Generating high-efficiency swimming kinematics using hydrodynamic eigenmode decomposition

Abstract

This paper explores the use of hydrodynamic eigenmode decomposition as a means of generating optimal swimming kinematics of slender three-dimensional bodies. The eigenvectors of the unsteady hydrodynamic system are used as basis functions for the response to external forcing, such as perturbations generated by the deformation of the body. Exploiting the orthogonality of the modes, we show that swimming according to a single appropriately selected hydrodynamic eigenmode results in high-efficiency swimming. To demonstrate this result, we use an inviscid three-dimensional vortex lattice model to investigate the hydrodynamic eigenmodes of a selection of geometries. We find that for all of the body geometries tested, hydrodynamic efficiency far exceeding that of pure heaving or pitching can be achieved. All eigenmodes tested produce high-efficiency motion, as long as the beat frequency is higher than the mode's “cut-in” frequency for thrust generation. The eigenmodes show qualitative similarity to swimming patterns observed in nature and also correspond well to the existing classifications of undulatory and oscillatory swimming. This study demonstrates that the hydrodynamic eigenmode analysis can generate high-efficiency swimming kinematics based only on information about the body and wake geometry, and as such, this method has significant potential for further development and application to autonomous underwater vehicle design.