Effect of Current on Spectrum of Breaking Waves in Water of Finite Depth
This paper presents an approximate method to compute the mean value, the mean square value and the spectrum of waves in water of finite depth taking into account the effect of wave breaking with or without the presence of current. It is assumed that there exists a linear and Gaussian ideal wave train whose spectrum is first obtained using the wave energy flux balance equation without considering wave breaking. The Miche wave breaking criteron for waves in finite water depth is used to limit the wave elevation and establish an expression for the breaking wave elevation in terms of the elevation and its second time derivative of the ideal waves. Simple expressions for the mean value, the mean square value and the spectrum are obtained. These results are applied to the case in which a deep water unidirectional wave train, propagating normally towards a straight shoreline over gently varying sea bottom of parallel and straight contours, encounters an adverse steady current whose velocity is assumed to be uniformly distributed with depth. Numerical results are obtained and presented in graphical form.
KeywordsWave Train Wave Spectrum Breaking Wave Surf Zone Finite Depth
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- 1.Abramowitz, M., and Stegun, I.A. Handbook of Mathematical Functions. Dover Publications, Inc., New York, NY, 1968Google Scholar
- 2.Battjes, J.A., Computation of Set-up, Long Shore Currents, Run-up and Overtopping due to Wind-generated Waves, Communications on Hydraulics No. 74-2, Department of Civil Engineering, Delft University of Technology, Delft, The Netherlands, 1974Google Scholar
- 3.Battjes, J.A., and Janssen, J.P.F.M. Energy Loss and Set-up due to Breaking of Random Waves, Proceedings of the 16th International Conference of Coastal Engineering, American Society of Civil Engineers, New York, NY, 1978, 569–587Google Scholar
- 4.Borgman, L.E., A Statistical Theory for Hydrodynamic Forces on Objects, Tech. Rept. HEL-9-6, Hydraulics Engineering Laboratory, University of California, Berkeley, CA, 1965Google Scholar
- 6.Erdely, A., Magnum, W., Oberhettinger, F. and Tricomi, F.G. Higher Transcendental Functions, Vol. 2, McGraw-Hill Book Co., Inc., New York, NY, 1953Google Scholar
- 7.Hedges, T.S., Burrows, R. and Mason, W.G. Wave-current Interaction and its Effect on Fluid Loading, Department of Civil Engineering, University of Liverpool, Rep. No. MCE/3/79, 1979Google Scholar
- 13.Phillips, O.M., The Dynamics of the Upper Ocean, Cambridge University Press, second edition, New York, NY, 1980Google Scholar
- 16.Yuan, Y., Tung, C.C. and Huang, N.E. Statistical Properties of Breaking Waves, Proceedings of the Symposium on Wave Dyanmics and Radio Probing of the Ocean Surface, (ed. O.M. Phillips and K.L. Hasselmann). Plenum Press, New York, NY, 1986, 293–302Google Scholar