Development of a vortex generator to perturb fish locomotion

Many studies have concluded that fish modulate the stiffness of their fins during swimming (Bainbridge, 1958; Hunter and Zweifel, 1971; McHenry, et al., 1995; Long and Nipper, 1996; Long, et al., 2006; Flammang and Lauder, 2008; Curet, et al., 2011; Flammang, et al., 2013) but this has not been tested directly on swimming fish. This is due, in large part, to a lack of experimental devices that can interrogate fins without impeding the fish's natural swimming motion. One method for understanding the mechanical properties of fish fins in vivo is to perturb the fins while they are used in locomotion, and observe the response to perturbations of various strengths.

Based on perturbation studies conducted to evaluate human physiological responses (Marmarelis and Marmarelis, 1977; Kearney and Hunter, 1982; Bennett et al., 1992; Tangorra, et al., 2003), it was hypothesized that a fin's stiffness could be evaluated by measuring its response to an external fluidic perturbation. The perturbation would have to be aimed and modulated in strength for different fins, develop and travel in free-stream flows of different speeds, be applied as the fish swims freely, interact with the fin over a short period relative to the fin beat duration, and cause measurable deflection in the fin without stopping the fish's natural swimming. The relative stiffness changes in the fin can be quantified by comparing the deflections in the fin caused by vortex rings of known strengths. The strengths of the vortex rings can be estimated using the vortex size, speed and circulation (McErlean, 2011). To meet these needs, we have developed a device that generates vortices suitable for conducting perturbation studies with sunfish swimming at speeds between 0 and 350 mm s⁻¹.

Previously, vortex generators have been developed as underwater thrusters (Gharib, et al., 1998; Krueger and Gharib, 2003; Dabiri and Gharib, 2005; Mohseni, 2006), but the designs are not, simultaneously, sufficiently small and adjustable to produce vortices with the desired range of size and strength. Studies of these vortex generators did not discuss the vortices as individual rings traveling over distances at which the fish was expected to swim, and most previous aquatic generators developed as thrusters produced a fluid jet and not a discrete perturbation pulse. To be applied to freely swimming fish, a new vortex generator design needed to be developed and individual vortex rings needed to be studied as stimuli, in both static and flowing water.

To be useful for biological studies, a vortex ring should form quickly, maintain its shape, size and speed while traveling to the swimming fish, have a minimum trailing jet, interact with the fin for a short duration, and be of appropriate strength to cause a measurable deformation of the fin without stopping the fish's natural swimming. Perturbation studies are conducted on different fish over a range of swimming speeds so it is crucial to be able to adjust attributes of the vortex. Based on preliminary experiments with fish, the diameter of the ring must range from 5 to 30 mm, speeds more than 400 mm s⁻¹ should be achieved, the ring must separate from the trailing jet within 100 mm of its initial travel so that the impact duration is short, the ring must maintain its shape and velocity for at least 150 mm so that it can impact the fish throughout the testing tank, and the ring should be discrete and well-formed when impacting the fin.

Physically, the vortex generator needs to be compact in size and capable of being inserted into an aquarium or flow tank and aimed at fish fins from different heights and angles. It also needs to have settings that can be adjusted whilst the generator is in the tank. Based on the size of the tank for these experiments and the expected positions of the fish, the device had to be no larger than 70×40×100 mm (length×width×height), and aim at angles between −60 and +60 deg.

The vortex generator consists of an underwater cavity from which the vortex is ejected, a reservoir (X2 Industries, St Croix Falls, WI, USA) of pressurized water that provides the motive force, and a computer-controlled electronic solenoid (STC Valve, Palo Alto, CA, USA) that controls the flow of water from the reservoir. The underwater cavity has an open end that is covered by an orifice plate and contains a ball that travels within the cavity. Vortices are created by accelerating the ball through the cavity and ejecting a slug of water through the orifice (Figs 1 and 2B). The ball provides a clean separation of the vortex from the orifice as it seals the cavity as the vortex departs, and minimizes the trailing jet.

The underwater cavity is machined out of clear polycarbonate so that the ball is visible when adjusting its initial position. Two cylinders with different diameters were used: cavity 1, 13 mm inner diameter (i.d.), and cavity 2, 20 mm i.d. The orifice plates were machined out of 0.5 mm aluminium and are held onto the ejection end of the cavity with a clip that allows orifice plates with different diameters to be used. The cavity is supported on a rod, which allows the cavity to be positioned at different angles.

