Bimodal Sea States Preserve Peak-Frequency Scaling for Submerged Flapping Hydrofoils

The arXiv preprint reports passive-pitching simulations across calm, transitional and storm bimodal spectra. Despite superimposed wave systems, time-averaged thrust peaks when the foil’s effective frequency matches the dominant energy-containing wave component, confirming the scaling framework’s robustness. Dimensional spring stiffness, however, must shift with spectral shape, implying that fixed-stiffness designs will underperform outside narrow sea-state bands. The work therefore isolates adaptive hydroelastic tuning as the remaining practical barrier to field deployment.

Prior monochromatic and unimodal campaigns had already mapped the frequency scaling; this study extends the map to realistic North-Atlantic-type spectra and quantifies the stiffness adjustment range. For ship designers the result supplies a single nondimensional tuning target plus a sea-state-dependent gain schedule, directly usable in control algorithms. Visualization of the instantaneous pressure and vorticity fields reveals that the foil still extracts energy from the longer swell even when wind-sea energy dominates, an effect missed by frequency-averaged metrics.

The principal limitation is the absence of free-surface nonlinearities and hull interaction; next-step basin or field trials at 1:5 scale would test whether the predicted thrust gains survive these additional physics. If confirmed, the technology offers a retrofit pathway for auxiliary propulsion on slow-steaming vessels, cutting fuel use in the 5–12 % range under typical mixed-sea conditions.

Maritime operators can therefore treat the scaling law as design-ready while budgeting for variable-stiffness actuators whose control logic is now specified by the bimodal results.