Scaling laws for the intermittent swimming performance of a flexible plate at low Reynolds number

Many species of fish and birds travel in intermittent style, yet the combined influence of intermittency and other body kinematics on the hydrodynamics of a self-propelled swimmer is not fully understood. By formulating a reduced-order dynamical model for intermittent swimming, we uncover scaling laws that link the propulsive performance (cursing Reynolds number Re_c, thrust T̄, input power P̄ and cost of transport COT to body kinematics (duty cycle DC, flapping Reynolds number Re_f). By comparing the derived scaling laws with the data from several previous studies and our numerical simulation, we demonstrate the validity of the theory. In addition, we found that Re_c, T̄, P̄ and COT all increase with the increase of DC, Re_f. The model also reveals that the intermittent swimming may not be inherently more energy efficient than continuous swimming, depending on the ratio of drag coefficients between active bursting and coasting.