• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Energetics comparison between zebrafish C-shaped turning and escape: self-propelled simulation with novel curvature models*

    2019-07-26 11:27:02WANGZhongweiYUYongliang

    WANG Zhongwei, YU Yongliang

    (School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China)

    Abstract The zebrafish C-start occurs not only in the escape response (C-escape), but also in the non-escape response (C-turn). They have different deforming modes and durations, and put in distinct kinematics performances. With the same bending amplitude, C-turns achieve larger turning angles, while C-escapes have higher velocities. However, little is known about their hydrodynamic mechanisms and energetics features. We proposed two novel curvature models based on the deformation characteristics of C-turn and C-escape, respectively. An optimization algorithm was used to determine the model parameters according to experimental data. Through self-propelled numerical simulation, we found that the positive moment at stage 1 of C-turn was large and the negative moment at stage 2 was small. So C-turn achieved a large turning angle. However, C-escape had a large thrust at stage 2, which led to the negative moment increasing and the turning angle reducing. We also found that the duration had little effect on the turning angle, but had a significant influence on escape velocity and energy consumption. Therefore, in order to save energy the duration of C-turn is usually over 100 ms, and the duration of C-escape is near 50 ms in order to pursue high speed.

    Keywords C-start; turning; curvature model; self-propelled swimming; energetics

    C-start is a type of burst maneuver pattern, in which the fish starts from rest and bends its body into a C shape, after which the tail flaps back and moves in a new direction[1]. It is widely believed that C-start occurs in the fish’s escape response[2]. In order to avoid predatory threats or external stimuli, fish can rapidly turn and escape by using C-start[3-4]. However, experimental studies have shown that, in the absence of predatory threats and external stimuli, the zebrafish also performs a C-start to make a turn starting from rest[5]. According to the purpose of swimming, this kind of C-start is called a C-turn, whereas the C-start in escape response is called a C-escape. Zebrafish C-turns and C-escapes have different deforming modes and durations, which result in the difference in the locomotion performance: with the same bending amplitude, the speed of C-turn is not as fast as that of C-escape, but it achieves a larger turning angle. In order to explain the difference in their swimming performance, it is necessary to compare the hydrodynamics and the energetics of zebrafish’s C-turn and C-escape.

    Researchers previously conducted extensive studies on the hydrodynamics of C-escape. Hu et. al. numerically studied the tail-flapping model of C-start[6]. Jing et al. conducted in-vivo experimental observations and theoretical analyses of C-escapes of crucian carp and yellow catfish[7-8]. Tytell and Lauder conducted the first in-vivo PIV experiment on C-escape and found that there were three jets in the flow field[9]. Witt et al.[10]studied the effects of flexibility on C-escape with simple physical models. Liu et al.[11]performed the self-propelled simulation of C-escape for the first time, and revealed the important role of the traveling curvature wave in the C-escape. Subsequently, Gazzola et al.[12]used evolutionary optimization to prove that C-escape is the best way to achieve maximum swimming distance. Li et al.[13-14]studied the effect of the head passing through a wake vortex on the trajectory of the locomotio. Borazjani et al.[15-16]studied the role of caudal and dorsal fins. Song et al.[17]studied the rapid turning problem in larval fish’s escape response. However, to the best of our knowledge, research on the hydrodynamics and energetics of zebrafish C-turn has not been reported.

    Self-propelled numerical simulation is an important method to study on hydrodynamics of C-starts, which has been used for researching C-escape[11-14]. During the self-propelled simulation, the deformation action of the fish body is needed as input conditions. For steady swimming, people commonly use sine waves to describe the undulation of the fish body[18-20]. For C-escape, due to the complexity of the deformation, many previous studies used the discrete experimental data directly[13-17]. However, this requires spatio-temporal interpolation and fairness, in which the calculation is easy to divergence and repeatability is poor. Moreover it is difficult to grasp the principal characters of deformation. Liu et al.[11]and Gazzola et al.[12]established a simplified curvature model for C-escape by superimposing sinusoidal traveling waves and standing waves. However this model may not be applicable to C-turns because of the difference in the deformation pattern between C-turns and C-escapes. How does one select the model parameters so that the model is in agreement with the experiment? This problem has not been resolved either.

    In this paper, we propose novel curvature models to describe the deformations of C-turn and C-escape of zebrafish. Parameters of curvature models are determined based on experimental data with an optimization algorithm. Then we perform self-propelled numerical simulation in order to explore the hydrodynamic mechanism and energetics features of C-turns and C-escapes. The influences of both the deforming mode and duration on the C-start swimming performance are discussed.

