The Diffraction of Second-Order Bichromatic Waves by a Semi-Immersed Horizontal Rectangular Cylinder

ISSN： 0889-9746

Source： Journal of Fluids and Structures, Vol.13, Iss.3, 1999-04, pp. : 381-397

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Abstract

The diffraction of second-order bichromatic Stokes waves by a semi-immersed horizontal rectangular cylinder (prism) is investigated theoretically. The problem is assumed two-dimensional and the fluid domain is divided into three regions: upwave, beneath and downwave of the structure. Analytical expressions for the velocity potentials in each region at both first- and second-order are obtained by an eigenfunction expansion approach. The solutions in each fluid region are linked through matching conditions on the imaginary fluid interfaces between them. Semi-analytical expressions are derived for the sum-and difference-frequency hydrodynamic loads and the free-surface elevations upwave and downwave of the structure to second-order. Numerical results are presented which illustrate the influence of the different wave and structural parameters on these quantities at both first- and second-order.