The formation number of vortex rings formed in uniform background co-flow

The formation of vortex rings generated by an impulsively started jet in the presence of uniform background co-flow is studied experimentally to extend previous results. A piston–cylinder mechanism is used to generate the vortex rings and the co-flow is supplied through a transparent shroud surrounding the cylinder. Digital particle image velocimetry (DPIV) is used to measure the development of the ring vorticity and its eventual pinch off from the generating jet for ratios of the co-flow to jet velocity ($R_{v})$ in the range 0 – 0.85. The formation time scale for the ring to obtain maximal circulation and pinch off from the generating jet, called the formation number ($F$), is determined as a function of $R_{v}$ using DPIV measurements of circulation and a generalized definition of dimensionless discharge time or ‘formation time’. Both simultaneous initiation and delayed initiation of co-flow are considered. In all cases, a sharp drop in $F$ (taking place over a range of 0.1 in $R_{v}$) is centred around a critical velocity ratio ($R_{crit}$). As the initiation of co-flow was delayed, the magnitude of the drop in $F$ and the value of $R_{crit}$ decreased. A kinematic model based on the relative velocities of the forming ring and jet shear layer is formulated and correctly predicts vortex ring pinch off for $R_{v} \,{>}\, R_{crit}$. The results of the model indicate the reduction in $F$ at large $R_{v}$ is directly related to the increased convective velocity provided to the ring by the co-flow

Vortex ring pinchoff in the presence of simultaneously initiated uniform background co-flow

Vortex rings were formed with a piston-cylinder mechanism in the presence of uniform background co-flow supplied through a shroud surrounding the cylinder. The jet and co-flow were started simultaneously. Ratios of the co-flow to jet velocity (Rv) in the range 0–1 were considered. The formation number (F) as a function of Rv was determined using the procedure of Gharib et al. [J. Fluid Mech. 360, 121 (1998)] and a generalized definition of formation time. The results show a sharp decrease in F as Rv increases from 0.5–0.75, suggesting possible performance limitations for pulsed-jet propulsion

Thrust augmentation and vortex ring evolution in a fully pulsed jet

The time-averaged thrust of an incompressible fully pulsed jet containing a period of no flow between pulses is studied experimentally as a function of pulsing duty cycle Sr_L and the ratio of the ejected slug length (per pulse) to the jet diameter L/D. The parameter ranges investigated were 2≤L/D≤6 and 0.1≤Sr_L≤0.98. Significant thrust augmentation by pulsing was observed over the entire parameter range tested, both in terms of thrust compared to an equivalent steady jet with identical mass flux, denoted F_(SJ) >1, and in terms of thrust compared to an equivalent intermittent jet where vortex ring formation by pulsation was ignored, denoted F_(IJ) >1. F_(SJ) as high as 1.90 (90% thrust augmentation) was observed for the smaller L/D as Sr_L approached 1.0 (with larger F_(SJ) at lower Sr_L). The F_(IJ) results, which directly measured overpressure at the nozzle exit plane developed during vortex ring formation as the mechanism responsible for thrust augmentation, showed reduced augmentation at large L/D and Sr_L. The L/D dependence of F_(IJ) parallels single-pulse (Sr_L =0) results previously studied by the authors. The Sr_L dependence of F_(IJ) was linked to the interaction of forming vortex rings with vorticity from preceding pulses using digital particle image velocimetry (DPIV) measurements of the vorticity field. DPIV also revealed that the vortex rings tended to wander off axis and disintegrate as Sr_L became sufficiently large

Turning Performance in Squid and Cuttlefish: Unique Dual-Mode, Muscular Hydrostatic Systems

Although steady swimming has received considerable attention in prior studies, unsteady swimming movements represent a larger portion of many aquatic animals\u27 locomotive repertoire and have not been examined extensively. Squids and cuttlefishes are cephalopods with unique muscular hydrostat-driven, dual-mode propulsive systems involving paired fins and a pulsed jet. These animals exhibit a wide range of swimming behavior, but turning performance has not been examined quantitatively. Brief squid, Lolliguncula brevis, and dwarf cuttlefish, Sepia bandensis, were filmed during turns using high-speed cameras. Kinematic features were tracked, including the length-specific radius of the turn (R/L), a measure of maneuverability, and angular velocity (ω), a measure of agility. Both L. brevis and S. bandensis demonstrated high maneuverability, with (R/L)min values of 3.4x10(-3)+/- 5.9x10(-4) and 1.2x10(-3)+/- 4.7x10(-4) (mean +/- s.e.m.), respectively, which are the lowest measures of R/L reported for any aquatic taxa. Lolliguncula brevis exhibited higher agility than S. bandensis (ωa,max=725.8 versus 485.0 deg s-1), and both cephalopods have intermediate agility when compared with flexible-bodied and rigid-bodied nekton of similar size, reflecting their hybrid body architecture. In L. brevis, jet flows were the principal driver of angular velocity. Asymmetric fin motions played a reduced role, and arm wrapping increased turning performance to varying degrees depending on the species. This study indicates that coordination between the jet and fins is important for turning performance, with L. brevis achieving faster turns than S. bandensis and S. bandensis achieving tighter, more controlled turns than L. brevis

