A computational study on the hydrodynamics of real-time pitch manipulation in dolphins during self-propulsion: The promoting effect of caudal fin under offset sinusoidal waveform

Inspired by the high maneuverability of dolphins in nature, this study proposes an offset sinusoidal waveform to control caudal fin oscillation, aiming to investigate the hydrodynamic mechanisms underlying real-time pitch manipulation in bio-inspired dolphins during self-propulsion. A path planning scheme comprising forward, transition, and upward phases is established through computational fluid dynamics (CFD), with overlapping mesh techniques employed to enable iterative coupling between localized flexible motions of driving sources and six-degree-of-freedom body movement within the computational domain. The results demonstrate that switching the caudal fin angle of attack from a symmetric to an offset sinusoidal waveform induces a transition into the upward phase, during which the vertical velocity exhibits an S-shaped growth profile, and the pitch moment curve alternates between “high-sharp” peaks and “shallow-flat” troughs. The fin offset angle and forward duty ratio are identified as key variables affecting real-time pitch performance during self-propulsion. An optimal offset angle range (δ = 20°–30°) is found to enhance vertical lift while maintaining sufficient stability. Moreover, initiating the upward phase earlier leads to greater maneuverability and improved path optimization capability, whereas later transitions offer increased momentum redundancy and control margin. From a bio-propulsion perspective, this study provides new insights into the functional role of the caudal fin in attitude regulation and offers theoretical guidance for the development of underwater robotic fish.