    1 Materials and methods

    1.1 The fish body model

    The contour of zebrafish’s body is symmetrical up and down, and it can be described by the function of the half width of the fish body:

    (1)

    wheresis the curve coordinate of the fish midline,L

    is the length of the fish body, andw1,w2,w3,w4,w5are coefficients whose values are fitted according to the real fish body contour and listed in Table 1. The cross section of the real fish body is approximately elliptical. According to the geometric properties of the ellipse, the average half width of the fish body isw(s)=wm(s)π/4. In this paper, a two-dimensional fish model is adopted, whose half width is equal to the average half width of the real fish.

    Table 1 Coefficients in the half width function

    1.2 Establishment of the curvature model

    Figure 1 gives experimental images of typical C-turn and C-escape of zebrafish, which are provided by Zhang Bingbing[5]. We can find that both the C-turn and C-escape have two stages, bending of the body and backward flapping of the tail, which is the main deformation characteristic of the C-start. The difference is that C-turns only flap back to the straight-line state at most, and the body is always bent to only one side and there is no reverse bending. However, C-escape has reversed bending after 43.7 ms. Domenici and Blake[3]classify C-start into single-bend and double-bend types based on the absence or presence of reverse bending. The C-turn is of the single-bend type, and the C-escape is of the double-bend type. In addition, the durations of C-turn and C-escape are significantly different, and the former is nearly three times the latter.

    Fig.1 Experimental images of zebrafish C-turn and C-escape

    The unilateral bending of C-turns means that the curvature of the fish midline is always positive. Therefore,we establish a curvature space modelκ(s) similar to a solitary wave as shown in Fig. 2(a). It consists of five parameters.Ais the amplitude of curvature, ands1,s2,s3, ands4are the coordinates along the fish midline. This model can be described by the function

    κ(s)=f(s,s1,s2,s3,s4,0,A),

    (2)

    wherefis a piecewise function defined as follows:

    f(ζ,ζ1,ζ2,ζ3,ζ4,f1,f2)=

    f1+(f2-f1)[ξ-sin(2πξ)/2π],

    (3a)

    (3b)

    whereζis an independent variable, andζ1,ζ2,ζ3,ζ4,f1, andf2are parameters. The five parameters of the curvature space model are all related to time. Their tendency to change over time is approximately illustrated in Fig. 2(b), i.e., the curvature time model, which reflects the growth and propagation of curvature. They can also be described by the functionfas follows:

    A(t)=f(t,0,ta,T,T,T,Am),

    (4a)

    s1(t)=f(t,t1,10T,10T,10T,s11,s12),

    (4b)

    s2(t)=f(t,t2,T,T,T,s21,L),

    (4c)

    s3(t)=f(t,0,t3,T,T,s31,L),

    (4d)

    s4(t)=f(t,0,t4,T,T,s41,L),

    (4e)

    whereTis the duration of C-turns;ta,Am,t1,s11,t2,s21,t3,s31,t4, ands41are parameters of the curvature time model. Each curve has two parameters, and their meanings are shown in Fig. 2(b) in detail. In order to makes1(t)=L,s12should be:

    Fig.2 Curvature models and flow chart of the optimization

    s12=s11+(L-s11)/

    For the C-escape, it is seen in Fig. 1 that the deformation in the bendding phase is very similar to the C-turn. The curvature is established gradually and propagates backward. Liu et al.[11]and Gazzola et al.[12]established a C-escape curvature model by superimposing standing waves and sinusoidal traveling waves. However, we find that this model can not reflect the deformation of the zebrafish C-escape accurately, because the standing wave does not meet the characteristics of backward propagation of curvature. Even so, the idea of superimposing sinusoidal traveling waves is worth learning. We utilise the curvature model of C-turn (i.e., Eqs. (2)-(4)), and add a sinusoidal traveling wave to model the curvature of C-escape. The sine curvature traveling wave is defined as follows:

    (5a)

    (5b)

    (5c)

    whereAsinrepresents the amplitude of the sine wave,λis the wavelength,Tsinis the period,φ0is the initial phase,a0anda1are coefficients of the amplitude distribution functionσ(s),shindicates the head length of the fish, andtsandteare parameters in the time functionτ(t).

