Planktonic propulsion: the hydrodynamics, kinematics, and design of metachrony
Murphy, David W.
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Locomotion is a key characteristic of almost all forms of life and is often accomplished, whether on land, in water, or in the air, by reciprocal motion of two or more appendages. Among the zooplankton, many species propel themselves by rhythmically beating multiple pairs of closely spaced leg-like appendages in a back-to-front (metachronal) pattern. The focus of this study is to understand the mechanical design, kinematic operation, and hydrodynamic result of metachrony in the zooplankton. In the first part of this study, Antarctic krill (Euphausia superba) are investigated as an ecologically important model species that metachronally beats its swimming legs (pleopods) to perform drag-based propulsion. Based on high speed videos of freely swimming Antarctic krill, hovering, fast forward swimming, and upside down swimming are identified as three distinct swimming modes with significantly different stroke amplitudes and beat frequencies. When transitioning between hovering and fast forward swimming, Antarctic krill first increase beat amplitude and secondarily increase beat frequency. In considering the design components that contribute to metachrony being a successful swimming technique, a comparison among many different species shows that the ratio between the appendage separation distance and appendage length is limited to a narrow range of values (i.e. 0.2 - 0.65). In the second part of this study, metachrony is examined at smaller length and time scales by examining the impulsive escape jump of a calanoid copepod (Calanus finmarchicus). The wake generated by the copepod's metachronally beating swimming legs is experimentally measured using a novel (and newly developed) tomographic particle image velocimetry (PIV) system capable of making volumetric 3D velocity measurements with high temporal and spatial resolution using IR illumination. The flow generated by the escaping copepod consisted of a stronger posterior vortex ring generated by the metachronally stroking swimming legs and a weaker one generated anteriorly around the body by the impulsive start of the escape, both of which decayed over time. The experiments also revealed azimuthal asymmetry in the vortices caused by body yawing and the action of the swimming legs, flow features not considered in previous axisymmetric computational and theoretical models of copepod jumps. While not accounting for this asymmetry, an impulsive stresslet is nonetheless useful in modeling the flow created by the escaping copepod and represents the flow more accurately than an impulsive Stokeslet. In the final part of this study, the flow associated with metachronal hovering in Antarctic krill is experimentally and theoretically investigated in regards to the energy requirements of the pelagic lifestyle. Volumetric flow measurements of a hovering Antarctic krill show that each stroking pleopod drags flow behind it such that a downward stream develops medially. The lateral exopodites induce tip vortices which add to the lift force on each appendage. Furthermore, the flow beneath the hovering krill develops into a pulsed jet with a Strouhal number in the 'high-efficiency zone' of 0.2 < St < 0.4. Actuator disk theory is used to make theoretical estimates of the induced power necessary to hover, the results of which match induced power values calculated from measured flow gradients contributing to viscous energy dissipation.