The transfer of momentum from an animal to fluid in its wake is fundamental to many swimming and flying

The vortex wake is the fluid dynamic footprint of swimming and flying animals. When an animal moves through fluid, Newton’s second and third laws together dictate that the locomotive force exerted by the fluid on the animal has a magnitude equal to the rate at which the animal imparts momentum to the fluid. Often the animal delivers this momentum in the form of rotating fluid masses called vortices. Since the vortex wake created by an animal during locomotion persists for some time after the forces needed to initiate locomotion have been achieved, the vortex wake serves as a temporary record of the animal–fluid interactions from which locomotion arises. A self-propelled animal moving at constant velocity experiences no net force and therefore delivers no net momentum to the wake via these fluid vortices. However, any time the animal accelerates, fluid momentum exists in the vortex wake that can be probed to deduce the locomotive forces generated by the animal. Despite the common approximation of ‘steady locomotion’, in which it is assumed that the animal does not accelerate from its nominal cruising speed, nearly all swimming and flying animals continually exhibit linear and angular accelerations during locomotion, both parallel and perpendicular to the direction of travel, which are related to starting, stopping, maneuvering and cruising. Hence, measurements of the vortex wake can elucidate physical principles governing nearly every aspect of swimming and flying locomotion. An exact determination of swimming and flying forces based on measurements of the surrounding fluid requires precise knowledge of both the flow in the wake of the animal and the flow near its body. Noca et al. (1997, 1999) derived the complete set of equations necessary to measure instantaneous, unsteady (time-dependent), forces on a body based on the velocity of flow around the body and in the wake. The Journal of Experimental Biology 208, 3519-3532 Published by The Company of Biologists 2005 doi:10.1242/jeb.01813