The effect of flow speed and body size on Kármán gait kinematics in rainbow trout

Abstract

Summary We have little understanding of how fish hold station in unsteady flows. Here we investigate the effect of flow speed and body size on the kinematics of rainbow trout Kármán gaiting behind a 5 cm diameter cylinder. We establish a set of criteria revealing that not all fish positioned in a vortex street are Kármán gaiting. By far the highest probability of Kármán gaiting occurred at intermediate flow speeds between 30 and 70 cm s-1. We show that trout Kármán gait in a region of the cylinder wake where the velocity deficit is about 40% of the nominal flow. We observed that the relationships between certain kinematic and flow variables are largely preserved across flow speeds. Tail-beat frequency matches the measured vortex shedding frequency, which increases linearly with flow speed. Body wave speed is about 25% faster than the nominal flow velocity. At speeds where fish have a high probability of Kármán gaiting, body wavelength is about 25% longer than the cylinder wake wavelength. Likewise, the lateral (i.e. cross-stream) amplitude of the tail tip is about 50% greater than the expected lateral spacing of the cylinder vortices, while the body centre (BC) amplitude is about 70% less. Lateral COM acceleration increases quadratically with speed. Head angle decreases with flow speed. While these values are different from those found in fish swimming in uniform flow, the strategy for locomotion is the same; fish adjust to increasing flow by increasing their tail-beat frequency. Body size also plays a role in Kármán gaiting kinematics. Tail beat amplitudes of Kármán gaiting increase with body size, as in freestream swimming, but are almost three times larger in magnitude. Larger fish have a shorter body wavelength and slower body wave speed than smaller fish, which is a surprising result compared to freestream swimming, where body wavelength and wave speed increases with size. In contrast to freestream swimming, tail beat frequency for Kármán gaiting fish does not depend on the body size and is a function of the vortex shedding frequency.