Doppler Shift Approximation for Predicting the Wave-Induced Response of Advancing Vessels in Following Waves

• Published in: Volume 5: Ocean Engineering
• Main Authors: Mounet, Raphaël E. G., Nielsen, Ulrik Dam, H. Brodtkorb, Astrid
• Format: Article in Journal/Newspaper
• Language: English
• Published: The American Society of Mechanical Engineers (ASME) 2023
• Subjects: Spectral analysis; Ship operation; Wave loads; Uncertainty quantification; Seakeeping; /dk/atira/pure/sustainabledevelopmentgoals/affordable_and_clean_energy; name=SDG 7 - Affordable and Clean Energy; Arctic
• Online Access: https://orbit.dtu.dk/en/publications/5c4c81d0-7010-4bda-86ac-5ea2a30e47ef; https://doi.org/10.1115/OMAE2023-107733

Being able to predict wave-induced responses of a ship is essential for assessment of safety and energy efficiency. The classical seakeeping theory has established a linear relationship between the wave spectrum and the induced response spectrum. However, for a ship sailing with non-zero forward speed, the wave components excite the structure at the encounter frequency, differing from the intrinsic wave frequency. In following seas, the Doppler shift introduces complications in the theoretical transformation of spectra from intrinsic- to encounter-frequency domains, and vice versa, the latter resulting in non-unique solutions. The present study proposes to mathematically substitute this nonbijective mapping with a bijective function approximating the true formulation of the Doppler shift. A case study is considered, simulating the motions of a Panamax containership in waves, to assess the quality of the response estimates computed through the approximation approach. The results demonstrate the ability and practicality of the method in accurately deriving response spectra for a wide range of forward speeds and headings, also in conditions that involve following waves.