Spectrograms of ship wakes: identifying linear and nonlinear wave signals

Abstract

A spectrogram is a useful way of using short-time discrete Fourier transforms to visualise surface height measurements taken of ship wakes in real world conditions. For a steadily moving ship that leaves behind small-amplitude waves, the spectrogram is known to have two clear linear components, a sliding-frequency mode caused by the divergent waves and a constant-frequency mode for the transverse waves. However, recent observations of high speed ferry data have identified additional components of the spectrograms that are not yet explained. We use computer simulations of linear and nonlinear ship wave patterns and apply time-frequency analysis to generate spectrograms for an idealised ship. We clarify the role of the linear dispersion relation and ship speed on the two linear components. We use a simple weakly nonlinear theory to identify higher order effects in a spectrogram and, while the high speed ferry data is very noisy, we propose that certain additional features in the experimental data are caused by nonlinearity. Finally, we provide a possible explanation for a further discrepancy between the high speed ferry spectrograms and linear theory by accounting for ship acceleration.

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

“…By following Pethiyagoda et al [24] we now use geometric arguments to determine the linear dispersion curve for ship waves in a finite depth channel. The key ideas here are borrowed from standard texts [14,16,32] and articles [12].…”

“…In this paper, we extend the analysis in [24] to apply to finite-depth channels. Ship wakes on a finite-depth fluid are interesting because they can be classified as either subcritical (F H < 1, where F H is the depth based Froude number) or supercritical (F H > 1), with qualitatively different wave patterns forming for each case.…”

“…Here the pressure distribution is used as an idealised mathematical representation of a ship and the strength of the pressure ( ) acts as a proxy for the volume of water displaced by the ship. In Section 3 we extend the geometric argument for determining the linear dispersion curve presented by Pethiyagoda et al [24] to include the effects of a finite depth fluid. We observe the effect of changing the width of the Gaussian pressure relative to the water depth (δ), where the regions of high intensity favour higher frequencies along the dispersion curves for smaller pressure widths.…”

Deformations of Frozen River Slopes at the Ancon in the Presence of Moving Vessels

“…В результате в начале закругления происходит увеличение скоростей у выпуклого берега и уменьшение их у вогнутого, ниже по течению максимум скорости постепенно передвигается к вогнутому берегу закругления. 4. Явление отжима (отрыва) потока от стенок и образование водоворотных зон при очень резком плановом искривлении.…”

“…Большая работа представлена в издании [3], где используя геометрические аргументы, нелинейный анализ и компьютерное моделирование автор определяет линейные и нелинейные особенности в волновой спектрограмме судна. В исследовании [4] использовался метод спектрограмм для определения дополнительных компонент судовых волн, которые не были описаны ранее. Оптический метод на основе лазерных лучей применялся для определения поля скоростей волн, исходящих от судна, на основе сравнения со свободной поверхностью [5].…”