Spectrogram analysis of surface elevation signals due to accelerating ships

Spectrograms provide an efficient way to analyze surface elevation signals of ship waves taken from a sensor fixed at a single point in space. Recent work based on a simplified model for the ship's disturbance suggests that matching the spectrogram heat-map patterns to a so-called dispersion curve has the potential for estimating of properties of a steadily moving ship, such as the ship's speed and closest distance to the sensor. Here we extend the theory behind the dispersion curve so that it can be applied to ships accelerating along arbitrary paths and demonstrate how acceleration affects the structure of the associated spectrograms. Examples are provided for a simple model of a ship accelerating/decelerating in a straight line or traveling in a circle with constant angular speed. We highlight a problem with nonuniqueness of the dispersion curve when comparing ships moving along different paths. Finally, we validate the new dispersion curve against experimental results of ship models accelerating in a finite depth basin. Our work will provide a basis for more comprehensive studies that extend the simplified model to take into account the shape of the hull in question.