest; mode C: the crest is round and smooth, significant breaking is absent.
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& STL\SSNIE, M 1994 Different forms for nonlinear standing waves in deep water.
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(a) Maximum wave profiles with crest at center for 3.32 Hz forcing in physical experiments.
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Small breaking at the dimpled crest. Forcing frequency is 3.17 Hz.
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The detected wave profiles tic al scale is 1.5 times tile horizontal scale. for column (a)
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In die detected wave profiles, tile vertical scale is 1.S times die honzontal scale.
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Tl~e forcing amplitude is 4.6 mm, forcing frequency is 3.20 Hz. Note that die time intervals between frames are not the same.
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Figure 18. Complex demodulated wave probe signal at forcing frequency 3.20 Hz and forcing amplitude 4.57 mm.
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Forcing frequency: 3.22 Hz Figure 25. The crest structure at tile maximum wave elevation of mode A
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DISCUSSION E Palm University of Oslo, Norway It is an interesting and important topic which is discussed in this paper.
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