Practical radiation stress calculations connected with equations of wave propagation |
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| Authors: | Graham JM Copeland |
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| Institution: | Department of Civil Engineering, University of Liverpool, PO Box 147, Liverpool, L69 3BX, United Kingdom |
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| Abstract: | Numerical models of combined surface gravity wave refraction, diffraction and reflection can be solved conveniently in terms of the water surface displacement, η, and a vertically integrated, wave-induced, water particle velocity, Q. However, the normal formulation for the radiation stress components, expressed in terms of the wave energy, wave number and water depth, is correct only for linear progressive waves.This paper describes a method of calculating the radiation stress for a linear progressive wave plus an arbitrary reflected or back-scattered wave in terms of variables η and Q. The calculations are related to a finite-difference scheme. Correction factors are given which compensate for the errors introduced by the use of finite differentials in the calculation of certain elements of radiation stress.The theory upon which the analytical method is based is only exact for water of uniform depth. However, results are presented which show that the errors are not significant (typical error less than ± 2%) for bed slopes of less than 1:3. |
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