Hydrodynamic Fin Function of Brief Squid, Lolliguncula Brevis

Although the pulsed jet is often considered the foundation of a squid\u27s locomotive system, the lateral fins also probably play an important role in swimming, potentially providing thrust, lift and dynamic stability as needed. Fin morphology and movement vary greatly among squid species, but the locomotive role of the fins is not well understood. To begin to elucidate the locomotive role of the fins in squids, fin hydrodynamics were studied in the brief squid Lolliguncula brevis, a species that exhibits a wide range of fin movements depending on swimming speed. Individual squid were trained to swim in both the arms-first and tail-first orientations against currents in a water tunnel seeded with light-reflective particles. Particle-laden water around the fins was illuminated with lasers and videotaped so that flow dynamics around the fins could be analyzed using digital particle image velocimetry (DPIV). Time-averaged forces generated by the fin were quantified from vorticity fields of the fin wake. During the low swimming speeds considered in this study [\u3c2.5 dorsal mantle lengths (DML) per second], L. brevis exhibited four unique fin wake patterns, each with distinctive vortical structures: (1) fin mode I, in which one vortex is shed with each downstroke, generally occurring at low speeds; (2) fin mode II, an undulatory mode in which a continuous linked chain of vortices is produced; (3) fin mode III, in which one vortex is shed with each downstroke and upstroke, and; (4) fin mode IV, in which a discontinuous chain of linked double vortex structures is produced. All modes were detected during tail-first swimming but only fin modes II and III were observed during arms-first swimming. The fins produced horizontal and vertical forces of varying degrees depending on stroke phase, swimming speed, and swimming orientation. During tail-first swimming, the fins functioned primarily as stabilizers at low speeds before shifting to propulsors as speed increased, all while generating net lift. During arms-first swimming, the fins primarily provided lift with thrust production playing a reduced role. These results demonstrate the lateral fins are an integral component of the complex locomotive system of L. brevis, producing lift and thrust forces through different locomotive modes

Turning Performance of Brief Squid Lolliguncula Brevis During Attacks on Shrimp and Fish

Although squid are generally considered to be effective predators, little is currently known of how squid maneuver and position themselves during prey strikes. In this study, high-speed video and kinematic analyses were used to study attacks by the brief squid Lolliguncula brevis on both shrimp and fish. Squid attack successwas high (\u3e80%) and three behavioral phases were identified: (1) approach, (2) strike and (3) recoil. Lolliguncula brevis demonstrated greater maneuverability (i.e. a smaller length-specific turning radius) and employed more body adjustments (i.e. mantle angle posturing) during approaches toward shrimp versus fish. Squid exhibited higher linear approach/strike velocities and accelerations with faster-swimming fish prey compared with slower shrimp prey. Agility (i.e. turning rate) during prey encounters was comparable to performance extremes observed during non-predatory turns, and did not differ according to prey type or distance. Despite having the ability to modulate tentacle extension velocity, squid instead increased their own swimming velocity rather than increasing tentacle velocity when targeting faster fish prey during the strike phase, but this was not the case for shrimp prey. Irrespective of prey type, L. brevis consistently positioned themselves above the prey target prior to the tentacle strike, possibly to facilitate a more advantageous downward projection of the tentacles. During the recoil, L. brevis demonstrated length-specific turning radii similar to those recorded during the approach despite vigorous escape attempts by some prey. Clearly, turning performance is integral to prey attacks in squid, with differences in attack strategy varying depending on the prey target

Pulsed Jet Dynamics of Squid Hatchlings at Intermediate Reynolds Numbers

Squid paralarvae (hatchlings) rely predominantly on a pulsed jet for locomotion, distinguishing them from the majority of aquatic locomotors at low/intermediate Reynolds numbers (Re), which employ oscillatory/undulatory modes of propulsion. Although squid paralarvae may delineate the lower size limit of biological jet propulsion, surprisingly little is known about the hydrodynamics and propulsive efficiency of paralarval jetting within the intermediate Re realm. To better understand paralarval jet dynamics, we used digital particle image velocimetry (DPIV) and high-speed video to measure bulk vortex properties ( e. g. circulation, impulse, kinetic energy) and other jet features [ e. g. average and peak jet velocity along the jet centerline (Uj and Ujmax, respectively), jet angle, jet length based on the vorticity and velocity extents (Lω and LV, respectively), jet diameter based on the distance between vorticity peaks (Dω), maximum funnel diameter (DF), average and maximum swimming speed (U and Umax, respectively)] in free-swimming Doryteuthis pealeii paralarvae (1.8 mm dorsal mantle length) (Resquid=25-90). Squid paralarvae spent the majority of their time station holding in the water column, relying predominantly on a frequent, high-volume, vertically directed jet. During station holding, paralarvae produced a range of jet structures from spherical vortex rings ( Lω/Dω=2.1, LV/DF=13.6) to more elongated vortex ring structures with no distinguishable pinch-off (Lω/Dω= 4.6, LV/DF=36.0). To swim faster, paralarvae increased pulse duration and Lω/Dω, leading to higher impulse but kept jet velocity relatively constant. Paralarvae produced jets with low slip, i.e. ratio of jet velocity to swimming velocity (Uj/U or Ujmax/Umax), and exhibited propulsive efficiency [ηpd=74.9 +/- 8.83% (+/- s.d.) for deconvolved data] comparable with oscillatory/ undulatory swimmers. As slip decreased with speed, propulsive efficiency increased. The detection of high propulsive efficiency in paralarvae is significant because it contradicts many studies that predict low propulsive efficiency at intermediate Re for inertial forms of locomotion