REVIEW OF SCIENTIFIC INSTRUMENTS 77, 114302 共2006兲

Novel method based on video tracking system for simultaneous measurement of kinematics and flow in the wake of a freely swimming fish Guanhao Wua兲 State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China

Yan Yangb兲 The Laboratory for Biomechanics of Animal Locomotion, Graduate University of Chinese Academy of Sciences, Beijing 100049, China

Lijiang Zengc兲 State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China

共Received 31 July 2006; accepted 2 October 2006; published online 15 November 2006兲 A novel method based on video tracking system for simultaneous measurement of kinematics and flow in the wake of a freely swimming fish is described. Spontaneous and continuous swimming behaviors of a variegated carp 共Cyprinus carpio兲 are recorded by two cameras mounted on a translation stage which is controlled to track the fish. By processing the images recorded during tracking, the detailed kinematics based on calculated midlines and quantitative analysis of the flow in the wake during a low-speed turn and burst-and-coast swimming are revealed. We also draw the trajectory of the fish during a continuous swimming bout containing several moderate maneuvers. The results prove that our method is effective for studying maneuvers of fish both from kinematic and hydrodynamic viewpoints. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2372741兴

I. INTRODUCTION

Experiments play an important role in studying fish swimming mechanisms. In recent years, biologists and hydrodynamicists have shown a much renewed interest in fish locomotion, owing to the advent of improved experimental techniques that have shed new light on a number of fish swimming mechanisms.1 In general, there are two experimental approaches to study locomotion mechanisms in fishes: kinematic measurements and analysis, and quantitative flow measurements in the wake of swimming fishes.2 Kinematic analyses require fish to swim naturally under controlled conditions. Videler3 summarized two fundamentally different approaches used to meet this requirement. One recorded voluntary movements of fish swimming in static water.4–9 The other fish was induced to swim against a water current at various speeds.10–16 The main advantage of the first approach is that fish can swim freely and they are not hampered by limited space or interfering flow.3 However, in this condition, the size of the area being imaged is restricted by the field of view of the camera mounted in fixed position. If the area is large, the fish covers only a small part of the field of view and details of the moving fins cannot be obtained. If the fish occupies an appropriate part of the field of view so that its fins are clearly shown, the swimming fish will soon be out of the field of view, and it is difficult to study the stride-to-stride variability of movement. The proba兲

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lem can be solved by using the second approach, because the fish is always kept in the fixed position with respect to the camera. Nevertheless, the confined space, the noise, and nonlaminar flow regimes might be expected to cause anxiety to the fish and affect their swimming behaviors.3 Furthermore, this method is not suitable for studying maneuvers of fish. The technique of digital particle image velocimetry 共DPIV兲 was widely used in quantitative measurements in the wake of swimming fishes.17–22 Similar to the kinematic measurements, the DPIV experiments were usually done under two conditions. First, during unrestricted swimming in steady water, recordings were made when the fish came into the field of view of the camera.17,18,20,23 Second, recordings were made during the fish swimming steadily in a recirculating flow tank, where the position of the fish was constantly kept in the field of view of the camera.19,21,22 Under the first condition, investigators would meet the same problem mentioned for the kinematic measurements. Although using a recirculating flow tank can enhance the space resolution of the view of the wake,21 the recirculating flow may cause background turbulence.21 In addition, as same as the disadvantage of this method in kinematic measurements, the experiment under the second condition is just fitted for investigating the steady swimming behaviors of fish. In most previous experimental studies on fish swimming mechanisms, the measurements of fish kinematics and flow were not made simultaneously so that the analysis of kinematics and hydrodynamics were difficult to link. Fortunately, the situation has been improved in recent years. Müller et al.18 derived a kinematic explanation of the flow pattern from detailed analysis of the movements and the flow in the wake

