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Mean flows generated by a progressing water wave packert

Published online by Cambridge University Press:  17 February 2009

R. Grimshaw
R. Grimshaw
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052
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Abstract

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Equations are derived which describe the evolution of the mean flow generated by a progressing water wave packet. The effect of friction is included, and so the equations are subject to the boundary conditions first derived by Longuet-Higgins [10]. Solutions of the equations are obtained for a wave packet of finite length, and also for a uniform wave train. The latter solution is compared with experiments.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 3 , January 1981 , pp. 318 - 347
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Andrews, D. G. and McIntyre, M. E., ‘An exact theory of nonlinear waves on a Lagrangianmean flow”, J. Fluid Mech. 89 (1978), 609–646.CrossRefGoogle Scholar
[2]Andrews, D. G. and McIntyre, M. E., “On wave-action and its relatives”, J. Fluid Mech. 89 (1978), 647–664.CrossRefGoogle Scholar
[3]Bretherton, F. P. and Garrett, C. J. R., “Wave trains in inhomogeneous moving media”, Proc. Roy. Soc. 302A (1969), 529–554.Google Scholar
[4]Chang, M.-S., “Mass transport in deep-water long-crested random gravity waves”, J. Geophys. Res. 74 (1969), 1515–1536.CrossRefGoogle Scholar
[5]Davey, A. and Stewartson, K., “On three-dimensional packets of surface waves”, Proc. Roy. Soc. 338A (1974), 101–110.Google Scholar
[6]Dore, B. D., “On mass transport velocity due to progressive waves”, Quart. J. Mech. Appl. Maths. 30 (1977), 157–173.CrossRefGoogle Scholar
[7]Grimshaw, R., “Mean flows induced by internal gravity wave packets propagating in a shear flow”, Phil. Trans. Roy. Soc. 292A (1979), 391–417.Google Scholar
[8]Huang, N. E., “Mass transport induced by wave motion”, J. Mar. Res. 34 (1970), 35–50.Google Scholar
[9]Liu, A-K. and Davis, S. H., “Viscous attenuation of mean drift in water waves”, J. Fluid Mech. 81 (1977), 63–84.CrossRefGoogle Scholar
[10]L.onguet-Higgins, M. S., “Mass transport in water waves”, Phil. Trans. Roy. Soc. 245A (1953), 535–581.Google Scholar
[11]Longuet-Higgins, M. S., “Mass transport in the boundary layer at a free oscillating surface”, J. Fluid Mech. 8 (1960), 293–306.CrossRefGoogle Scholar
[12]Madsen, O. S., ”, J. Phys. Ocean. 8 (1978), 1009–1015.2.0.CO;2>CrossRefGoogle Scholar
[13]Phillips, O. M., The dynamics of the upper ocean (Cambridge University Press, 1969), Section 3.4.Google Scholar
[14]Russell, R. C. H. and Onsorio, J. D. C., “An experimental investigation of drift profiles in a closed channel”, Proc. 6th Conf.Coastal Eng.,Miami1957, 171–193.CrossRefGoogle Scholar
[15]Stokes, G. G., “On the theory of oscillating waves”, Trans. Camb. Phil. Soc. 8 (1847), 441–455.Google Scholar
[16]Ünlüata, U. and Mci, C. C., “Mass transport in water waves”, J. Geophys. Res. 75 (1970), 7611–7618.CrossRefGoogle Scholar