Research Article: How Archer Fish Achieve a Powerful Impact: Hydrodynamic Instability of a Pulsed Jet in Toxotes jaculatrix

Date Published: October 24, 2012

Publisher: Public Library of Science

Author(s): Alberto Vailati, Luca Zinnato, Roberto Cerbino, Andrew Pelling. http://doi.org/10.1371/journal.pone.0047867

Abstract

Archer fish knock down insects anchored to vegetation by hitting them with a precisely aimed jet of water. The striking force of the jet at the impact is such to overcome the strong anchoring forces of insects. The origin of the effectiveness of such hunting mechanism has been long searched for inside of the fish, in the unsuccessful attempt to identify internal structures dedicated to the amplification of muscular power. Here we perform a kinematic analysis of the jet emitted by two specimens of Toxotes jaculatrix. We estimate that at the impact the jet conveys a typical specific power of about 3000 W/kg, which is well above the maximum specific power of the order of 500 W/kg deliverable by a vertebrate muscle. Unexpectedly, we find that the amplification of muscular power occurs outside of the fish, and is due to a hydrodynamic instability of the jet akin to those occurring in Drop-on-Demand inkjet printing. The investigated fish are found to modulate the velocity of the jet at the orifice to favor the formation of a single, large, water drop that hits the prey abruptly with a large momentum. The observed mechanism represents a remarkable example of use of an external hydrodynamic lever that does possibly not entail the high evolutionary cost needed for the development of highly specialized internal structures dedicated to the storing of mechanical energy.

Partial Text

Archer fish have developed a unique method for capturing the insects populating the canopy of vegetation overhanging the mangrove swamps where they live. Once that they spot their prey, they shot it down by squirting a precisely aimed jet of water with their mouth, so that the prey falls into water where it gets readily devoured. Preys are usually firmly anchored to vegetation, with anchoring forces being typically of the order of ten times their body weight [1]–[3]. The origin of the effectiveness of the predation mechanism in archer fish has been long debated [4]–[11], since the first account on the hunting behaviour of archer fish in 1764. The striking force of the jet at the impact suggested that the squirting could be driven by internal structures able to amplify muscular power [9], so to overcome the strong anchoring forces of insects. Examples of structures dedicated to the amplification of muscular power are present in chameleons [12]–[14] and salamanders [15], [16], where the muscular energy gets slowly stored into collagen fibers, and then released abruptly to project their tongues with acceleration as high as 500 m/s2. Similar structures have been searched for inside of archer fish [9], but accurate morphological analysis and electromiography measurements on the muscles involved in the squirting process ruled out their presence [10]. The problem of the origin of the effectiveness of the jet remains thus still unsolved.

Archer fish are able to hit aerial preys with a powerful jet of water in a fraction of a second. The investigation of the mechanism leading to the effectiveness of the impact requires the utilization of a technique able to characterize the force and power delivered by the jet. In principle, the use of a strain gauge would allow the direct measurement of the force at the impact. However, such a solution would not allow to investigate the dynamics of the jet during its propagation to the prey, which proves to be essential to understand the physical mechanism that leads to a powerful impact. Therefore, in order to attain a time resolved characterization of the jet we employed a high-speed video recording technique. This non-invasive diagnostics allows us to determine the kinematics of the jet and to estimate the time evolution of the characteristic size and volume of different parts of the jet. The main requirement of the method is the availability of lateral movies of the jet, free from distortions due to the refraction at the lateral walls of the tank hosting the fish. Lateral movies are obtained by obliging fish to align parallel to a lateral window of the tank when they squirt a jet of water to prey. The alignment of fish has been obtained by placing a narrow slit on top of the water tank, so that they are able to localize the prey precisely with both eyes only when their sagittal plane is parallel to the side of the tank used as observation window [19]. A typical lateral-view image sequence of the flight (Video S1) of the jet to the prey involves an initial acceleration phase (Fig. 1A–C), followed by a nearly ballistic phase (Fig. 1D–E), and by the impact (Fig. 1F). The jet appears as being composed of a thin tail and a bulged head, with the volume of the head of the jet progressively increasing during the flight (Fig. 1G, I). In the investigated range of shooting distances (97–153 mm), the motion of the head of the jet is compatible with a linear trajectory (Fig. 1H), independently of the shooting angle. The distribution of the elevation angle of the jet above the horizon (Fig. 1J) peaks around 74°. Data for the velocity and acceleration of the head of the jet as a function of time (Fig. 2A–B) have been obtained from the same shooting sequences of Fig.1H. The jet of water is ejected from the mouth of the fish with a typical velocity of about 2 m/s. At such small velocities the drag of the surrounding air on the jet can be neglected [20]. Initially the head of the jet undergoes a strong acceleration phase, where the acceleration drops from 200–400 m/s2 to zero in about 15 ms. This phase is followed by a nearly-ballistic phase lasting 20–30 ms. The initial acceleration brings the head to a velocity of about 4 m/s. The accelerated motion of the head of the jet and the increase of its volume indicate that during the acceleration phase the velocity of the tail of the jet is larger than that of the head. The head gets progressively inflated by the liquid incoming from the tail, which also provides the thrust responsible of the acceleration of the head. This behaviour of the jet is achieved by modulating the velocity at the orifice, so that it increases gradually at the beginning of the emission of the jet. Incidentally, the modulation of the velocity at the orifice does not require specialized structures and is intrinsic in the dynamics of the spitting process: quite generally, during the pulsed emission of liquid from a nozzle the liquid starts at rest and its velocity increases gradually during the leading part of the pulse. The fact that the initial velocity of the jet is not zero suggests that before spitting the fish inhales a small amount of air into the orifice. During the acceleration phase the trajectory is not significantly affected by gravity. At the impact, vertical deviations from a linear trajectory due to the presence of gravity are estimated to be of the order of 0.5 mm, corresponding to about 10% of the size of the head of the jet. The fact that the trajectory of the head of the jet is linear allows a fast optimization of the aiming process.

Our results point to the existence of an external, hydrodynamic amplification mechanism. The understanding of the mechanism responsible of the amplification of power at the impact can be achieved in the framework of the physics of liquid jets.

Source:

http://doi.org/10.1371/journal.pone.0047867