    1.3 Determination of model parameters

    There are 10 and 19 parameters in the C-turn and C-escape curvature models, respectively. The curvature models have to be consistent with the experiment. In order to identify their parameters, we used an optimization algorithm to fit the experimental data. First, we extract several discrete points on the midline of the fish body from the experimental image and convert them to the fish head coordinate system. Then we calculate the model midline with the curvature model in the fish head system. The optimal objective function is

    (6)

    The optimization process is shown in Fig. 2(c), wherepiis theithparameter andδiexpresses the iterative step length ofpi, whose value is 0.01 time the unit ofpi. For the C-turn, in each iteration, all the parameters are traversed in three cases,pi-δi,pi, andpi+δi. There are 310(59 049) cases, and the parameter combination of the least error is selected. If the deviation does not converge, then the iterations continue; If the opposite is true, then the iterations terminate. For the C-escape, the parameters of the ‘C-turn’ model are firstly determined by the above method, and then the parameters of sine wave. The parameters should meet certain physical constraints, such as 0

    Table 2 displays the parameters of the optimized curvature model. The midline of the fish body is calculated by the curvature model and compared with the experimental points under the fish head coordinate system, as shown in Fig. 3(a), 3(b). It is observed that there is some error in the model curve compared to the experiment. At the end of the C-turn, the fish body is not completely straightened, but the model curve is fully straightened. The error for C-escape is largest att/T=1/11, as shown in Fig. 3(b). However, as a whole, the curvature model describes the deformation of zebrafish C-turn and C-escape very well. Their errors are only 2.18% and 1.44%, respectively.

    Table 2 Values of the curvature model parameters

    Fig.3 Deformations of C-turn and C-escape in the fish head and center-of-mass frames

    Although the curvature model established in this paper has 19 parameters at most, it is much lower than the 204 discrete experimental points (12 maps, 17 points for each map). Moreover, the curvature model grasps the main features of deformation, and the curvature is smooth, which facilitates numerical simulation. The curvature model has practical guiding significance for robotic fish[21].

    1.4 Governing equations of the self-propelled swimming

    The self-propelled swimming of fish is jointly controlled by the equations of fluid mechanics anddeforming body dynamics. The fluid control equations are incompressible Navier-Stokes equations

    ·u=0,

    (7a)

    (7b)

    whereu,p,ρandνare the velocity, pressure, density, and kinematic viscosity of the fluid, respectively.

    In the fish center-of-mass coordinate system, the swimming velocity of the fishu, can be decomposed into the translational velocityuc, the rotation velocityΩ, and the deformation velocityu′:

    u=uc+Ω×r′+u′,

    (8)

    wherer′ is the coordinate of the fish body in the center-of-mass reference system. The deformation satisfies the linear and angular momentum conservation laws

    What Fig.3(a), 3(b) shows is under the head system. To satisfy Eq. (9), it should be transformed into the center-of-mass system, as shown in Fig. 3(c). The rotational angle of the center-of-mass reference system relative to the head system is computed using Newton’s iteration method according to Eq. (9b). The deformation speed is determined by the deformation under the center-of-mass system. The translation and rotation of the fish body are governed by Newton’s second law of motion

    The finite-volume method,artificial compression, and overlapping grids were used to solve the hydrodynamic equations. The Newton iteration method was used to couple the hydrodynamics and the deforming body dynamics. Those methods have been verified and validated, and has been used in the study of fishlike C-escape[11].

    1.5 Dimensionless parameters

    In the experiment shown in Fig.1, the fish body length isL=3.31 cm, the duration of the C-turn isTturn=145.6 ms, and the duration of the C-escape isTescape=53.4 ms. TakeLandTescapeas the characteristic length and time, then the characteristic velocity isU=L/Tescape=0.62 m/s, the Reynolds number isRe=UL/ν=2.05×104, and the dimensionless duration of C-turn is 2.73. Whereν=1.003 ×10-6m2/s is the kinematic viscosity coefficient of water. According to the two-dimensional fish body model defined by Eq. (1), dimensionless fish mass and initial moment of inertia are 6.36×10-2and 4.01×10-3, respectively.

    To measure hydrodynamic and energetics properties, we define the thrust, torque, and power coefficients as follows:

    Where thrust is the component of the fluid force along the direction of the fish movement, the sign of the torque indicates whether it is in the same direction with the angular speed, and Power is the mechanical power consumed during the fish’s self-propelled swimming, which is defined as

    (11)

    2 Results and Discussions

    Both thedeformation and duration of C-turns and C-escapes are different. In order to explore their effects separately, we investigated four cases, as shown in Table 3. Case1 and case3 are the C-turn and C-escape of zebrafish in the experiment shown in Fig. 1. Case2 and case4 have the same deformation with case1 and case2, respectively, but the duration is different.

