The Ageing of the Low-Frequency Water Disturbances Caused by Swimming Goldfish and Its Possible Relevance to Prey Detection

Hydrodynamic receptor systems are well known from many aquatic and semiaquatic animals (for a review, see Bleckmann, 1994). They are used, for example, to detect predators, prey or conspecifics. Hydrodynamic receptor systems have been the subject of extensive morphological, physiological and behavioural investigations (e.g. Görner, 1963; Tautz and Sandeman, 1980; Budelmann and Bleckmann, 1988; Coombs and Janssen, 1989; Dehnhardt et al., 1998). However, despite recent advances in the investigation of hydrodynamic sensory systems, data on biologically relevant hydrodynamic stimuli, e.g. data on water disturbances caused by moving aquatic animals or by midwater animals performing certain behaviours, are still rare.

Animal-generated water movements can be measured using a laser Doppler anemometer (LDA) (e.g. Bleckmann et al., 1991) or a hot-wire anemometer (e.g. Kirk, 1985; Coombs et al., 1989). Both techniques have a high time resolution and are very sensitive (e.g. Blickhan et al., 1990, 1992; Bleckmann et al., 1991; Krick et al., 1997). However, they detect and measure water movements at a single point only. Moving aquatic animals produce flow fields whose spatial dimensions are often complex and thus may contain additional information relevant to other aquatic animals. Unfortunately, it is not possible to reconstruct the spatial aspects of a hydrodynamic flow field completely from single point measurements. To visualize directly the complex flow fields caused by animals, one can seed non-toxic dyes (e.g. Merzkirch, 1987) or neutrally buoyant particles (Vogel and Feder, 1966; Merzkirch, 1987) into the water. Rosen (1959) used a milk layer to visualize the spatial aspects of the water movements caused by a swimming fish. However, the study was performed in a narrow raceway which prevented the fish-generated water movements from spreading laterally. The stratified water method used by McCutchen (1977) to visualize fish-generated water movements also led to some useful observations. However, neither Rosen (1959) nor McCutchen (1977) measured fish-generated water movements for longer than 15 s. In addition, neither of the two studies yielded water velocity vector fields.

The most recent approach to measuring animal-generated water movements is particle image velocimetry (PIV) (Adrian, 1991). Using this technique, water movements of various scales can be investigated with a certain time resolution over a preselected space. The principle of PIV is to seed the water with neutrally buoyant particles, illuminate a thin layer of the seeded water with a suitable device and film or photograph the illuminated particles from a direction perpendicular to this layer. Using the PIV method, researchers have recently described the water disturbances surrounding aquatic invertebrates (Stamhuis and Videler, 1995) and those that can be measured for up to several seconds behind a swimming fish (Müller et al., 1997).

To date, no-one has attempted to measure fish-generated water movements over a time span exceeding 15 s (in most cases, measurement periods are only 1 or 2 s), although swimming fish leave hydrodynamic tracks in the water that last much longer. Some piscivorous predators can use these hydrodynamic tracks to aid prey capture (G. Dehnhardt and B. Mauck, unpublished data). We have used a PIV system developed in our laboratory (Hanke and Bleckmann, 1997) to visualize and measure the water disturbances caused by swimming goldfish over a period of up to 5 min. Particle flow was analyzed using custom-designed software adapted to match the specific requirements of our experiments (Hanke and Brücker, 1998).

Two goldfish (Carassius auratus L., body length 6 and 10 cm) were trained to swim in a straight line through the middle of a water tank (100 cm×100 cm×50 cm, water level at least 40 cm; size of tank chosen to minimize wall effects) to reach a small compartment situated at the opposite wall, where they received a food reward. Before each measurement, the fish was kept in a small compartment at the start of the swimming route. Training consisted of conditioning the fish to a green flashing light (a bright light-emitting diode flashing at approximately 2 Hz). The flashing light was mounted at the lower end of a feeding tube that allowed the fish to be rewarded with a single mosquito larva.

A custom-made PIV device was used to measure the flow in a horizontal plane (termed the measuring plane) around and behind a freely swimming goldfish. Data were analyzed by cross correlation of sequential frames in multiple time scales. The horizontal plane in which the flow was measured was illuminated with an array of 10 diode lasers (laser pointers, <5 mW each). The beam of each laser was passed through a glass rod which served as a cylinder lens and spread the beam in one direction, thus generating a light sheet approximately 1 mm thick. To visualize water movements, neutrally buoyant seeding particles (Vestosint 1101, donated by Hüls AG, Marl, Germany) were put into the water. Neither the illumination nor the particles harmed the fish.