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of a freely swimming fish. The kinematics and flow data were obtained from the top-view images 共512 pixel ⫻ 512 pixel兲 recorded by one camera with a field of view of 195⫻ 195 mm2. The results of just a few cycles were given because of the limitation of the field of view of camera. Tytell and Lauder22 examined in detail the kinematics and wake of the American eel, swimming steadily in a recirculating flow tank. They provided the first quantitative comparison of the predictions of elongated body theory to empirical forces estimated using DPIV and demonstrated a partial correlation. Nonetheless, they encountered the problems mentioned above about experiments made in recirculating flow tanks. The uses of tracking techniques make long-time investigation of the fish swimming in a large area possible. Studies using an ultrasonic telemetry tracking method have provided essential knowledge about several basic aspects of the behavior of fish, such as position, swimming speed, activity rhythms, and movement patterns.24–27 However, this technique applied without a video system cannot provide details of the movements of the fins of fish. Video tracking techniques developed quickly in robotics,28–31 and it was applied in underwater observation32 but rarely used in measuring the fin kinematics of fish. To our knowledge, none of the DPIV measurements were done using a video tracking method until now. We developed a two-dimensional 共2D兲 tracking system that contained an X-Y translation stage and two chargecoupled device 共CCD兲 cameras for simultaneous measurement of kinematics and flow in the wake of a freely swimming fish. The two cameras were fixed on the stage which was controlled to track the fish. While the fish swam freely in steady water, its continuous behaviors containing several moderate maneuvers were recorded by the two cameras. After image processing, kinematic data of body and tail together with the velocity field and vorticity in the wake were obtained. II. EXPERIMENT AND METHOD A. Experimental object and environment

The experiments were performed on a variegated carp 共Cyprinus carpio兲, which was a subcarangiform swimmer. The fish 共body length of 55.2 mm兲 was housed in a glass tank 共100⫻ 40⫻ 30 cm3兲 containing 40 l of fresh water at temperature of 共24± 2兲 ° C. B. Experimental setup and procedure

The experimental setup is shown in Fig. 1. The tank has a working area of 50⫻ 25⫻ 10 cm3 共length⫻ width ⫻ height兲 and is illuminated by a uniform light source 共ULS兲. Under the tank there is a 2D translation stage in two orthogonal directions driven by two servo motors 共SM1 and SM2兲. The translation stage has a travel range of 50 ⫻ 30 cm2, a position accuracy of 5 ␮m, a maximum speed of 0.5 m s−1, and a maximum acceleration of 10 m s−2. We set up a global coordinate system 共shown in Fig. 1兲 with the origin coinciding at the end of the Y rail and at the beginning of the X rail 共the side of a rail where a motor is fastened is

Rev. Sci. Instrum. 77, 114302 共2006兲

FIG. 1. Schematic drawing of the video tracking and recording setup. The fish swam freely in the tank which was illuminated by a uniform light source. 共We used white papers to cover a halogen lamp.兲 The emission spectrum of the light source peaks in red to yellow region. The flow around the fish was exposed by an expanded light sheet from a cw laser. A high speed CCD camera 共HSC兲 covered by an optical bandpass filter was used to catch the particle images 关picture 共B兲兴, and another CCD camera covered by a red glass plate was used to catch the swimming kinematics 关picture 共A兲兴. The two cameras were fixed on a two dimensional translation stage, which was controlled to track the fish.

defined as the beginning, and the other side is the end兲. The servo motors are controlled by a control box 共CB兲 which is connected to a personal computer 共PC兲. A cw laser 共100 mW兲 with a wavelength of 0.532 ␮m is expanded by two cylindrical lenses 共CL1 and CL2兲 to generate a light sheet. A mirror 共M兲 fixed on the bracket 共B兲 at the end of the Y rail is used to reflect the light sheet into the water tank. The flow is visualized by seeding the water with hollow glass beads 共10 ␮m, 1.1 g cm−3; TSI, Inc., Shoreview, MN兲 to reflect the laser light. The stage moves the mirror M in the X direction, tracking the fish, so that the flow in the wake can be visualized by the light sheet during swimming. Two CCD cameras 共C and HSC兲 used for obtaining the ventral views of fish are mounted on the stage which can move in both X and Y directions to track the fish. The camera C 关MTV-1881EX, 25 fps 共frame per second兲, 768 pixel⫻ 576 pixels; Mintron Inc., China兴 used to record the swimming kinematics is fitted with a lens of 16 mm focal length and a red-glass optical filter. The camera HSC 共AM1101, 100 fps, 640 pixel ⫻ 480 pixels; Joinhope Ltd., China兲 used to record the particle images in the wake is fitted with a lens of 25 mm focal length and an optical band pass filter with a wavelength of 534± 20 nm. Because the working area was simultaneously illuminated by the uniform light source and the laser light sheet, the two optical filters were placed in front of the two cameras to improve their imaging qualities. Actually, camera C is a little inclined to make sure that the centers of the fields of view of the two cameras are matched. Examples of images

