Title: Time-frequency analysis of ship wave patterns in shallow water: modelling and experiments,
Abstract: 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.