Wave–current interaction

In fluid dynamics, wave–current interaction is the interaction between surface gravity waves and a mean flow. The interaction implies an exchange of energy, so after the start of the interaction both the waves and the mean flow are affected.

For depth-integrated and phase-averaged flows, the quantity of primary importance for the dynamics of the interaction is the wave radiation stress tensor.

Wave–current interaction is also one of the possible mechanisms for the occurrence of rogue waves, such as in the Agulhas Current. When a wave group encounters an opposing current, the waves in the group may pile up on top of each other which will propagate into a rogue wave.^[1][2]

Classification

Peregrine (1976) identifies five major sub-classes within wave–current interaction:

• interaction of waves with a large-scale current field, with slow – as compared to the wavelength – two-dimensional horizontal variations of the current fields;
• interaction of waves with small-scale current changes (in contrast with the case above), where the horizontal current varies suddenly, over a length scale comparable with the wavelength;
• the combined wave–current motion for currents varying (strongly) with depth below the free surface;
• interaction of waves with turbulence; and
• interaction of ship waves and currents, such as in the ship's wake.

See also

• generalized Lagrangian mean
• rip current

Footnotes

1. Dysthe, Kristian; Krogstad, Harald E.; Müller, Peter (2008), "Oceanic rogue waves", Annual Review of Fluid Mechanics, 40: 287–310, Bibcode:2008AnRFM..40..287D, doi:10.1146/annurev.fluid.40.111406.102203
2. Peregrine (1976)

References

• Bretherton, F. P.; Garrett, C. J. R. (1968), "Wavetrains in inhomogeneous moving media", Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 302 (1471): 529–554, Bibcode:1968RSPSA.302..529B, doi:10.1098/rspa.1968.0034
• Bühler, O. (2014), Waves and mean flows (2nd ed.), Cambridge University Press, ISBN 978-1-107-66966-6
• Peregrine, D. H. (1976), "Interaction of water waves and currents", Advances in Applied Mechanics, 16, Academic Press, pp. 9–117, ISBN 978-0-12-002016-4
• Phillips, O. M. (1977), The dynamics of the upper ocean (2nd ed.), Cambridge University Press, ISBN 0-521-29801-6
• Craik, A. D. D. (1988), Wave interactions and fluid flows, Cambridge University Press, ISBN 0-521-36829-4
• Prandle, D. (1992), Dynamics and exchanges in estuaries and the coastal zone, Coastal and estuarine studies, 40, American Geophysical Union, ISBN 0-87590-254-5
• Jonsson, I. G. (1990), "Wave–current interactions", in B. Le Méhauté and D. M. Hanes, Ocean Engineering Science, The Sea, 9A, Wiley Interscience, pp. 65–120, ISBN 0-471-11543-6