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D. Methods for hydrodynamics

FIG. 2. Coordinate system and notation used to describe the kinematics and wake of the fish. The bold arrow indicates the jet flow.

taken by cameras C and HSC are shown in Figs. 1共A兲 and 1共B兲, respectively. All the images recorded by the two cameras are imported to the PC by two image grabbers. The fish was placed into the working area of the tank one day prior to the experiments. We did not train or stimulate the fish in any way. So all the behaviors recorded were spontaneous. When the measurement system was in operation, the two cameras caught images at full rate and sent these to the computer. After the computer calculated the deviation between fish’s center and the center of the field of view of camera C, a control signal was sent to the driver of the stage to track the fish, keeping the fish in the central region of the field of view of camera C. The calculation and control function were performed by an interface program written in VISUAL C⫹⫹6.0. Although the frame rates of the two cameras were not the same, the start and stop operations were synchronized by this program. The program could also record the position of the stage and the time when the computer acquired each image. The tracking duration per trial was 16.7 s, limited by the capacity of the cache memory of the image grabbers. 共We used 1 Gbyte cache memory.兲

We used a “mpiv” toolbox, which had been tested, was shown to be robust, and had sufficient accuracy,34 to obtain the flow velocity vectors and vorticity. The interrogation window we used was 16 pixels⫻ 16 pixels 共2.7 ⫻ 2.7 mm2兲, and the overlap between two consecutive windows was 50%. The movements of the camera would result in background velocity vector field. Therefore, we marked some position where the flow was not affected by the fish and considered the mean velocity vector at these positions as the background velocity vector, which was used to modify the results. We used the vortex ring model35,36 which assumes that all the energy shed by a swimming fish is contained in circular vortex rings. The cross-sectional view through a vortex ring consists of two vortices of opposite rotational sense. Location of the vortices in the velocity fields was aided by plotting the contours of vorticity. The morphology of a vortex was described by the vortex center, the core radius R0, and ring radius R. Vortex centers were marked manually. Prior to calculating R0 and R, we defined a coordinate system in which x⬙ is the longitudinal axis of the vortex ring through the centers of the pair of vortices, and axis y ⬙ is perpendicular to x⬙ 共see Fig. 2兲. Following Müller et al.,18 we estimated R0 and R by plotting the profiles of the velocity component u⬙ parallel to x⬙ and the velocity component v⬙ parallel to y ⬙, respectively. More details are described in Sec. III. The momentum angle ␸ of a vortex pair was the angle between x⬘ and x⬙. The angle ␣ between the jet flow and x⬘ was obtained as a mean value from the angles of the velocity vectors in the jet. The impulse 共I兲 of single vortex can be calculated as35 I = ␳¯⌫A,

C. Methods for fish kinematics

Camera C was in interlaced scanning mode. Using the auxiliary software of the image grabber, we could obtain 50 images/ ps from camera C after division and interpolation. The images were binarized using a custom made program. After clearing the stray points, we programed applications to obtain the midlines and the geometric centers of the fish. The midlines were smoothed using quintic polynomial. Subsequently, we calculated the mean length of all the midlines and adjusted every midline to make its length equal to the mean length. Figure 2 shows the kinematic and wake parameters of a swimming fish. The x⬘ axis was obtained from the linear regression line through the points of the anterior half 共from head tip to the middle兲 of the midline. The change in angle of x⬘ axis defined the turning angle of the fish, and the instantaneous turning rate was calculated from the turning angles between frames. The radius of the trace of the geometric centers during turning is defined as turning radius, following Domenici and Blake33 共who used center of mass instead of geometric center兲. The instantaneous swimming speed U was calculated from the displacement of the geometric centers between frames. The distance between the x⬘ axis and the given point on the midline was defined as lateral excursion, denoted by d.

