Unsteady motion: escape jumps in planktonic copepods, their kinematics and energetics

Abstract

We describe the kinematics of escape jumps in three species of 0.3 -3.0 mm-sized planktonic copepods. We find similar kinematics between species with periodically alternating power strokes and passive coasting and a resulting highly fluctuating escape velocity. By direct numerical simulations, we estimate the force and power output needed to accelerate and overcome drag. Both are very high compared with those of other organisms, as are the escape velocities in comparison to startle velocities of other aquatic animals. Thus, the maximum weight-specific force, which for muscle motors of other animals has been found to be near constant at 57 N (kg muscle) 21, is more than an order of magnitude higher for the escaping copepods. We argue that this is feasible because most copepods have different systems for steady propulsion (feeding appendages) and intensive escapes (swimming legs), with the muscular arrangement of the latter probably adapted for high force production during short-lasting bursts. The resulting escape velocities scale with body length to power 0.65, different from the size-scaling of both similar sized and larger animals moving at constant velocity, but similar to that found for startle velocities in other aquatic organisms. The relative duration of the pauses between power strokes was observed to increase with organism size. We demonstrate that this is an inherent property of swimming by alternating power strokes and pauses. We finally show that the Strouhal number is in the range of peak propulsion efficiency, again suggesting that copepods are optimally designed for rapid escape jumps.

Hydrodynamics and energetics of jumping copepod nauplii and copepodids

“…The Acartia tonsa nauplius uses its antennules (A1) and antennae (A2) for propulsion (Andersen Borg et al, 2012). The copepodid uses its swimming legs (L1-L5) for propulsion and the urosome (U) for steering (Kiørboe et al, 2010). Copepodids have a variable number of pairs of swimming legs, and the final adult stage is shown here.…”

“…An alternative approximation of a copepod body as a prolate spheroid results only in small quantitative differences, and for simplicity we chose the sphere approximation. We used the width of the copepod at the thickest part of the prosome as the diameter of the sphere, D, calculated from the body length L using the aspect ratios of 0.5 and 0.38 for nauplii and copepodids, respectively (Kiørboe et al, 2010;Andersen Borg et al, 2012). We thus modelled the drag (F d ) on the copepod using the quasi-steady expression, where V is the instantaneous swimming velocity.…”

Hydrodynamic coupling of two sharp-edged beams vibrating in a viscous fluid

“…The proposed framework is anticipated to find use in the design of MEMS-based devices operating in liquids, including novel viscosimeters relying on multiple sensing microelements [48], arrays of piezoelectric fans [43,44], systems of ionic polymer metal composites [45] and energy harvesters based on coupled active beams [46]. Such methodology may also contribute to improve our understanding of natural systems comprising arrays of coupled slender structures, such as mechanoreceptive setal hairs of copepods [51,52] domain is simulated and the selected dimensions are 10 b × (20 + γ ) b to minimize boundary effects. No-slip boundary conditions are enforced at the fluid-lamina interfaces and at the right edge of the computational domain, a symmetry condition is set along the left edge, while outflow boundary conditions are imposed at the top and bottom edges, as depicted in figure 13.…”

The Kinematics of Jumping of Globular Springtail

“…(11) Eq. (17) shows that the height of springtail jump depends on the Reynolds number and the mass of springtail.…”

“…In the same manner as the jump analysis in planktonic copepoda [17], the radius of the sphere R is given as follows:…”