A Reconciliation of Viscous and Inviscid Approaches to Computing Locomotion of Deforming Bodies

We present a formulation for coupled solutions of fluid and body dynamics in problems of biolocomotion. This formulation unifies the treatment at moderate to high Reynolds number with the corresponding inviscid problem. By a viscous splitting of the Navier–Stokes equations, inertial forces from the fluid are distinguished from the viscous forces, and the former are further decomposed into contributions from body motion in irrotational fluid and ambient fluid vorticity about an equivalent stationary body. In particular, the added mass of the fluid is combined with the intrinsic inertia of the body to allow for simulations of bodies of arbitrary mass, including massless or neutrally buoyant bodies. The resulting dynamical equations can potentially illuminate the role of vorticity in locomotion, and the fundamental differences of locomotion in real and perfect fluids.