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.

14 pages, 7 figures

References in corpus (5)

• What is the apparent angle of a Kelvin ship wave pattern?
• Ship waves on uniform shear current at finite depth: wave resistance and critical velocity
• Spectrograms of ship wakes: identifying linear and nonlinear wave signals
• Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns
• Surface waves on arbitrary vertically-sheared currents

Cited by in corpus (3)

• Kelvin wake pattern at small Froude numbers
• On the problem of modeling the boat wake climate; the Florida intracoastal waterway
• Three dimensional free-surface flow over arbitrary bottom topography