Calculation of Evanescent Wave Modes
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 114, Issue 3
Abstract
The numerical solution of the linear dispersion relation for water waves is considered for the case of the evanescent modes. A two-point Padeó approximation is constructed based upon correct asymptotic behavior at both high and low frequencies. This overcomes some difficulties experienced with a previous one-point Padeó approximation based on correct behavior at low frequencies. The two-point approximation is quite accurate but entails considerable preliminary work to obtain the coefficients. A completely different approach is also presented which only involves the solution of a quadratic equation. The results of this method are accurate to better than 0.35% for the first evanescent mode and are considerably better for the higher modes. They form reliable first estimates for use in the Newton iteration if very accurate results are required.
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References
1.
Abramowitz, M., and Stegun, I. A. (1964). Handbook of mathematical functions. Dover Publications, Mineola, N.Y.
2.
Bender, C. M., and Orszag, S. A. (1978). Advanced mathematical methods for scientists and engineers. McGraw‐Hill Book Co., New York, N.Y.
3.
Chen, H. S., and Thompson, E. F. (1985). “Iterative and Padé solutions for the water‐wave dispersion relation.” Miscellaneous paper CERC‐85‐4, U.S. Army Corps of Engineers, Washington, D.C.
4.
Conte, S. D., and de Boor, C. (1980). Elementary numerical analysis. McGraw‐Hill Book Co., New York, N.Y.
5.
Hunt, J. N. (1979). “Direct solution of wave dispersion equation.” J. Waterways, Ports, Coast., and Oc. Div., ASCE, 105(4), 457–459.
6.
Kirby, J. T., and Dalrymple, R. A. (1983). “Propagation of obliquely incident water waves over a trench.” J. Fluid Mech., 133, Aug., 47–63.
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Copyright © 1988 ASCE.
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Published online: May 1, 1988
Published in print: May 1988
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