Optimisation of two-dimensional undulatory swimming at high Reynolds number

The propulsion performance of a flexible plate undergoing an arbitrary harmonic motion in a two-dimensional and inviscid fluid is addressed. This plate being free of external forces, heaving and pitching cannot be imposed and are the results of recoil conditions on the body. Linear unsteady airfoil theory is first used to calculate the average thrust and power required for swimming. The propulsive performance is then discussed in terms of hydrodynamic efficiency, energy consumption and average swimming speed and two different asymptotic regimes are identified: the low-velocity regime and the high-velocity regime. The optimal swimming gaits are calculated in the different regimes as a function of the plate mass ratio and leading-edge suction. Finally an empirical non-linear model is proposed to complement the linear model and the optimal swimming modes are calculated and discussed within this framework. For a fixed number of degrees of freedom, it is found that the Strouhal number of the optimal mode is almost constant, independently of the swimming regime.