Wake structure of a deformable Joukowski airfoil

We examine the vortical wake structure shed from a deformable Joukowski airfoil in an unbounded volume of inviscid and incompressible fluid. The deformable airfoil is considered to model a flapping fish. The vortex shedding is accounted for using an unsteady point vortex model commonly referred to as the Brown–Michael model. The airfoil’s deformations and rotations are prescribed in terms of a Jacobi elliptic function which exhibits, depending on a dimensionless parameter mm, a range of periodic behaviors from sinusoidal to a more impulsive type flapping. Depending on the parameter mm and the Strouhal number, one can identify five distinct wake structures, ranging from arrays of isolated point vortices to vortex dipoles and tripoles shed into the wake with every half-cycle of the airfoil flapping motion. We describe these regimes in the context of other published works which categorize wake topologies, and speculate on the importance of these wake structures in terms of periodic swimming and transient maneuvers of fish.

► The wake structure of a deformable Joukowski airfoil is examined as a function of its flapping profile.
► The deformable airfoil affords a range of exotic wakes, some are advantageous to forward locomotion.
► For sinusoidal flapping and ‘optimal’ Strouhal numbers, the wake consists of a reverse von Kármán street.
► For impulsive, yet periodic, flapping, the wake propagates diagonally to the direction of the airfoil locomotion.