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A spectrogram of a ship wake is a heat map that visualises the time-dependentfrequency spectrum of surface height measurements taken at a single point asthe ship travels by. Spectrograms are easy to compute and, if properlyinterpreted, have the potential to provide crucial information about variousproperties of the ship in question. Here we use geometrical arguments andanalysis of an idealised mathematical model to identify features ofspectrograms, concentrating on the effects of a finite-depth channel. Ourresults depend heavily on whether the flow regime is subcritical orsupercritical. To support our theoretical predictions, we compare with datataken from experiments we conducted in a model test basin using a variety ofrealistic ship hulls. Finally, we note that vessels with a high aspect ratioappear to produce spectrogram data that contains periodic patterns. We canreproduce this behaviour in our mathematical model by using a so-calledtwo-point wavemaker. These results highlight the role of wave interferenceeffects in spectrograms of ship wakes.

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