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

## TL;DR

This paper combines theoretical analysis and experiments to understand how ship wake spectrograms are affected by water depth and flow regime, revealing wave interference effects and periodic patterns.

## Contribution

It introduces a mathematical model to interpret spectrogram features, emphasizing the impact of finite water depth and flow regime on ship wake analysis.

## Key findings

- Spectrogram features vary with subcritical and supercritical flow regimes.
- Wave interference causes periodic patterns in spectrograms of high aspect ratio vessels.
- Experimental data supports theoretical predictions about wave behavior in shallow water.

## 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.