共1兲

where ␳ is the density of fresh water, A is the area surrounded by the vortex ring, and ¯⌫ is the mean absolute value of the circulations of the pair of vortices. Circulation G of single vortex can be estimated as ⌫=



v⬙dy ⬙ ,

共2兲

C

d where C is a closed curve around the vortex center. The time-averaged propulsive force F can be calculated as F=

I , T

共3兲

where T is the time over which force is generated. III. RESULTS A. Trajectory of the freely swimming fish

The tracking trials were repeated 21 times. After observing the recorded images, we found that the fish rarely swam steadily but frequently performed some moderate maneuvers such as burst-and-coast swimming and low-speed turning. One swimming sequence, continuous swimming containing several moderate maneuvers, was analyzed. The trajectories of the tip of head, geometric center, and the tail tip are shown

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FIG. 3. 共Color online兲 Trajectory of the freely swimming variegated carp. The time interval between the positions is 0.02 s.

in Fig. 3. The head sometimes moves in a yawing motion, while the trajectory of geometric center is smooth. Furthermore, the trajectory of the geometric center is nearly an arc during the turn. Because the fish did not swim steadily, the tail movements in this figure are hard to recognize as undulations. B. Kinematics in low-speed turn and burst-and-coast swimming

Body curves and position of the fish during a low-speed turn and burst-and-coast swimming are depicted by the midlines in Fig. 4. Plotted tips of the head indicate the direction of the movement. The variations of the lateral excursions at the posterior half of the fish at BL/2, BL/3, BL/6 from the tail tip and the tail tip are shown in Fig. 5共a兲 共BL means body

FIG. 4. 共Color online兲 Midlines of the fish body during low-speed turn and burst-and-coast swimming. For the sake of clarity the midlines are shown every 0.08 s in this figure. The different colors of the lines indicate the sequence.

FIG. 5. Lateral excursions of body and tail, instantaneous turning rate, and instantaneous speed during the variegated carp performance of a turn and a sequence of burst-and-coast swimming. 共a兲 The lateral excursions at positions BL/2, BL/3, BL/6 from the tail tip and the tail tip. The dash-dot lines 关共A兲–共C兲兴 indicate the time when the flow and vorticity field are plotted in Figs. 6共a兲–6共c兲. 共b兲 The variations in instantaneous turning rate. 共c兲 The variations in instantaneous speed.

length兲. During the turn 共between 0 and 0.44 s兲, the tail made two half cycles in the same direction. The tail beat was slight during the first half cycle, where the turning angle was 8 deg with a mean turning rate of 59 deg s−1. During the second half cycle, the fish bent its body into a loose C curve prior to recoiling to a straight line. As a consequence, the direction of the body changed 38 deg at a mean turning rate of 130 deg s−1. The radius of the turn during the second half cycle was 0.28 BL. Considering that the first half cycle was very short and the turning angle was tiny, we did not calculate the turning radius during the first half cycle. The instantaneous turning rate 关Fig. 5共b兲兴 and speed 关Fig. 5共c兲兴 varied according to the movements of body and tail. The peak turning rate 共at 0.18 s兲 appeared prior to the instance when the tail reached the maximum excursion 共at 0.24 s兲. The instantaneous speed decreased during the body bending stage and increased during the recoil, except between 0.3 and 0.4 s.

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During that period the fish stretched its left pectoral fin. As a consequence, the increased resistance probably resulted in a decrease of speed. During the burst-and-coast swimming 共between 0.46 and 0.96 s兲, the tail also made two half cycles in the same direction. The burst stage 共midlines 6–10, Fig. 4兲 coincided with a slight turn over an angle of 8 deg and the coast stage 共midlines 11–13, Fig. 4兲 with movement in lateral direction. During burst stage 共between 0.46 and 0.78 s兲, amplitudes along the body increased and the phase differences among the movements at different positions of the midlines 关Fig. 5共a兲兴 indicated that the posterior half of the body and the tail performed undulation. The instantaneous speed increased during a burst and decreased during coasting. This is similar to the results of Videler and Weihs.37 Furthermore, the variations in instantaneous speed of the body 关Fig. 5共c兲兴 showed a phase delay with respect to the movements of tail 关Fig. 5共a兲兴. C. Hydrodynamics in low-speed turn and burst-and-coast swimming