    Table 3 The setups and numerical simulation results of the four cases

    2.1 Numerical simulation results and comparisons with experiment

    Figure 4 shows the trajectory of the fish midline of C-turn (case 1) and C-escape (case 3) obtained from experiments and numerical simulations. We use the position and angle of the fish head of the end moment to represent errors between numerical simulations and experiments. In Fig. 4(a), the dashed line is the fish midline of numerical simulation, and the black line is that of experiment. It can be seen that the head position error of C-turn is 9.3%, the turning angle error is 7.1% (1-78.5/84.5), and the position error of C-escape is 9.6%, the angle error is 4.8% (55.1/52.6-1). All the error was lower than 10%. Because what we used in this paper was a two-dimensional and uniform density fish model, and the pectoral and caudal fins, three-dimensional fish body and flow field, and the density distribution was not taken into consideration, the error within 10% is acceptable. Overall, numerical simulations were basically consistent with experiments, which reflected the kinematics characteristics of C-turns and C-escapes.

    Table 3 demonstrates that, case1 has the lowest energy consumption and the highest relative propulsion efficiency and relative turning efficiency, while case 3 achieves the fastest swimming velocity. They have different deformation and duration, whose influence will be discussed separately in the succeeding sections.

    2.2 Effects of deformation patterns

    C-turn (case 2) and C-escape (case 3) are numerically simulated with the same duration (53.4 ms). As shown in Table 3, C-turn still have greater turning angles and lower energy consumption than C-escape, even with the same duration. Figure 5 displays the time curves of the velocity, angular velocity, turning angle, thrust coefficient, torque coefficient and power coefficient of C-turn (case 2) and C-escape (case 3). According to the definition in Fig. 3,t/T=0-0.4 is the bending phase (stage 1), andt/T=0.4-1 is the backward flapping phase (stage 2).

    Figure 5 (a) shows that velocity of C-turn and C-escape is very close at stage 1. Aftert/T=0.4, velocity of C-escape increase rapidly, peak at aroundt/T=0.7 (17.5L/s), and then decline slightly. However, the velocity enhancement of C-turn is not as significant as C-escape, whose peak value is 11.2L/s at aroundt/T=0.9. At the end time, the speed of C-escape (13.9L/s) is 40.4% higher than that of C-turn (9.9L/s). The difference in speed is due to the thrust of the fluid. It can be seen from Fig. 5 (d), both the thrust coefficients of C-turn and C-escape peak at aboutt/T=0.57 in stage 2. The peak of the C-escape (0.46) is 2.4 times that of the C-turn (0.19).

    Fig.4 Comparison of the fish midline trajectory between the experiment and numerical simulation

    Fig.5 Time curves of C-turn (case 2) and C-escape (case 3)

    As shown in Fig.5 (e), both the torque coefficients of C-turn and C-escape present positive torque at first and then negative torque. Positive torque has a large number and last a short time, however negtive torque has a relative little number and last a long time. This leads the angular velocity in Fig. 5 (b) to raise rapidly first and then decrease slowly. Time integration of the angular velocity results in the change of turning angle in Fig. 5 (c). Although the positive torque peak of C-turn (0.12) is slightly lower than C-escape (0.14), the duration of positive torque of C-turn (t/T=0-0.3) is longer than C-escape (t/T=0-0.22), which result that C-turn has a greater peak angular velocity (3.6(°)/ms) than C-escape (3.1(°)/ms). On the other hand, C-escape has a larger negative torque peak (-0.1) than C-turn (-0.048 ), which results that the angular velocity of C-turn decline slowly and almost stays positive all the time, however the angular velocity of C-escape fall quickly and reduce to negative att/T=0.7. So the turning angle of C-turn increase constantly, while the turning angle of C-escape begins to decrease att/T=0.7. Figure 5 (c) shows that the gap of turning angle between C-turn and C-escape expands aftert/T=0.7. At last, the turning angle of C-turn (85.7°) is 46% larger than C-escape (58.7°).

