Time-Harmonic Ship Waves From the Perspective of an Earth-Fixed Observer

Time-harmonic flows around a ship advancing in waves are usually described in the coordinate system moving with the ship’s average speed. Within this moving reference system, detailed descriptions of ship waves have been made in many previous studies. Recent works in [1, 2] revealed that essential physical features such as different wave systems and their wavelengths, cusp angles, phase, and group velocities, are directly related to wavenumber curves determined by the dispersion relation on the mathematical Fourier plane. Insightful physical results have been achieved and applied in developing numerical tools to predict ship seakeeping. However, the description of time-harmonic ship waves in the Earth-fixed coordinate system is missing although a few studies exist on steady ship waves like that in [3, 4] It is not trivial to transform results in the moving coordinate system to the fixed coordinate system. Much caution is needed to obtain consistently the phase and group velocities which are closely associated with wave crestlines. In the present study, after summarising classical results in the moving coordinate system, detailed analyses of time-harmonic ship waves in the Earth-fixed coordinate system are presented with numerical illustrations. The results obtained in both coordinate systems are believed to be useful in the prediction of ambient waves due to the passage of ships.