Semi-analytical solution to the second-order wave loads on a vertical cylinder in bi-chromatic bi-directional waves

Cong, PW, Bai, W, Teng, B and Gou, Y (2018) Semi-analytical solution to the second-order wave loads on a vertical cylinder in bi-chromatic bi-directional waves. Ocean Engineering, 161. pp. 205-220. ISSN 0029-8018

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Abstract

A complete solution is presented for the second-order wave loads experienced by a 15 uniform vertical cylinder in bi-chromatic bi-directional waves. The solution is obtained 16 based on the introduction of an assisting radiation potential without explicitly 17 evaluating the second-order diffraction potential. The semi-analytical formulation for 18 calculating the wave loads is provided and an efficient numerical technique is 19 developed to treat the oscillatory free-surface integral that appears in the force 20 formulation. After validating the present solution by comparing with the predictions 21 based on other methods, numerical studies are conducted for different combinations of 22 incident wave frequencies and wave headings, and the influence of frequencies and 23 headings of dual waves on the second-order wave loads is investigated. In addition, by 24 expressing the second-order wave loads in a power expansion with respect to the wave 25 frequency difference and wave heading difference which are both assumed to be small, 26 approximations on the calculation of wave loads are developed. The accuracy of 27 different approximations is assessed by comparing the approximate results with those 28 based on the complete solution.