A GENERALIZED KDV TYPE EQUATION  FOR UNEVEN DEPTHS

Serdar Beji

doi:10.9753/icce.v35.waves.13

No. 35 (2016), Waves

No. 35 (2016)

A GENERALIZED KDV TYPE EQUATION FOR UNEVEN DEPTHS

Waves

https://doi.org/10.9753/icce.v35.waves.13

Published 2017-06-23

Serdar Beji⁺⁻

Serdar Beji

Faculty of Naval Arch. and Ocean Engineering, Istanbul Technical University, Maslak 34469, Istanbul, Turkey

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Keywords

KdV type equation
improved linear dispersion
improved linear shoaling

How to Cite

Beji, S. (2017). A GENERALIZED KDV TYPE EQUATION FOR UNEVEN DEPTHS. Coastal Engineering Proceedings, 1(35), waves.13. https://doi.org/10.9753/icce.v35.waves.13

Abstract

A Korteweg & de Vries type equation with improved dispersion characteristics for uneven water depths is presented. The new KdV type equation contains mixed dispersion and shoaling terms, which extend its applicable range of relative depths to virtually deep waters. The wave equation also satisfies an important consistency condition that there is an exact agreement between the shoaling rate of the equation itself and the rate obtained from the constancy of energy flux. A finite-difference scheme is devised for simulating several linear and nonlinear cases over varying bathymetry. The performance the new KdV type equation is observed to be quite satisfactory.

https://doi.org/10.9753/icce.v35.waves.13

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References

Beji, S. 2016. Improved Korteweg & de Vries type equation with consistent shoaling characteristics. Coastal Engineering, 109, 128-133.

Beji, S. and J.A. Battjes. 1994. Numerical simulation of nonlinear wave propagation over a bar. Coastal Engineering, 23, 1-16.

Benjamin, T.B., Bona, J.L., and J.J. Mahony. 1972. Model equations for long waves in nonlinear dispersive systems. Phil. Trans. Roy. Soc. Lond. A 272, 47-78.

Boussinesq, J. V. 1872. Theory of waves and surges which propagate the length of a horizontal rectangular canal, imparting to the fluid contained within the canal velocities that are sensibly the same from the top to the bottom. (Translated by A. C. J. Vastano and J. C. H. Mungall, March 1976.) J. Math. Pures and Appl. 17, 55-108.

Korteweg, D.J., and G. de Vries. 1895. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Phil. Mag. 39, 422-443.

Peregrine, D. H. 1966. Calculations on the development of an undular bore. J. Fluid Mech., 25-02, 321-330.

Peregrine, D. H. 1967. Long waves on a beach. J. Fluid Mech., 27-04, 815-827.

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