Wave–current interaction on a free surface

Crisan, Dan; Holm, Darryl D.; D., Street, Oliver

doi:10.1111/sapm.12425

Cited by 4 publications

(8 citation statements)

References 53 publications

(166 reference statements)

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“…Remark 2.1 (Separation of wave and current circulation.). The decoupling of the Kelvin-Noether circulation theorem into its wave and current components, leading to the reduction of the current flow to the Euler result in equation (2.14), was also observed in [6]. This behaviour is consistent with the Carney-Drazin 'non-acceleration' theorem [4,20].…”

Section: A Tale Of Two Maps: Currents and Wavessupporting

confidence: 71%

“…In terms of these fluid variables, Hamilton's principle for wave-current interaction of a free surface is obtained by following [6] for the variational modelling framework and [21,5] for the potential energy…”

Section: A Tale Of Two Maps: Currents and Wavesmentioning

confidence: 99%

“…Namely, in certain circumstances, wave activity does not create circulation in the mean current. A modification that allows exchange of circulation between wave (vertical) and current (horizontal) components of the flow was proposed in [6]. The instabilities observed around the edges of eddies in the satellite imagery shown in figure 1 suggests that a coupling of this sort may exist at high wave number.…”

Section: A Tale Of Two Maps: Currents and Wavesmentioning

confidence: 99%

“…In[6] the potential energy was linear in ζ. This linearity neglected the restoring force due to vertical pressure gradient via Archimedes' principle.…”

mentioning

confidence: 99%

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Coupling of waves to sea surface currents via horizontal density gradients

Holm¹,

Ruiao²,

D.³

2022

Preprint

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The mathematical models and numerical simulations reported here are motivated by satellite observations of horizontal sea surface fluid motions that are closely coordinated with the vertical motion of waves or, after an approximation, an envelope of rapidly oscillating waves. This coordination of fluid movements with wave envelopes tends to occur when strong horizontal buoyancy gradients are present. The nonlinear models of this coordinated movement presented here may provide future opportunities for the optimal design of satellite imagery that could simultaneously capture the dynamics of both waves and currents directly.The models derived here appear first in their unapproximated form, then again with a slowly varying envelope (SVE) approximation using the WKB approach.The WKB wave-current-buoyancy interaction model derived here for a free surface with horizontal buoyancy gradients indicates that the mechanism for these correlations is the ponderomotive force of the slowly varying envelope of rapidly oscillating waves acting on the surface currents via the horizontal buoyancy gradient. In this model, the buoyancy gradient appears explicitly in the WKB wave momentum, which in turn generates density-weighted potential vorticity whenever the buoyancy gradient is not aligned with the wave-envelope gradient.

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Section: A Tale Of Two Maps: Currents and Wavessupporting

confidence: 71%

Section: A Tale Of Two Maps: Currents and Wavesmentioning

confidence: 99%

Section: A Tale Of Two Maps: Currents and Wavesmentioning

confidence: 99%

“…In[6] the potential energy was linear in ζ. This linearity neglected the restoring force due to vertical pressure gradient via Archimedes' principle.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Coupling of waves to sea surface currents via horizontal density gradients

Holm¹,

Ruiao²,

D.³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In terms of these fluid variables, one could propose a Hamilton's principle for wavecurrent interaction of a free surface by following [8] for the variational modelling framework and applying [24,7] for the potential energy to find 1…”

Section: Submesoscale Sea-surface Motion: Composition Of Two Time-dep...mentioning

confidence: 99%

Coupling of Waves to Sea Surface Currents Via Horizontal Density Gradients

Holm

Ruiao

2022

Mathematics of Planet Earth

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The mathematical models and numerical simulations reported here are motivated by satellite observations of horizontal gradients of sea surface temperature and salinity that are closely coordinated with the slowly varying envelope of the rapidly oscillating waves. This coordination of gradients of fluid material properties with wave envelopes tends to occur when strong horizontal buoyancy gradients are present. The nonlinear models of this coordinated movement presented here may provide future opportunities for the optimal design of satellite imagery that could simultaneously capture the dynamics of both waves and currents directly.The model derived here appears in two levels of approximation: first for rapidly oscillating waves, and then for their slowly varying envelope (SVE) approximation obtained by using the WKB approach. The WKB wave-current-buoyancy interaction model derived here for a free surface with significant horizontal buoyancy gradients indicates that the mechanism for the emergence of these correlations is the ponderomotive force of the slowly varying envelope of rapidly oscillating waves acting on the surface currents via the horizontal buoyancy gradient. In this model, the buoyancy gradient appears explicitly in the WKB wave momentum, which in turn generates density-weighted potential vorticity whenever the buoyancy gradient is not aligned with the wave-envelope gradient.

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Lagrangian reduction and wave mean flow interaction

Holm

Ruiao

2023

Physica D: Nonlinear Phenomena

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Wave–current interaction on a free surface

Cited by 4 publications

References 53 publications

Coupling of waves to sea surface currents via horizontal density gradients

Coupling of waves to sea surface currents via horizontal density gradients

Coupling of Waves to Sea Surface Currents Via Horizontal Density Gradients

Lagrangian reduction and wave mean flow interaction

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