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 waves perturbed by a broad sill. Part 1. Propagation across the sill
Stability of a solitary wave disturbed by a submerged flat sill is investigated experimentally. For sills narrow compared with the solitary wave, the transmitted waves are found to be unaffected in waveform and amplitude. A wider sill disturbs the solitary wave resulting in the formation of a dispersive wavetrain following the transmitted wave. In some cases, the wave amplitude recovers, despite being perturbed, to the state of an unobstructed solitary-wave state at a certain distance beyond the sill. Wider sills cause wave breaking that occurs over the sill or, in some cases, after the wave passes through the sill. Details of waveform transformation leading toward the breaking and subsequent energy dissipation are discussed.
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- Award ID(s):
- 1830024
- NSF-PAR ID:
- 10181595
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 880
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- 916 to 934
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Bathymetric sills are important features in the ocean-filled cavities beneath a few fast-retreating ice shelves in West Antarctica and northern Greenland. The sills can be high enough to obstruct the cavity circulation and thereby modulate glacial melt rates. This study focuses on the idealized problem of diabatically driven, sill-constrained overturning circulation in a cavity. The circulation beneath fast-melting ice shelves can generally be characterized by an inflow of relatively warm dense water (with temperatures of a few degrees Celsius above the local freezing point) at depth and cold, less-dense, outflowing water, which exhibits an approximately two-layer structure in observations. We use a two-layer isopycnal hydrostatic model to study the cross-sill exchange of these waters in ice shelf cavities wide enough to be rotationally dominated. A quasigeostrophic constraint is determined for the transport imposed by the stratification. Relative to this constraint, the key parameters controlling the transport and its variability are the sill height relative to the bottom layer thickness and the strength of the friction relative to the potential vorticity (PV) gradient imposed by the sill. By varying these two key parameters, we simulate a diversity of flow phenomena. For a given meridional pressure gradient, the cross-sill transport is controlled by sill height beyond a critical threshold in the eddy-permitting, low-friction regime, while it is insensitive to friction in both the low-friction and high-friction regimes. We present theoretical ideas to explain the flow characteristics: a Stommel boundary layer for the friction-dominated regime; mean–eddy PV balances and energy conversion in the low-friction, low-sill regime; and hydraulic control in the low-friction, high-sill regime, with various estimates for transport in each of these regimes.
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Abstract Linear theory has long been used to study mountain waves and has been successful in describing much of their behaviour. In the simplest theoretical context, that of two‐dimensional steady‐state flow with constant Brunt–Väisälä frequency (
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2019.712
