Spectral Representation of Ship-Generated Waves in Finite-Depth Water

Recent efforts to compare the waves generated by different vessels traveling in finite-depth water have struggled with difficulties presented by various data sets of wave elevations (either measurements or predictions) corresponding to different lateral distances from the ship. Some of the attempts to shift the data to a common reference location have relied upon crude and potentially misleading approximations. The use of free-wave spectral-methods not only overcomes such difficulties, but is also provides us the means to accurately extend CFD results into the far field. As in the deep-water case, one can define a free-wave spectrum that is valid for all lateral positions and distances astern of the vessel. The free-wave spectrum contains a complete description of the Kelvin wake, and wave elevations at any far-field position can be readily calculated once the spectrum is known. For the case of infinitely deep water, Eggers, Sharma, and Ward [1] presented a method by which free-wave spectra can be determined from appropriate measurements of the far-field wave elevations. The current paper discusses the use of free-wave spectra for finite-depth problems and presents a method for the determination of free-wave spectra based upon fitting predicted wave elevations to a corresponding data set. The predicted wave elevations can be calculated from an unknown distribution of finite-depth Havelock singularities. The unknown singularities are determined by minimizing the mean-square-difference between predicted and measured wave fields. The method appears to be quite general and can be used to calculate either finite or infinite-depth free-wave spectra from experimental data or from local CFD predictions.