Vortex characteristics are tuned by adjusting the pressure in the reservoir, the duration for which the solenoid valve is open, the ratio of the orifice to the cavity diameter, and the ball's initial position. Reservoir pressure and the time the valve is open are controlled using a regulator (Norgren B07-202-A1KA) and microcontroller (Arduino Duemilanove, ATmega328), respectively. The ratio of orifice and cavity diameters is adjusted by selecting the appropriate orifice plate (Fig. 1B). The amount of water that will be released from the cavity is set by manually positioning the ball at the beginning of each experiment. The water pressure (P), duration the valve is open (t_valve), ratio of orifice and cavity diameters (d/D), and distance traveled by the ball (stroke length, L_stroke) are collectively referred to as the ‘perturber settings’. Once the perturber settings are configured, the test is initiated by opening the solenoid via the microcontroller.

Experiments were conducted to understand how the perturber settings affected the formation, size and speed of the vortex. The effect of flow on the vortex was also considered. Each cavity (13 and 20 mm) was tested at reservoir pressures of 7–217 kPa, at intervals of 14 and 24 kPa. These increments were selected because they led to measurable changes in the vortex outcomes during the prototyping phase. At each pressure, two t_valve values (20 and 40 ms) and two d/D values (0.9 and 0.6) were tested. The 13 mm cavity was tested using two L_stroke values (25 and 45 mm) and the 20 mm cavity was tested with one (35 mm). All fish were handled ethically according to Harvard University Institutional Animal Care and Use Committee guidelines(IACUC protocol 20-03).

The vortices were imaged using high-speed cameras (Exilim Pro EX-F1, Casio, USA, at 300 frames s⁻¹ or PCI 1024, Photron Inc., San Diego, CA, USA, at 1000 frames s⁻¹). The attributes of vortices were determined from images using MATLAB (http://www.mathworks.com/matlabcentral/fileexchange/24279-image-measurement-utility).

Vortices were analyzed during formation, propagation and impact. During formation, the pressurized water pushed the ball, which accelerated a fluid slug out of the cavity. The vortex separated from an axial jet (‘starting jet’, Fig. 2D) at a distance referred to as the ‘separation distance’. During separation, the length of the residual jet is called the ‘trailing jet length during separation’ (Fig. 2D) (Gharib, et al., 1998). During propagation, the vortex translated, and any trailing jet either dissipated or traveled with the vortex. Vortex size and translation speed were measured. During impact, the vortex interacted with a fin or foil placed about 100 mm away from the perturber. The length of the residual jet was measured again and is called the ‘trailing jet length during impact’. In experiments with no fin or foil, the trailing jet's length was measured when the vortex had traveled 100 mm. These parameters (size, speed, separation distance and lengths of trailing jets) will be referred to as ‘vortex characteristics’.

The device successfully produced vortices that met the criteria for perturbing the fins of freely swimming fish (Fig. 2C,E; Movie 1). The vortices formed quickly and maintained their shape, size and speed for desired travel distances (up to 150 mm) in static and moving water. Vortices interacted with fins for a short duration and caused measurable deformations in the fins at various tested swimming speeds [0–1.5 body lengths per second (BL s⁻¹)]. In most experiments, the fish returned to its normal swimming gait after being perturbed.

Vortex characteristics were well controlled by the perturber settings, which were easily and quickly tuned by the user. Below, we discuss the range of vortex characteristics in static flow and how these characteristics changed with perturber settings.

During formation, the vortices produced by cavity 1 (13 mm) and 2 (20 mm) separated from the starting jet (Fig. 2D) at distances between 0 and 103±1 mm (mean±s.e.m) and between 0 and 113±4 mm, respectively. Separation distance increased with increases in P and t_valve, and decreased with increases in d/D. It is important to know this distance so that vortices are not initiated unless fish are positioned beyond the separation distance.