    Figure 5 (f) shows that the peak power coefficient at stage 1 is much larger than stage 2. Integrate the power coefficient, we could see that the energy consumed by C-turn and C-escape at stage 1 account for 77% and 63% of the total energy, respectively. This indicates that energy is mainly consumed at stage 1 in C-start, especially in C-turn. On the other hand, both the peak power coefficient of C-escape at stage 1 and stage 2 are larger than C-turn. At stage 1 the peak power coefficient of C-escape (3.36) is 1.78 times that of C-turn (1.89), and at stage 2 the peak power coefficient of C-escape (0.94) is 2.76 times that of C-turn (0.34).

    In addition, we found that there were two peaks in each curve of C-turn at stage 1. This is due to the two mechanismsof C-bend: curvature growth and propagation, as shown in the curvature-time model in Fig. 2 (b). The twin peaks in the time curves of C-turn reflect the curvature growth and curvature propagation, respectively. Parametertaindicates the speed of curvature growth.ta=0.15T, 0.3Tfor C-turn and C-escape, respectively, as shown in Table 2. Due totaof C-turn is small, before the curvature of the C-turn begin to propagate, it has reached a peak. However,taof C-escape is large, so when the curvature starts to propagate, it’s still increasing, and the growth and spread of curvature overlap with each other.

    In order to further understand the hydrodynamics and energetics mechanism of C-turns and C-escapes, we ploted the vorticity of the flow field, the center-of-mass reference system and the fluid stress distribution in Fig.6. Since the Reynolds number in this paper is 2.05×104, so the viscous stress is much smaller than the pressure stress and we only show the pressure distribution. The pressure on the two sides of the fish was concentrated to the midline, and the length of the arrow indicates the relative magnitude of the pressure.

    Fig.6 The vorticity field, the fluid stress distribution, and the center-of-mass frame

    As was stated above, we decomposed the fish swimming into translation, rotation and deformation. The translation and rotation is the motion of the center-of-mass coordinate system in Fig. 6, and the deformation is under the center-of-mass system, which is exactly the same with that in Fig. 3(c). The so-called self-propelled numerical simulation is to determine the acceleration and angular acceleration of the fish body, and then the velocity, angular velocity, position and angle of the center-of-mass system, according to the fluid force and torque, at the given predetermined deformation under the center-of-mass system.

    Figure 6 demonstrates that C-turn and C-escape have similar flow field. At stage 1, a positive vortex sheds from the head and a negative vortex sheds from the tail. At stage 2, another positive vortex sheds from the tail. However, due to the reversed bending at stage 2 of C-escape, a negative vortex generates att/T=0.9 near to the tail. Moreover, the positive vortex of C-escape near to the tail is stronger than that of C-turn (for example,t/T=0.5, 0.6), and the time of shedding is earlier. The positive vortex sheds from the tail completely att/T=0.8 in C-escape, while at the end time in C-turn. The vortex will result in the generation of jet in the flow field, which will induce the fluid force and torque on the fish.

    In Fig.5(f), power coefficient peaks att/T=0.2 in C-turn, and att/T=0.1 in C-escape. Form Fig. 6 we found that the fluid stress also peaks att/T=0.2 and 0.1 in C-turn and C-escape, respectively. This indicates that the power at stage 1 is mainly used to overcome the fluid stress generated by the C-shaped bending. At stage 1, there are three alternating reversed fluid stress on the head, the middle of the fish body, and the tail. Att/T=0-0.4 in C-turn andt/T=0-0.2 in C-escape, the stress on the head causes a negative torque and the stress on the tail causes a positive torque. Although the stress on the head is greater, the range of stress on the tail is larger, and the tail is further away from the center-of-mass so the arm of force is longer. The positive torque on the tail will overcome the negative torque on the head, and the fish will subject to a positive torque overall. However, att/T=0.5-0.8 in C-turn andt/T=0.3-0.7 in C-escape, the direction of stress will reverse. The stress on the head will generate a positive torque and the stress on the tail will generate a negative torque, and the negative torque at the tail will dominate for the same reason as above. The thrust coefficient of C-escape peaks att/T=0.6 in Fig. 5(d), and the stress on the tail also reaches the peak of stage 2 and along the direction of body movement. The stress peak at stage 2 of C-escape is greater than C-turn, which leads to a large enhancement of the velocity in C-escape. However, the larger stress will generate a larger negative torque. Att/T=0.7, the stress on the tail in C-escape is almost perpendicular to the body, so the arm of force is large, and the negative torque reaches a peak. However, the stress on the tail in C-turn is smaller and the arm is short, so the negative torque of C-turn is smaller than C-escape.

