Diffraction–radiation of regular water waves and irregular frequencies: A straightforward flow-modeling approach and analysis

Abstract

Diffraction–radiation of regular waves by a body such as an offshore structure or a moored ship is considered within the classical framework of potential-flow theory, which is commonly used because it is realistic and practical. A simple analysis that is based solely on straightforward applications of Green’s classical identity to a ‘free-waterplane’ flow-model and a ‘rigid-waterplane’ flow-model is expounded. These alternative flow-models and the related straightforward applications of Green’s identity yield an elementary yet rigorous justification of the practical and effective method, called ‘combined boundary integral equation method’ (CBIEM), of Lau and Hearn for preventing irregular frequencies. This method is shown to be significantly more efficient, and arguably simpler and more logical, than the widely-used extended boundary integral method of Lee and Newman. A modification of the ‘combined boundary integral equation method’ is also given. This modification involves a pair of boundary integral equations that are mathematically equivalent to the pair of integral equations solved in the CBIEM, but are weakly singular.