Coordination of multiple appendages in drag-based swimming

Abstract

Krill are aquatic crustaceans that engage in long distance migrations, either vertically in the water column or horizontally for 10 km (over 200,000 body lengths) per day. Hence efficient locomotory performance is crucial for their survival. We study the swimming kinematics of krill using a combination of experiment and analysis. We quantify the propulsor kinematics for tethered and freely swimming krill in experiments, and find kinematics that are very nearly metachronal. We then formulate a drag coefficient model which compares metachronal, synchronous and intermediate motions for a freely swimming body with two legs. With fixed leg velocity amplitude, metachronal kinematics give the highest average body speed for both linear and quadratic drag laws. The same result holds for five legs with the quadratic drag law. When metachronal kinematics is perturbed towards synchronous kinematics, an analysis shows that the velocity increase on the power stroke is outweighed by the velocity decrease on the recovery stroke. With fixed time-averaged work done by the legs, metachronal kinematics again gives the highest average body speed, although the advantage over synchronous kinematics is reduced.