During turning, a pair of counterrotating vortices was shed into the flow 共see vortices 1 and 2 in Fig. 6兲 when the fish body bend into a C curve, and another pair of vortices 共3 and 4 in Fig. 6兲 was shed when the body recoiled to a straight line. This is similar to the results of Sakakibara et al.38 In Fig. 6, vortex 4 was mainly outside of the field of view. The jet between vortices 1 and 2, named side jet, was directed nearly lateral 共␣ = 121 deg兲, so the momentum must have helped the body to turn. The jet between vortices 3 and 4 was called thrust jet,38 which was originally observed by Wolfgang et al.23 This jet had a considerable rearward component 共␣ = 8 deg兲. Consequently, the moving speed increased quickly when the body of fish recoiled to straight during turning 关Fig. 5共c兲, 0.22– 0.3 s兴. The direction of the lateral component of the thrust jet was nearly opposite to that of the side jet, so the thrust jet presumably also helped the fish body to stop rotating 关Fig. 5共b兲, 0.2– 0.3 s兴. While the fish performed burst-and-coast swimming 共Fig. 5兲, only one vortex 共see 5 in Fig. 6兲 appeared during the first half tail beat cycle. The jet 共␣ = −30 deg兲 near vortex 5 provided the main momentum to explain the speed increase 关Fig. 5共c兲, 0.44– 0.62 s兴. The slight lateral component of this jet also made the fish turn the small angle mentioned in the description of the kinematics. The tail beat was very slight during the second half cycle, and only vortex 6 共in Fig. 6兲 was visible. Wake parameters and momentum calculations of vortices 1–6 are summarized in Table I. The velocity component u⬙ profile of vortex 1 along y ⬙ and v⬙ profiles of vortices 1 and 2 along x⬙ 共right panel of Fig. 7兲 resembled the main characteristics of a Rankine vortex39 共left panel of Fig. 7兲. The velocity component u⬙ profiles of other vortices were similar to the results of vortex 1. The u⬙ / y ⬙ profile of the vortex showed two sharp extremes used for calculating vortex core radius R0.18 The velocity u⬙ decreases curvilinearly beyond the extremes, indicating a potential flow region. In the v⬙ / x⬙ profile, the two points where v⬙ equals to zero indicate the centers of the pair of vortices that were used to calculate the ring radius R. Velocity v⬙ between the two centers represents the jet flow velocity.

FIG. 6. 共Color online兲 The wake of a variegated carp performing a lowspeed turn and burst-and-coast swimming. The vortices are numbered for identification. The missing part in 共a兲 was caused by the shadow created by the tail blocking the light sheet; the missing parts in 共b兲 and 共c兲 were caused by the fine mesh scattering laser light. 共a兲 Velocity vector fields and vorticity of vortices 1–4 at time 0.54 s. 共b兲 Velocity vector fields and vorticity of vortices 1, 2, and 5 at time 0.66 s. 共c兲 Velocity vector fields and vorticity of vortices 1, 2, 5, and 6 at time 0.78 s.

IV. DISCUSSION A. Method

So far, most studies of extreme fish swimming behaviors have focused on the kinematics and hydrodynamics of steady swimming or mainly focused on kinematics while examining rapid maneuvering. Watching fish swimming in nature reveals that most fishes rarely swim steadily or perform fast maneuvers but perform burst-and-coast swimming and some moderate maneuvers frequently. Webb40 mentioned that most of the time fish swimming is filled with low-speed turns and small accelerations. Our measurement system offers a suit-

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Wu, Yang, and Zeng TABLE I. Wake parameters and momentum calculations. Vortex number

R0 共mm兲

R 共mm兲

␸a 共deg兲

␣a 共deg兲

1 2 3 4 5 6

3.5 3.0 3.0 2.2 3.4 2.6

6.8

−28

121

5.4

85

−8

¯ ¯

¯ ¯

−30 19

⌫ 共m2 s−1兲

I 共kg m s−1兲

F 共mN兲

1.68⫻ 10−3 1.25⫻ 10−3 1.30⫻ 10−3 0.5⫻ 10−3 1.42⫻ 10−3 0.60⫻ 10−3

2.1⫻ 10−4

2.7

0.8⫻ 10−4

0.5

¯ ¯

¯ ¯

Angles ␸ and ␣ in vortex pair 1 and 2 were calculated using x⬘ before turn; angles ␸ and ␣ in vortex pair 3 and 4 were calculated using x⬘ after turn. Angle ␣ in vortex 5 and in vortex 6 was determined using the jet near the vortices, because the pair of vortices was not observed. a

