Undulatory underwater swimming: Linking vortex dynamics, thrust, and wake structure with a biorobotic fish

Abstract

Flapping-based propulsive systems rely on fluid-structure interactions to produce thrust. At intermediate and high Reynolds numbers, vortex formation and organization in the wake of such systems are crucial for the generation of a propulsive force. In this work, we experimentally investigate the wake produced by a tethered robotic fish immersed in a water tunnel. By systematically varying the amplitude and frequency of the fish tail as well as the free-stream speed, we are able to observe and characterize different vortex streets as a function of the Strouhal number. The produced wakes are three-dimensional and exhibit a classical V-shape, mainly with two oblique trains of vortex rings convecting outward. Using two-dimensional Particle Image Velocimetry (PIV) in the mid-span plane behind the fish and through extensive data processing of the velocity and vorticity fields, we demonstrate the strong couplings at place between vortex dynamics, thrust production and wake structure. We first measure the evolution of the vortex velocity with the Strouhal number, and model it using a momentum balance equation directly related to thrust production. We then focus on the wake structure, such as wake angle as well as vortex ring orientation, diameter and vorticity. The wake structure is modelled in a simple geometrical framework where the vortex ring velocity is composed of the free-stream speed and the ring self-advecting speed. This framework is tested and validated by our experimental measurements as well as literature data collapsing on master curves, highlighting a universal behavior dominated by the Strouhal number. This allows us to establish a comprehensive understanding of how the wake structure varies with this number and, thus, thrust production.