Vertical Structure of Horizontal Velocity in Regular Shoaling Waves
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 123, Issue 3
Abstract
We investigate the parameterization of the vertical structure of horizontal velocity in a family of weakly nonlinear, weakly dispersive (Boussinesq) models developed by Nwogu. That model contains a free parameter that specifies the depth about which the assumed quadratic velocity profiles are expanded, with most standard formulations recovered by particular choices of this free parameter. Nwogu chose to optimize this model by selecting the parameter to best fit the linear dispersion relation. Here we test the model by applying it to the nonlinear case of shoaling of regular (cnoidal) waves. A new data set documenting the vertical dependence of horizontal velocity is presented and is used to evaluate the range of values of the free parameter for which the model gives good results. We show that the Boussinesq model optimized for the best linear dispersion relation also gives the best approximation to the local vertical structure in this strongly nonlinear case.
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References
1.
Benjamin, T., Bona, J., and Mahoney, J.(1972). “Model equations for long waves in non-linear dispersive systems.”Philosophical Trans. of the Royal Soc., London, England, 272, 47–78.
2.
Goring, D. G. (1978). The propagation of long waves onto a shelf, PhD thesis, California Inst. of Technol., Pasadena, Calif.
3.
Madsen, O., and Mei, C.(1969). “The transformation of a solitary wave over an uneven bottom.”J. Fluid Mech., Cambridge, England, 39(5), 781–791.
4.
McCowan, A. D. (1987). “The range of Boussinesq type numerical short wave models.”Proc., 22nd IAHR Congr., Int. Assn. for Hydr. Res.
5.
Nwogu, O.(1993). “An alternative form of the Boussinesq equations for nearshore wave propagation.”J. Wtrwy., Port, Coast., and Oc. Engrg., 119, 618–638.
6.
Peregrine, D. H.(1967). “Long waves on a beach.”J. Fluid Mech., Cambridge, England, 27(4), 815–827.
7.
Wei, G., Kirby, J. T., Grilli, S. T., and Subramanya, R.(1995). “A fully nonlinear Boussinesq model for surface waves. I. Highly nonlinear, unsteady waves.”J. Fluid Mech., Cambridge, England, 294, 71–91.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 123 • Issue 3 • May 1997
Pages: 130 - 136
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: May 1, 1997
Published in print: May 1997
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