Hydrodynamics and scaling laws for intermittent S-start swimming

Abstract

The hydrodynamics of a self-propelling swimmer undergoing intermittent S-start swimming are investigated extensively with varying duty cycle $DC$ , swimming period $T$ , and tailbeat amplitude $A$ . We find that the steady time-averaged swimming speed $\bar {U}_x$ increases directly with $A$ , but varies inversely with $DC$ and $T$ , where there is a maximal improvement of $541.29\,\%$ over continuous cruising swimming. Our results reveal two scaling laws, in the form of input versus output relations, that relate the swimmer's kinematics to its hydrodynamic performance: swimming speed and efficiency. A smaller $DC$ causes increased fluctuations in the swimmer's velocity generation. A larger $A$ , on the other hand, allows the swimmer to reach steady swimming more quickly. Although we set out to determine scaling laws for intermittent S-start swimming, these scaling laws extend naturally to burst-and-coast and continuous modes of swimming. Additionally, we have identified, categorized and linked the wake structures produced by intermittent S-start swimmers with their velocity generation.