    The Strouhal numbers (St=A/uT) in fish steady swimming is in the range of 0.25-0.35, where A is the width of the wake. In zebrafish C-start, we define A as the amplitude of the tail’s deformation in the center-of-mass frame, as shown in Fig. 3(c). Then the Strouhal number of C-turn and C-escape is 0.59 and 0.57, respectively, as listed in Table 4. Such Strouhal numbers are very high, which will induce a sharp thrust and a low propulsive efficiency. Strouhal numbers of C-turn and C-escape have little difference, and the velocity is proportional to the amplitude of the tail. This indicates that due to the reverse bending in C-escape the deformation amplitude of tail increases, and the velocity will increase accordingly.

    Table 4 Strouhal numbers of C-turn and C-escape

    2.3 Effects of duration

    The effect of duration on the velocity, the turning angle and the energy consumption of C-turn and C-escape were studied in this section.

    Table 3 shows that, if the duration of C-turn increase from 53.4 ms (case 2) to 145.6 ms (case 1), the swimming velocity will reduce by 69% (1-3.1/9.9), but the energy consumption can reduce by 86% (1-4.47/32.9), and the turning angle only reduce by 8% (1-78.5/85.7). However, if the duration of C-escape decrease from 145.6 ms (case 4) to 53.4 ms (case 3), the energy consumption will increase by 6.3 times (46.9/6.44-1), swimming velocity will increase by 2.2 times (13.9/4.3-1), and the turning angle only increase by 10% (58.7/53.3-1). This demonstrates that the duration has little effect on the turning angle, but has a significant effect on the velocity and energy consumption. Increasing duration of C-turn can significantly reduce energy consumption, and decreasing duration of C-escape can greatly increase the velocity. The reason may be that the turning angle is a dimensionless quantity, but the dimension of velocity (L/T) is proportional to the reciprocal of time and the dimension of energy consumption (ρL4/T2) is proportional to the square of time’s reciprocal.

    By comparing the four cases in Table 3, we find that the C-turn in reality (case 1) consumes the least amount of energy, and its relative propulsion and turning efficiency are the highest, but it has the slowest swimming velocity. However, the C-escape in reality (case 3) has the fastest swimming velocity, but meanwhile it consumes the most energy, and the relative propulsion and turning efficiency are the lowest. Moreover, the highest turning angle is in case 2, and the second is case1. This indicates that zebrafish pursues relatively high turning angles and to save energy in C-turn, while pursues the fastest swimming velocity at the cost of high energy consumption in C-escape.

    3 Conclusion

    In conclusion, we established models of zebrafish’s C-turn and C-escape. Parameters were derived with an optimization algorithm according to the experimental data. The deformation obtained by the curvature model accorded with the experiment very well. We performed self-propelled numerical simulation, and the patterns of the midline of fish was also consistent with experiment(the error was within 10%).

    By comparing C-turn and C-escape models, there are three points worth noting. Firstly,the difference in swimming velocity and turning angle between the C-turn and C-escape mainly occurred at stage 2. Secondly, the mechanism of the turning was that a large positive torque was generated at stage 1 and a relative small reverse torque was generated at stage 2, which led to the positive angular velocity to maintain for a long period of time and to obtain turning angle. Furthermore, the reverse bending of C-escape at stage 2 increased the tail’s deformation amplitude, resulting in a strong fluid stress and a high velocity. Meanwhile, the reverse bending also led to the negative torque to increase, which resulted in that the angular velocity decreased rapidly and the turning angle reduced.

    We conclude that the duration had little effect on the turning angle, but had a significant influence on the swimming speed and energy consumption. Improving the duration of C-turn significantly reduced the energy consumption and maintained a relatively high turning angle at the same time. Decreasing the duration of C-escape dramatically increased the swimming velocity, but it required much more energy.

    In fact, fishes need to adjust their turning angles and the swimming velocity to perform various swimming behavior,and fishes have different shapes in general. In the future, we will study the impact of different curvature model parameters and fish shapes on the performance of C-start.

    Supplementarymaterial: Original experimental images and animations of numerical simulation are available at https:∥pan.baidu.com/s/1TlOU3_-ycWdqdtXIUeBAVw.

    The authors thank Zhang Bingbing for providing zebrafish experimental images.

