Scaling laws for caudal fin swimmers incorporating hydrodynamics, kinematics, morphology and scale effects

Many species of fish, as well as biorobotic underwater vehicles (BUVs), employ body–caudal fin (BCF) propulsion, in which a wave-like body motion culminates in high-amplitude caudal fin oscillations to generate thrust. This study uses high-fidelity simulations of a mackerel-inspired caudal fin swimmer across a wide range of Reynolds and Strouhal numbers to analyse the relationship between swimming kinematics and hydrodynamic forces. Central to this work is the derivation and use of a model for the leading-edge vortex (LEV) on the caudal fin. This vortex dominates the thrust production from the fin and the LEV model forms the basis for the derivation of scaling laws grounded in flow physics. Scaling laws are derived for thrust, power, efficiency, cost-of-transport and swimming speed, and are parametrised using data from high-fidelity simulations. These laws are validated against published simulation and experimental data, revealing several new kinematic and morphometric parameters that critically influence hydrodynamic performance. The results provide a mechanistic framework for understanding thrust generation, optimising swimming performance, and assessing the effects of scale and morphology in aquatic locomotion of both fish and BUVs.