Investigation of depth-effects on the doppler shift and the consequence in spectral response calculations for ships

Reliable prediction of wave-induced ship responses is an important part in digital twins and decision support systems focused on ship safety and crew/passenger comfort with both post-voyage and real-time applications in mind. Often, the prediction is made via spectral calculations, combining a wave spectrum and transfer functions. If the on-the-ship observed spectrum is of interest, the calculations must include the Doppler shift, relating the intrinsic wave frequency to the encountered frequency. For ships sailing in seaways at deep water, no complexities are faced in this context, as closed-form solutions exist between the set of frequencies. However, at finite/intermediate water depth, this is not the case because, here, the dispersion of waves is governed by a transcendental equation. This paper investigates depth effects on the Doppler shift and the consequences in spectral response calculations. The paper shows that it is, in fact, crucially important to include the exact dispersion relation when computing response spectra for a ship sailing in water depths lower than 40–50 m. With the paper, we include the developed algorithm for computing the response spectra.