    久久亚洲精品不卡| 十八禁网站网址无遮挡| 久久精品久久久久久噜噜老黄| 欧美午夜高清在线| 国产精品熟女久久久久浪| 国产极品粉嫩免费观看在线| 日韩,欧美,国产一区二区三区| 在线观看www视频免费| 一本色道久久久久久精品综合| 亚洲av日韩精品久久久久久密| 在线亚洲精品国产二区图片欧美| 人妻久久中文字幕网| 日本a在线网址| 久久狼人影院| 黄网站色视频无遮挡免费观看| 国产一区二区 视频在线| 麻豆国产av国片精品| 宅男免费午夜| 国产精品99久久99久久久不卡| 丰满人妻熟妇乱又伦精品不卡| 老鸭窝网址在线观看| 啦啦啦 在线观看视频| 91麻豆精品激情在线观看国产 | h视频一区二区三区| 热99国产精品久久久久久7| 窝窝影院91人妻| 精品欧美一区二区三区在线| 制服诱惑二区| 麻豆av在线久日| 欧美激情高清一区二区三区| 一个人免费在线观看的高清视频 | 亚洲欧美日韩另类电影网站| 高清黄色对白视频在线免费看| 十八禁网站免费在线| av不卡在线播放| 各种免费的搞黄视频| 午夜福利在线观看吧| 黄色视频不卡| 亚洲第一av免费看| 妹子高潮喷水视频| 别揉我奶头~嗯~啊~动态视频 | 久久久久精品国产欧美久久久 | 9色porny在线观看| 久久精品久久久久久噜噜老黄| 久久精品亚洲av国产电影网| 日韩欧美免费精品| 在线精品无人区一区二区三| 久久亚洲国产成人精品v| 欧美97在线视频| 极品少妇高潮喷水抽搐| av不卡在线播放| 黄片大片在线免费观看| 80岁老熟妇乱子伦牲交| 国产在线观看jvid| 久久精品aⅴ一区二区三区四区| 欧美97在线视频| 精品亚洲成国产av| 午夜激情av网站| 日日摸夜夜添夜夜添小说| 在线av久久热| 99精品久久久久人妻精品| 色精品久久人妻99蜜桃| 老鸭窝网址在线观看| 亚洲人成77777在线视频| 男人舔女人的私密视频| 99久久99久久久精品蜜桃| 两个人看的免费小视频| 欧美久久黑人一区二区| 精品欧美一区二区三区在线| 伊人亚洲综合成人网| 久久av网站| 精品人妻1区二区| 老熟妇乱子伦视频在线观看 | 日日摸夜夜添夜夜添小说| 老司机福利观看| av片东京热男人的天堂| 90打野战视频偷拍视频| 久久久精品免费免费高清| 久久精品aⅴ一区二区三区四区| 美女中出高潮动态图| 日日爽夜夜爽网站| 波多野结衣一区麻豆| 中文字幕人妻丝袜制服| 亚洲精品中文字幕一二三四区 | 两个人免费观看高清视频| 久久人人97超碰香蕉20202| 久久久久久久大尺度免费视频| 久久久久久久大尺度免费视频| 久久久久久久大尺度免费视频| 国产成人a∨麻豆精品| 亚洲av欧美aⅴ国产| 精品国产一区二区三区久久久樱花| 国产精品九九99| av在线app专区| 老司机亚洲免费影院| 久久久久久久精品精品| 亚洲国产中文字幕在线视频| 99热网站在线观看| 免费观看a级毛片全部| 久久人妻熟女aⅴ| 一二三四社区在线视频社区8| 亚洲av片天天在线观看| 午夜日韩欧美国产| 9色porny在线观看| 国产精品免费大片| 99久久精品国产亚洲精品| 日韩有码中文字幕| 国产三级黄色录像| 午夜福利乱码中文字幕| 久久亚洲精品不卡| a级片在线免费高清观看视频| 国产日韩欧美在线精品| 午夜久久久在线观看| 欧美日韩成人在线一区二区| 成年人午夜在线观看视频| 久久ye,这里只有精品| 高潮久久久久久久久久久不卡| 久久影院123| 99香蕉大伊视频| 久久这里只有精品19| 日本wwww免费看| 国产成人免费观看mmmm| 欧美另类亚洲清纯唯美| 精品久久蜜臀av无| 老司机午夜福利在线观看视频 | 亚洲国产毛片av蜜桃av| 精品亚洲成国产av| 黄色 视频免费看| 亚洲五月色婷婷综合| 