The size of the vortex rings produced using cavity 1 ranged from 14±1 to 27±1 mm (mean±s.e.m) in diameter and 6±0 to 17±2 mm in width, while those produced using cavity 2 ranged from 19±1 to 32±1 mm in diameter and 9±1 to 18±1 mm in width. The size of the vortices increased with increases in P, t_valve, d/D and L_stroke. Overall, the width increased by a larger percentage than the diameter. For instance, on average, the width increased by 57% while the diameter increased by only 26% when the pressure was increased.

Vortex rings produced using cavity 1 and 2 traveled at speeds between 371±31 and 2155±31 mm s⁻¹ (mean±s.e.m.) and between 464±2 and 1613±25 mm s⁻¹, respectively. The speed of vortices increased with increases in P, t_valve and L_stroke, and decreased with increases in d/D. Vortex speed was most sensitive to changes in pressure. For example, a 100% increase in pressure caused a 40% increase in speed, but a 100% increase in t_valve caused a 3% increase in speed.

The length of the trailing jet produced during separation ranged from 0 to 100±2 mm and from 0 to 89±1 mm (mean±s.e.m.) for cavity 1 and 2, respectively. The length of the trailing jet produced during impact ranged from 0 to 104±3 mm and from 0 to 102±4 mm for cavity 1 and 2, respectively. The trailing jet was measured as 0 mm when there was no visible trailing jet in the videos. For most settings, the length of the trailing jet during impact was smaller for cavity 1 than for cavity 2. The length of the trailing jet increased with increases in P, t_valve and L_stroke, and decreased with increases in d/D. In some cases, the trailing jet was weak enough to dissipate before vortices made impact. For perturbation studies with fish, the production of a trailing jet was acceptable if the jet did not travel with the vortex and impact the fish at the same time. Although trailing jets were undesirable, when fast (>500 mm s⁻¹) vortices were produced, they were unavoidable.

Depending on the desired vortex characteristics, which depended on the experimental conditions such as the fin that needed to be perturbed, flow speed and the fish's position, the perturber settings were altered by the user. As discussed above, a change in a perturber setting (P, t_valve, d/D, L_stroke) generally caused a change in all the vortex characteristics (size, speed, separation distance, length of trailing jet). To adjust the vortex size and speed simultaneously, one perturber setting could be altered. To adjust only one of the two characteristics, generally two perturber settings needed to be altered. There was more than one way to adjust the vortex characteristics, and Fig. 3 illustrates a few examples of how the vortex size and speed could be adjusted.

Vortices maintained their characteristics well under different flow conditions. Flow perpendicular to the direction of vortex travel moved vortices 8±3 to 15±3 mm (mean±s.e.m.) downstream. An increase in flow speed caused no changes to vortex size, but decreased speed by an average of 16±1%. The increase in speed could be compensated for by changing the perturber settings.

Vortices caused measurable bending in fins and elicited an active response from multiple fins. Fin bending, measured in the initial 20–40 ms of impact (Fig. 2E), for the caudal fin decreased as the swimming speed increased, suggesting stiffening of the tail at higher speeds. To accurately quantify changes in the fin's stiffness, the force of the vortex can be estimated using circulation and speed measurements (McErlean, 2011), and the deflections caused by a constant force perturbation can be compared at different swimming speeds. The fins also showed an active multi-fin control against disturbances. For example, when the pectoral fin was perturbed at 0.5 BL s⁻¹, it did not show an active change, but the pelvic and caudal fins showed rapid (within 25 ms) changes in area and position. The detailed response of the fish to perturbations and estimates of fin compliance will be discussed in detail in a forthcoming publication.

Perturbation of fins is a key technique that can be used to uncover mechanical properties and control systems that cannot be understood through the study of normal locomotion alone. The generator successfully produced vortex rings of adjustable size and speed that facilitated perturbation experiments with live freely swimming sunfish swimming at different speeds. The circulation of the vortex rings will be measured for all our future biological experiments and will be used to characterize the force of the perturbation. The perturber was designed and built within the size restrictions and allowed an adequate range of motion to either aim at different fins or correct the direction of vortex propagation. The design allowed the control of four design parameters that could be tuned to produce vortex rings with desired characteristics. This device can be used to learn about the mechanical properties of fish fins as well as to understand how fish use multiple fins to stabilize body position in the face of disturbances.

We thank the members of Lauder Lab at Harvard University and Laboratory of Biological Systems Analysis at Drexel University for their help.