Pictures were taken using two highly sensitive CCD camera modules (Conrad Electronic) mounted above the tank. One camera was mounted above the centre of the tank, the other camera was set up next to it to extend the field of view laterally up to the wall of the tank. The use of two cameras improved the spatial resolution and the use of light. The cameras were equipped with CCTV objectives with a fixed focal length of 8 mm and an aperture of f=1.2. Pictures were recorded using Panasonic NV-F70 HQ VCRs and digitized with a video-capture card (Miro Video DC30). The capture card supplies a hardware compression which was set to 1:10. This compression does not affect the quality of PIV results (Freek et al., 1997) and is sufficient to work at the speed of standard hard disk drives (data rate 1.9 Mbyte s⁻¹ for 50 half-frames of 720 pixels×540 pixels).

The digitized pictures were stored on recordable compact discs and analyzed using a custom-designed correlation program. The range of water velocities that can occur in the wake of a fish is quite large. In principle, the velocity range of PIV depends on the adaptation of various parameters, the particle image diameter, the spatial resolution and the time scale (Adrian, 1997). While the time scale is usually fixed by the separation of the laser pulses, PIV with chronological time series recording offers the possibility of choosing different time periods between the correlation frames (multiple time scale processing). We used this method to improve the velocity range analyzed. A maximum time separation of 2 frames s⁻¹ resulted in a correlation uncertainty below 0.1 mm s⁻¹, which was of the order of the background fluctuations in the tank after a 10 min settling time. Interrogation areas (the interrogation area is a section of the recorded frame that is subjected to the correlation procedure, see, for example, Keane and Adrian, 1992) were 64 pixels×64 pixels or 32 pixels×32 pixels depending on particle density, with an overlap of less than 50 %. Since our experiments were designed to investigate the long-term behaviour of the wake over its full width, the analysis procedure was not optimized regarding the velocity and vorticity resolution. The measurement of velocity and vorticity is biased towards zero because of the following effects.

First, seeding density was not always optimal as a result of experimental constraints. A seeding density of less than 12 particles per interrogation area biases the velocity measurement towards zero, partly because the rate of false vectors (‘outliers’) produced by the correlation procedure is enhanced, particularly for higher velocities (Host-Madsen and McCluskey, 1994). Outliers were removed as far as possible using a moving average validation algorithm (Host-Madsen and McCluskey, 1994).

Second, since the field of view was wide enough to cover the width of the wake, limited spatial resolution resulted in considerable velocity gradients within interrogation areas. Velocity gradients within an interrogation area bias the velocity measurement towards zero as a result of various effects (Keane and Adrian, 1992; Westerweel, 1997).

Third, the resolution of the smaller structures of the vortices was limited. Vorticity was calculated on the basis of a limited set of vectors using a linear approach (Landau and Lifshitz, 1966), which also biases the measured value towards zero (Lourenco and Krothapalli, 1995). Since all these error sources are effective in the same direction, our results give a lower boundary for the true values. This effect is greatest for the large velocity and vorticity values at the leading edge and can be assumed to fall below the noise level for the lowest measured values.

Below, we present velocity profiles and dimensions for 10 wakes produced by the goldfish. Fig. 1 shows the water velocities as vector fields (left) and the corresponding vorticities as contour lines (right) in a typical example (trial 1) for t=0.6 s, 1.5 s, 2.3 s and 7.8 s where t=0 is the time when the snout of the fish enters the field of view. Vorticity, rot(v), is defined as:

Fig. 2A,B shows the development of the maximum and mean water velocity over time for the 10 trials; Fig. 2C shows the corresponding vorticity. Both the velocity and the vorticity reach a maximum when the fish is in the field of view. Fig. 3 describes the changes in velocity with time in the 10 trials, plus an additional wake from a coasting fish (Fig. 3K). In most of the examples, the range of high velocity moved laterally according to the moving vortices.

The propagation trajectory of the water disturbances in trial 1 was compared with the propagation trajectories of laminar vortex rings studied by Saffman (1970) and Weigand and Gharib (1997). This comparison allows us to investigate further whether swimming goldfish produce a wake composed of laminar vortex rings. The vortex ring model is in accord with the observation that the vertical spread of fish-generated wakes was considerably less than its horizontal spread. This qualitative observation was made in trials in which the fish passed the field of view above or below the illuminated layer.

