Time-frequency analysis of ship wave patterns in shallow water: modelling and experiments

• Published in: Ocean engineering Vol. 158; pp. 123 - 131
• Main Authors: Pethiyagoda, Ravindra, Moroney, Timothy J., Macfarlane, Gregor J., Binns, Jonathan R., McCue, Scott W.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15-06-2018
• Subjects: Interference effects; Mathematical model; Shallow water; Ship wakes; Spectrograms; Interference effects; Ship wakes; Mathematical model; Shallow water; Spectrograms
• ISSN: 0029-8018; 1873-5258
• DOI: 10.1016/j.oceaneng.2018.01.108

A spectrogram of a ship wake is a heat map that visualises the time-dependent frequency spectrum of surface height measurements taken at a single point as the ship travels by. Spectrograms are easy to compute and, if properly interpreted, have the potential to provide crucial information about various properties of the ship in question. Here we use geometrical arguments and analysis of an idealised mathematical model to identify features of spectrograms, concentrating on the effects of a finite-depth channel. Our results depend heavily on whether the flow regime is subcritical or supercritical. To support our theoretical predictions, we compare with data taken from experiments we conducted in a model test basin using a variety of realistic ship hulls. Finally, we note that vessels with a high aspect ratio appear to produce spectrogram data that contains periodic patterns. We can reproduce this behaviour in our mathematical model by using a so-called two-point wavemaker. These results highlight the role of wave interference effects in spectrograms of ship wakes.
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•Time-frequency analysis of ship wave patterns can be facilitated using spectrograms.•A geometric argument is used to identify the key features of spectrograms.•This prediction is validated using a mathematical model with an applied pressure.•Comparisons are made with data taken from experiments we conducted in a model test basin.•The match is very good for a variety of ship velocities and hull types.