NOCA, F.: Added mass in swimming and flying

We will show, through a rigorous formalism, that the fluid dynamic force acting on a bluff body performing unsteady motions can actually be decomposed into a force due to apparent mass (as evaluated from potential theory) and a “wake” force resulting from surface friction and the near-wake vorticity. The concept of added, virtual, apparent, or additional mass is well known in potential flow theory. It is added mass (or more exactly, the time derivative of virtual momentum) that wholly contributes to fluid dynamic forces in unsteady, vorticity-free and inviscid flows. Added mass has lost much of its appeal in real (vortical and viscous) flows because it is widely accepted that the contribution of added mass to the fluid dynamic force is intertwined in a complex way with the total force resulting from wake and boundary layer vorticity. Also, within the commonly accepted theories of insect flight, several (erroneous) arguments have been given for why added mass does not contribute to the flight dynamics. Moreover, the advent of novel flow visualization techniques has strongly favored the study of complex vortical structures occurring during flight and swimming, over the study of added mass effects. The proposed decomposition is a seminal result in the science of unsteady aero/hydrodynamics. The formulation explicitly extracts the separate contributions of added mass and near-wake vorticity to the total force, and may, thus, provide new insights about animal flight and swimming. The form of the decomposition also provides a convenient experimental method for evaluating fluid forces using near-wake vorticity data obtained with techniques such as Digital Particle Image Velocimetry (DPIV). The decomposition will be applied to flat plates and elliptical bodies performing “hovering” motions.