  Recent research suggests that studying the time-frequency response of ship
wave signals has potential to shed light on a range of applications, such as
inferring the dynamical and geometric properties of a moving vessel based on
the surface elevation data detected at a single point in space. We continue
this line of research here with a study of mathematical models for thin ships
using standard Wigley hulls and Wigley transom-stern hulls as examples.
Mathematical models of varying sophistication are considered. These include
basic minimal models which use applied pressure distributions as proxies for
the ship hull. The more complicated models are Michell's thin ship theory and
the Hogner model, both of which explicitly take into account the shape of the
hull. We outline a methodology for carefully choosing the form and parameter
values in the minimal models such that they reproduce the key features of the
more complicated models in the time-frequency domain. For example, we find that
a two-pressure model is capable of producing wave elevation signals that have a
similar time-frequency profile as that for Michell's thin ship theory applied
to the Wigley hull, including the crucially important features caused by
interference between waves created at the bow and stern of the ship. One of the
key tools in our analysis is the spectrogram, which is a heat-map visualisation
in the time-frequency domain. Our work here extends the existing knowledge on
the topic of spectrograms of ship waves. The theoretical results in this study
are supported by experimental data collected in a towing tank at the Australian
Maritime College using model versions of the standard Wigley hulls and Wigley
transom-stern hulls.
