Identification of ship wake structures by a time–frequency method

Abstract The wake of a ship that sails at relatively large Froude numbers usually contains a number of components of different nature and with different heights, lengths, timings and propagation directions. We explore the possibilities of the spectrogram representation of one-point measurements of the ship wake to identify these components and to quantify their main properties. This representation, based on the short-time Fourier transform, facilitates a reliable decomposition of the wake into constituent components and makes it possible to quantify their variations in the time–space domain and the energy content of each component, from very low-frequency precursor waves up to high-frequency signals within the frequency range of typical wind-generated waves. A method for estimation of the ship speed and the distance of its sailing line from the measurement site is proposed, which only uses information available within the record of the ship wake surface elevation, but where it is assumed that the wake pattern does not deviate significantly from the classical Kelvin wake structure. The wake decomposition using the spectrogram method allows investigation of the energy content that can be attributed to each individual component of the wake. We demonstrate that the majority (60–80 %) of wake energy from strongly powered large ferries that sail at depth Froude numbers ${\sim}0.7$ is concentrated in components that are located near the edge of the wake wedge. Finally, we demonstrate that the spectrogram representation offers a convenient way to identify a specific signature of single types of ships.