Burrow ventilation in the tube-dwelling shimp Callianassa subterranea (Decapoda: thalassinidea). III. Hydrodynamic modelling and the energetics of pleopod pumping.

The process of flow generation with metachronally beating pleopods in a tubiform burrow was studied by designing a hydrodynamic model based on a thrust-drag force balance. The drag of the tube (including the shrimp) comprises components for accelerating the water into the tube entrance, for adjusting a parabolic velocity profile, for accelerating the flow into a constriction due to the shrimp's body and another constriction due to the extended tail-fan, for shear due to separation and for the viscous resistance of all tube parts. The thrust produced by the beating pleopods comprises components for the drag-based thrust and for the added-mass-based thrust. The beating pleopods are approximated by oscillating flat plates with a different area and camber during the power stroke and the recovery stroke and with a phase shift between adjacent pleopod pairs. The added mass is shed during the second half of the power stroke and is minimized during the recovery stroke. A force balance between the pleopod thrust and the tube drag is effected by calculating the mean thrust during one beat cycle at a certain flow velocity in the tube and comparing it with the drag of the tube at that flow velocity. The energetics of the tube and the pump are derived from the forces, and the mechanical efficiency of the system is the ratio of these two. Adjusted to standard Callianassa subterranea values, the model predicts a mean flow velocity in the tube of 1.8 mm s-1. The mean thrust force, equalling the drag, is 36. 8 microN, the work done by the pleopod pump per beat cycle is 0.91 microJ and the energy dissipated by the tube system is 0.066 microJ per cycle. The mechanical efficiency is therefore 7.3 %. Pump characteristics that may be varied by the shrimp are the beat frequency, the phase shift, the amplitude and the difference in pleopod area between the power and recovery strokes. These parameters are varied in the model to evaluate their effects. Furthermore, the moment of added mass shedding, the distance between adjacent pleopods, the number of pleopods and the total tube drag were also varied to evaluate their effects.