Volumetric measurements of wake impulse and kinetic energy for evaluating swimming performance

Abstract

Volumetric flow measurements are a valuable tool for studies of aquatic locomotion. In addition to visualizing complex propulsive behaviors (e.g., highly three-dimensional kinematics or multi-propulsor interactions), volumetric wake measurements can enable direct calculation of metrics for locomotive performance including the hydrodynamic impulse and wake kinetic energy. These metrics are commonly used in PIV and PTV studies of swimming organisms, but derivations from planar data often rely on simplifying assumptions about the wake (e.g., geometry, orientation, or interactions). This study characterizes errors in deriving wake impulse and kinetic energy directly from volumetric data in relation to experimental parameters including the level of noise, the flow feature resolution, processing parameters, and the calculation domain. We consider three vortex ring-like test cases: a synthetic spherical vortex with exact solutions for its impulse and energy, volumetric PIV measurements of a turbulent vortex ring, and volumetric PIV measurements of a turning fish. We find that direct calculations of hydrodynamic impulse are robust when derived from a volumetric experiment. We also show that kinetic energy estimates are feasible at experiment resolutions, but are more sensitive to experiment design and processing parameters, which may limit efficiency estimates or comparisons between studies or organisms. Graphical abstract