able approach to study moderate maneuvers of fish. Especially, it has the advantage to examine the stride-to-stride variability of continuous movements. In our DPIV measurement, 1 pixel in the image represents 0.17 mm, and the interrogation window we used was 2.7⫻ 2.7 mm2. The space resolution is higher than that in the DPIV results conducted by Müller et al.,18 Hanke et al.,20 and Wolfgang et al.23 It is close to the resolution of the results obtained by Nauen and Lauder21 and Tytell and Lauder,22 who conducted the DPIV experiments in a recirculating flow tank where fish swims steadily. B. Turn

The turning radius of the geometric center of a variegated carp is 0.28 BL at a mean turning rate of 130 deg s−1. Domenici et al.41 used displacements of the center of mass during C starts of a spiny dogfish and found a mean turning radius of 0.06 BL at an average turning rate of 1121 deg s−1. Some investigators42,43 claimed that turning radius was independent of velocity but proportional to body length. However, the relation between turning radius and velocity during low-speed and moderate-speed turns needs further studies. Most investigators33,41,42 assumed the center of mass of fish as the point on the midline, at 0.33 BL from the tip of head. But the center of mass of a fish will move away from

the midline when the fish bends its body. We assumed the density of fish body to be uniform and used the geometric center instead of the center of mass. Which of the two assumptions is more reasonable needs further discussion. The angle ␸ 共−28 deg兲 and angle ␣ 共121 deg兲 of the vortices 1 and 2 shed during bending of the body are very different from the values obtained during steady swimming. Müller et al.18 reported an angle ␸ of 40 deg and angle ␣ of 44.5 deg during steady swimming at 1.4 BL s−1 of a mullet. The relative lateral force component during a turn is used to rotate the body and is therefore expected to be more considerable than lateral forces occurring during steady swimming. The impulses and time-averaged forces 共Table I兲 of the side jet during turning are in good accordance with the results of Sakakibara et al.,38 who measured the flow around a turning goldfish 共Carassius auratus兲. C. Burst-and-coast swimming

Burst-and-coast swimming is used frequently by variegated carp and many other species of fish. The body is kept motionless and straight followed by one or more tail beats during each cycle. In our results, the tail did not beat symmetrically. Consequently, there was a visible lateral movement during coasting 共Fig. 4兲. A similar phenomenon has not been reported in previous studies.

FIG. 7. Comparison of the theoretically predicted velocity profiles with the results obtained from the vortices shed by the variegated carp. The left panels show the profiles of the Rankine vortex rings. The right panels show the velocity profiles of vortices 1 and 2 shown in Fig. 6. The profiles are also used to determine the core radius and ring radius of the vortex. x⬙ and y ⬙ are depicted in Fig. 2. 共a兲 Velocity component u⬙ profiles of vortices 1 and 2 along y ⬙. 共b兲 Velocity component v⬙ profiles of vortex 1 along x⬙.

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During the first half beat cycle of the tail, only vortex 5 appeared. The reason could be that the tail tip was moving close to the jet formed by vortices 3 and 4 during this half cycle, and that the vortex pairs with vortex 5 were destroyed by the jet. In the second half cycle only a very slight tail beat occurred. We assume that this beat was more passive and only produced vortex 6. The flow in the wake needs further attention during consecutive maneuvers. In conclusion, we introduce a novel method based on a video tracking system for simultaneous measurements of kinematics and flow in the wake of a freely swimming fish. Spontaneous and continuous swimming behaviors of a variegated carp 共Cyprinus carpio兲 are recorded by two cameras. The kinematic and hydrodynamic results of a low-speed turn and a burst-and-coast swimming sequence are given. The results prove that our method is effective for studying maneuvers of fish both from kinematic and hydrodynamic viewpoints. ACKNOWLEDGMENT

This work is supported by the National Natural Science Foundation of China 10332040. 1

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Tracking measurement of fish

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Novel method based on video tracking system for ...

A novel method based on video tracking system for simultaneous measurement of kinematics and flow in the wake of a freely swimming fish is described.

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