An Elastic Collision Model for Impulsive Jumping by Small Planktonic Organisms

Abstract

Many small marine planktonic organisms converge on similar propulsion mechanisms that involve impulsively generated viscous wake vortex rings, and small-scale fluid physics is key to mechanistically understanding the adaptive values of this important behavioral trait. Here, a theoretical fluid mechanics model is developed for plankton jumping, based on observations that the initial acceleration phase for a jumping plankter to attain its maximum speed is nearly impulsive, taking only a small fraction of the viscous timescale, and therefore can be regarded as nearly inviscid, analogous to a one-dimensional elastic collision. Flow circulation time-series data measured by particle image velocimetry (PIV) are input into the model and Froude propulsion efficiencies are calculated for several plankton species. Jumping by the tailed ciliate Pseudotontonia sp. has a high Froude propulsion efficiency ~0.9. Copepod jumping also has a very high efficiency, usually >0.95. Jumping by the squid Doryteuthis pealeii paralarvae has an efficiency of 0.44 ± 0.16 (SD). Jumping by the small medusa Sarsia tubulosa has an efficiency of 0.38 ± 0.26 (SD). Differences in the calculated efficiencies are attributed to the different ways by which these plankters impart momentum on the water during the initial acceleration phase as well as the accompanied different added mass coefficients.