Drag Reduction over Dolphin Skin via the Pondermotive Forcing of Vortex Filaments

Abstract

The skin of Tursiops Truncatus is corrugated with small, quasi-periodic ridges running circumferentially about the torso. These ridges extend into the turbulent boundary layer and affect the evolution of coherent structures. The development and evolution of coherent structures over a surface is described by the formation and dynamics of vortex filaments. The dynamics of these filaments over a flat, non-ridged surface is determined analytically, as well as through numerical simulation, and found to agree with the observations of coherent structures in the turbulent boundary layer. The calculation of the linearized dynamics of the vortex filament, successful for the dynamics of a filament over a flat surface, is extended and applied to a vortex filament propagating over a periodically ridged surface. The surface ridges induce a rapid parametric forcing of the vortex filament, and alter the filament dynamics significantly. A consideration of the contribution of vortex filament induced flow to energy transport indicates that the behavior of the filament induced by the ridges can directly reduce surface drag by up to 8%. The size, shape, and distribution of cutaneous ridges for Tursiops Truncatus is found to be optimally configured to affect the filament dynamics and reduce surface drag for swimming velocities consistent with observation.