Using computational fluid dynamics to calculate the stimulus to the lateral line of a fish in still water.

This paper presents the first computational fluid dynamics (CFD) simulations of viscous flow due to a small sphere vibrating near a fish, a configuration that is frequently used for experiments on dipole source localization by the lateral line. Both two-dimensional (2-D) and three-dimensional (3-D) meshes were constructed, reproducing a previously published account of a mottled sculpin approaching an artificial prey. Both the fish-body geometry and the sphere vibration were explicitly included in the simulations. For comparison purposes, calculations using potential flow theory (PFT) of a 3-D dipole without a fish body being present were also performed. Comparisons between the 2-D and 3-D CFD simulations showed that the 2-D calculations did not accurately represent the 3-D flow and therefore did not produce realistic results. The 3-D CFD simulations showed that the presence of the fish body perturbed the dipole source pressure field near the fish body, an effect that was obviously absent in the PFT calculations of the dipole alone. In spite of this discrepancy, the pressure-gradient patterns to the lateral line system calculated from 3-D CFD simulations and PFT were similar. Conversely, the velocity field, which acted on the superficial neuromasts (SNs), was altered by the oscillatory boundary layer that formed at the fish's skin due to the flow produced by the vibrating sphere (accounted for in CFD but not PFT). An analytical solution of an oscillatory boundary layer above a flat plate, which was validated with CFD, was used to represent the flow near the fish's skin and to calculate the detection thresholds of the SNs in terms of flow velocity and strain rate. These calculations show that the boundary layer effects can be important, especially when the height of the cupula is less than the oscillatory boundary layer's Stokes viscous length scale.

Jet flow in steadily swimming adult squid.

Although various hydrodynamic models have been used in past analyses of squid jet propulsion, no previous investigations have definitively determined the fluid structure of the jets of steadily swimming squid. In addition, few accurate measurements of jet velocity and other jet parameters in squid have been reported. We used digital particle imaging velocimetry (DPIV) to visualize the jet flow of adult long-finned squid Loligo pealei (mantle length, L(m)=27.1+/-3.0 cm, mean +/-S.D.) swimming in a flume over a wide range of speeds (10.1-59.3 cm s(-1), i.e. 0.33-2.06 L(m) s(-1)). Qualitatively, squid jets were periodic, steady, and prolonged emissions of fluid that exhibited an elongated core of high speed flow. The development of a leading vortex ring common to jets emitted from pipes into still water often appeared to be diminished and delayed. We were able to mimic this effect in jets produced by a piston and pipe arrangement aligned with a uniform background flow. As in continuous jets, squid jets showed evidence of the growth of instability waves in the jet shear layer followed by the breakup of the jet into packets of vorticity of varying degrees of coherence. These ranged from apparent chains of short-lived vortex rings to turbulent plumes. There was some evidence of the complete roll-up of a handful of shorter jets into single vortex rings, but steady propulsion by individual vortex ring puffs was never observed. Quantitatively, the length of the jet structure in the visualized field of view, L(j), was observed to be 7.2-25.6 cm, and jet plug lengths, L, were estimated to be 4.4-49.4 cm using average jet velocity and jet period. These lengths and an average jet orifice diameter, D, of 0.8 cm were used to calculate the ratios L(j)/D and L/D, which ranged from 9.0 to 32.0 and 5.5 to 61.8, respectively. Jets emitted from pipes in the presence of a background flow suggested that the ratio between the background flow velocity and the jet velocity was more important than L/D to predict jet structure. Average jet velocities in steadily swimming squid ranged from 19.9 to 85.8 cm s(-1) (0.90-2.98 L(m) s(-1)) and were always greater in magnitude than swimming speed. Maximum instantaneous fluid speeds within squid jets ranged from 25.6 to 136.4 cm s(-1). Average jet thrust determined both from jet velocity and from three-dimensional approximations of momentum change in successive jet visualizations showed some differences and ranged from 0.009 to 0.045 N over the range of swimming speeds observed. The fraction by which the average jet velocity exceeded the swimming speed, or 'slip', decreased with increasing swimming speed, which reveals higher jet propulsive efficiency at higher swimming speeds. Jet angle, subtended from the horizontal, decreased from approximately 29 degrees to 7 degrees with increasing swimming speed. Jet frequency ranged from 0.6 to 1.3 Hz in the majority of swimming sequences, and the data suggest higher frequencies at the lowest and highest speeds. Jet velocity, angle, period and frequency exhibited increased variability at speeds between 0.6 and 1.4 L(m) s(-1). This suggests that at medium speeds squid enjoy an increased flexibility in the locomotive strategies they use to control their dynamic balance.