| Title | Mechanisms of the Scour at the Head of a Breakwater |
| Dept | Transportation Technology and Information Division |
| Year | 2004 |
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| Summary | Published in April 2004 IOT SERIAL No. 93-67-7100, 46pp. This paper considers deep-water gravity waves propagating obliquely on a steady three-dimensional, strongly sheared current. The current varies slowly in the horizontal directions and deviates slightly from a linear profile in the vertical direction, so that a WKBJ description of wave modulations can be developed by using an approach which is not separate from the perturbation scheme but can however simplify the formulation significantly to take up the rather complicated situation. The resulting modulation equation is compared with the two-dimensional action conservation equation, which represents a natural extension of the one-dimensional one derived by Jonsson, Brink-Kjœr & Thomas (1978) and therefore takes the vorticity of the current into account but ignores the rotational perturbation velocity that may occur in the present situation. This comparison and the numerical computations indicate that unless certain restrictions are imposed on the distribution of the underlying current, the wave action defined by Jonsson et al. is not conserved in this three-dimensional flow. When these restrictions are imposed, the approach by Jonsson et al., which considers the slow modulations of the integral properties of the combined wave and current motion across a fixed vertical section, can also be applied in the three-dimensional case and results in an equation consistent with the two-dimensional action conservation equation and the equation derived by the present approach. This analysis, while representing a non-trivial extension of the result derived by Jonsson et al., can also explain why the approach by Jonsson et al. and also the action conservation equation have a restricted application and why the definition of the wave action density cannot include the rotational perturbation velocity which may have the same order of magnitude as the irrotational one in a general situation. In a less general situation, even when the rotational perturbation velocity is negligible, as long as the restrictions mentioned above are not fully imposed, the approach by Jonsson et al. may still fail and the wave action defined without ambiguity may not be conserved. However, in this or in an even more general situation, the modulation equation derived by the present approach remains valid. |
| Post date | 2005/08/15 |
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