Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T20:45:36.892Z Has data issue: false hasContentIssue false
  • English
  • Français

On surface gravity waves crossing weak current jets

Published online by Cambridge University Press:  20 April 2006

Jerome Smith
Jerome Smith
Affiliation:
Department of Oceanography, Naval Postgraduate School, Monterey, CA 93940
Get access Rights & Permissions [Opens in a new window]

Abstract

Variations in wave amplitude and steepness across current jets have been described for broad smooth-sided jets. Here, narrow jets are modelled by a top-hat pattern; an approximate solution is found for linear waves, based on conservation of wave action and vertical averaging. The results join remarkably well to those for a broad cosine-shaped jet (cf. McKee 1975). For jet widths less than about a third of a wavelength, there is little change in amplitude; the enhancement predicted by a WKB analysis is suppressed owing to interference with reflections from the far side of the jet. For directional spectra not too different from cos2 θ, some suppression occurs near the middle of jets of all scales, owing to exclusion of the glancing wave components by reflection from the near side; this suppression can be significant for jets more than a wavelength wide. For monochromatic waves, maximum amplitudes occur some distance outside the jet owing to interference; the net reflection appears to have a positive phase shift along the near caustic of about ¼ cycle.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 134 , September 1983 , pp. 277 - 299
Copyright
© 1983 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. 1965 Handbook of Mathematical Functions. Dover.
Andrews, D. G. & Mcintyre, M. E. 1978 On wave-action and its relatives J. Fluid Mech. 89, 647–664.Google Scholar
Craik, A. D. D. 1977 The generation of Langmuir circulation by an instability mechanism J. Fluid Mech. 81, 209–223.Google Scholar
Evans, D. V. 1975 The transmission of deep-water waves across a vortex sheet J. Fluid Mech. 68, 389–401.Google Scholar
Garrett, C. 1976 Generation of Langmuir circulation by surface waves: a feedback mechanism. J. Mar. Res. 34, 117–130.
Jones, D. S. & Morgan, J. D. 1972 The instability of a vortex sheet on a subsonic stream under acoustic radiation Proc. Camb. Phil. Soc. 72, 465–488.Google Scholar
Langmuir, I. 1938 Surface motion of water induced by wind Science 87, 119–123.Google Scholar
Leibovich, S. 1977 Convective instability of stably stratified water in the ocean J. Fluid Mech. 82, 561–581.Google Scholar
Longuet-Higgins, M. S. 1977 Some effects of finite steepness on the generation of waves by the wind. In A Voyage of Discovery: George Beacon 70th Anniversary Volume (ed. M. Angel), pp. 393–403. Pergamon press.
Mckee, W. D. 1974 Waves on a shearing current: a uniformly valid asymptotic solution. Proc. Camb. Phil. Soc. 75, 295–301.
Mckee, W. D. 1975 A two-turning point problem in fluid mechanics Math. Proc. Camb. Phil. Soc. 77, 581–590.Google Scholar
Mckee, W. D. 1977 The reflection of water waves by shear currents Pure Appl. Geophys. 115, 937–949.Google Scholar
Miles, J. W. 1958 On the disturbed motion of a plane vortex sheet J. Fluid Mech. 4, 538–552.Google Scholar
Myer, G. E. 1971 Structure and mechanism of Langmuir circulations on a small lake. PhD dissertation, S. Univ. of N.Y. and Albany, Dept of Limnology.
Peregrine, D. H. 1976 Interaction of water waves and currents Adv. Appl. Mech. 16, 9–117.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean, 2nd edn. Cambridge University Press.
Phillips, O. M. & Banner, M. L. 1974 Wave breaking in the presence of wind drift and swell J. Fluid Mech. 66, 625–640.Google Scholar
Smith, J. A. 1980 Waves, currents, and Langmuir circulation. PhD thesis, Dept of Oceanography, Dalhousie U., Halifax, N.S., Canada.
Smith, R. 1976 Giant waves J. Fluid Mech. 77, 417–431.Google Scholar
Stewart, R. H. & Joy, J. W. 1974 HF radio measurements of surface currents Deep-Sea Res. 21, 1039–1049.Google Scholar