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Evolution of a solitary wave travelling along a submerged sill is studied. The disturbance from the sill creates a phase lag along the wave crest between the ambient water depth and the shallower depth over the sill. This phase lag causes wave diffraction between the different parts of the wave, which induces radiating waves off the edge of the sill. The radiating waves act as an outlet for wave energy, resulting in significant and continual amplitude reduction of the solitary wave. Findings from laboratory experiments are confirmed numerically by simulating a much longer propagation distance with different sill breadths. When the sill breadth is narrow, the solitary wave slowly attenuates by wave radiation, maintaining a quasi-steady wave pattern. This is not the case for a broader sill. The resulting phase lag on the sill continually changes the wave pattern and the attenuation rate is substantially greater than the rate for the case of the narrow sill. The significant energy radiation together with the continual change in the wave formation eventually leads to the complete annihilation of the solitary wave in a wave tank. We also report a wave-breaking process along the sill observed in laboratory experiments. This breaking is induced when the wave amplitude on the sill is smaller than the maximum amplitude of a solitary wave in a uniform depth. Also found is the wake-like formation of gravity–capillary waves behind the breaking crest forming on the sill. Other features associated with the breaking are presented.
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Solitary wave fission of a large disturbance in a viscous fluid conduit
This paper presents a theoretical and experimental study of the long-standing fluid mechanics problem involving the temporal resolution of a large localised initial disturbance into a sequence of solitary waves. This problem is of fundamental importance in a range of applications, including tsunami and internal ocean wave modelling. This study is performed in the context of the viscous fluid conduit system – the driven, cylindrical, free interface between two miscible Stokes fluids with high viscosity contrast. Owing to buoyancy-induced nonlinear self-steepening balanced by stress-induced interfacial dispersion, the disturbance evolves into a slowly modulated wavetrain and further into a sequence of solitary waves. An extension of Whitham modulation theory, termed the solitary wave resolution method, is used to resolve the fission of an initial disturbance into solitary waves. The developed theory predicts the relationship between the initial disturbance’s profile, the number of emergent solitary waves and their amplitude distribution, quantifying an extension of the well-known soliton resolution conjecture from integrable systems to non-integrable systems that often provide a more accurate modelling of physical systems. The theoretical predictions for the fluid conduit system are confirmed both numerically and experimentally. The number of observed solitary waves is consistently within one to two waves of the prediction, and the amplitude distribution shows remarkable agreement. Universal properties of solitary wave fission in other fluid dynamics problems are identified.
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- Award ID(s):
- 1816934
- PAR ID:
- 10177608
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 883
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2019.830