Weigand and Gharib (1997) presented measurements of the trajectories of laminar vortex rings with a diameter of 3 cm generated by a step-motor-driven piston. The Reynolds number Re=г/ν was between 830 and 1650, ν was assumed to be 0.01 cm² s⁻¹, the kinematic viscosity of water at 20 °C, and was measured using a laser Doppler anemometer. They found their data to be consistent with equation 2 with the best fit yielding k=14.4 and k′=7.8. All measured data were within the range of k=13.6, k′=7.5 (upper bound) to k=14.5, k′=10.6 (lower bound).

Lines b, c and d in Fig. 4 show plots of equation 3 with k=14.5, k′=10.6 (line b), k=14.4, k′=7.8 (line c) and k=13.6, k′=7.5 (line d); i.e. the upper and lower bounds and the best fit to the experimental data of Weigand and Gharib (1997). As can be seen, the fish-generated water disturbance in the present study spread considerably less far than the laminar vortices produced by a step-motor-driven piston (Weigand and Gharib, 1997). However, equation 3 derived from the propagation velocity of a laminar vortex trajectory fitted our data well (note that the gradient of line a is shallower than our data above t*=0.03).

Our measurements show that a small swimming fish leaves a hydrodynamic trail in the water that potentially could inform other animals, such as predators, about its presence even several minutes after its passage. Even after this period, the trails contain information about the direction in which the fish has moved and the time that has passed since it swam by. The latter is indicated by the decay of vorticity in the vortex street. Vorticity cannot be measured directly, but must be derived from multiple point velocity measurements. However, some fish, including goldfish, have up to several hundred superficial neuromasts on each side of the body (e.g. Puzdrowski, 1989).

Thus, in principle, their lateral line should be able to make simultaneous velocity measurements at multiple points, an important prerequisite for the estimation of the vorticity in a fish-generated wake.

The swimming direction of a fish can be derived from the velocity gradient in its wake and, at least when a fish is gliding, from the direction of gross water flow in the wake (see Fig. 1), which will persist for more than 60 s. The width of a track and the amount of water velocity depend on the body size of the track generator, i.e. the size of a potential prey object (Table 1; Fig. 3).

A comparison of our data with the theoretical model of Saffman (1970) and the experimental data of Weigand and Gharib (1997) provides further evidence that fish-generated water disturbances partially propagate as vortex-ring-like structures. Compared with the data of Weigand and Gharib (1997), the fish-generated vortices had a lower propagation distance. This may partly be due to turbulent regions in fish-generated vortices (Bleckmann et al., 1991). In addition, interaction between the vortices in the vortex street will pull the vortices towards the middle of the street. These effects could not be quantified in our analysis. The shape of the cross section of a laminar vortex ring will influence its propagation behaviour (e.g. Shariff and Leonard, 1992). The proportionality constant k should range between zero for a Rankine vortex with small core size and 16 for a spherical Hill’s (Hill, 1894) vortex. The value of k=15.9 obtained from the best fit to our data (see Fig. 4) therefore indicates that fish-generated vortices have a horizontal cross section that is more similar to a Rankine vortex (Blickhan, 1992, 1997; Müller et al., 1997) than to a Hill’s vortex. Thus, we can obtain an idea of the three-dimensional structure of the wake which could not be measured directly using our two-dimensional PIV device.

It has never been demonstrated conclusively that fish use hydrodynamic wakes when hunting prey. However, blindfolded seals can track the hydrodynamic wake caused by a model submarine (G. Dehnhardt and B. Mauck, unpublished data), suggesting that seals might be able to hunt fish by following their vortex trails. Behavioural experiments are under way in our laboratory to investigate this further. Lateral line thresholds are 2–3 orders of magnitude more sensitive than the hydrodynamic thresholds of seals (e.g. Bleckmann, 1994; Dehnhardt et al., 1998). In addition, fish can discriminate not only between water motions that differ in frequency, amplitude or frequency modulation (Bleckmann, 1994) but also between those caused by moving objects that differ in size, shape or speed and direction of movement (D. Vogel and H. Bleckmann, unpublished data). Thus, the lateral line of fish could potentially detect and analyze fish-produced vortex trails such as those recorded here.

We thank Dr Joachim Mogdans for helpful comments on the manuscript, Hüls AG (Marl) for donating the neutrally buoyant particles and Dr Denise R. McCluskey for supplying literature on the validation of PIV measurements obtained under non-ideal conditions. The research reported herein was performed under the guidelines established by the current German animal protection law (‘Tierschutzgesetz’).