免费在线观看视频国产中文字幕亚洲 | 国产伦人伦偷精品视频| 一二三四社区在线视频社区8| 80岁老熟妇乱子伦牲交| av在线老鸭窝| 韩国精品一区二区三区| 亚洲专区中文字幕在线| 动漫黄色视频在线观看| 在线观看www视频免费| 亚洲专区中文字幕在线| tube8黄色片| 国产在线观看jvid| 国产在线一区二区三区精| 午夜91福利影院| 午夜福利视频精品| 国产精品 欧美亚洲| 国产亚洲欧美精品永久| 一级毛片电影观看| 日本猛色少妇xxxxx猛交久久| 美女主播在线视频| 嫁个100分男人电影在线观看| 亚洲一区二区三区欧美精品| 久久精品人人爽人人爽视色| 捣出白浆h1v1| 91麻豆精品激情在线观看国产 | 欧美成狂野欧美在线观看| 久9热在线精品视频| 久久久久久亚洲精品国产蜜桃av| 色婷婷av一区二区三区视频| 波多野结衣一区麻豆| 亚洲av日韩在线播放| 中文字幕另类日韩欧美亚洲嫩草| 国产av精品麻豆| 19禁男女啪啪无遮挡网站| 十八禁网站网址无遮挡| 午夜福利一区二区在线看| 热re99久久精品国产66热6| 999精品在线视频| 好男人电影高清在线观看| 巨乳人妻的诱惑在线观看| 日韩视频在线欧美| av在线老鸭窝| 宅男免费午夜| 国产精品二区激情视频| 黄色视频不卡| 电影成人av| 18禁黄网站禁片午夜丰满| 亚洲avbb在线观看| 国产成人a∨麻豆精品| 精品卡一卡二卡四卡免费| 99久久综合免费| 啪啪无遮挡十八禁网站| 国产亚洲欧美在线一区二区| 日本黄色日本黄色录像| 国产免费现黄频在线看| 69av精品久久久久久 | 丝袜喷水一区| 啦啦啦 在线观看视频| 国产有黄有色有爽视频| 欧美日韩亚洲综合一区二区三区_| 成年美女黄网站色视频大全免费| 91av网站免费观看| 肉色欧美久久久久久久蜜桃| 在线看a的网站| 人人妻人人澡人人看| 免费久久久久久久精品成人欧美视频| 真人做人爱边吃奶动态| 国产成人免费无遮挡视频| 777米奇影视久久| av片东京热男人的天堂| 成人黄色视频免费在线看| 久久99一区二区三区| 欧美日韩中文字幕国产精品一区二区三区 | 国产亚洲午夜精品一区二区久久| 久久影院123| 久久久久久久精品精品| 国产精品 欧美亚洲| 国产成人免费观看mmmm| 爱豆传媒免费全集在线观看| 一级片'在线观看视频| 成人18禁高潮啪啪吃奶动态图| 亚洲欧美日韩高清在线视频 | 国产免费福利视频在线观看| 久久免费观看电影| 99香蕉大伊视频| 亚洲一卡2卡3卡4卡5卡精品中文| 色94色欧美一区二区| 欧美激情 高清一区二区三区| 国产欧美日韩精品亚洲av| 少妇裸体淫交视频免费看高清 | 热99re8久久精品国产| 一进一出抽搐动态| 欧美精品一区二区免费开放| 免费高清在线观看视频在线观看| 亚洲av国产av综合av卡| 日本一区二区免费在线视频| 国产男人的电影天堂91| 高潮久久久久久久久久久不卡| 我要看黄色一级片免费的| 无限看片的www在线观看| 精品国产超薄肉色丝袜足j| 精品人妻1区二区| 美女高潮喷水抽搐中文字幕| 色94色欧美一区二区| 亚洲黑人精品在线| 欧美人与性动交α欧美精品济南到| 国产成人免费观看mmmm| 青青草视频在线视频观看| 色老头精品视频在线观看| 成人国产一区最新在线观看| 欧美黑人精品巨大| 久久亚洲精品不卡| 欧美日本中文国产一区发布| 国产成人精品在线电影| 性色av乱码一区二区三区2| 别揉我奶头~嗯~啊~动态视频 | 自线自在国产av| 久久精品国产亚洲av香蕉五月 | 久久综合国产亚洲精品| 大片免费播放器 马上看| 丝袜脚勾引网站| 成人国产一区最新在线观看| 高清视频免费观看一区二区| 国产亚洲欧美在线一区二区| 交换朋友夫妻互换小说| 一本色道久久久久久精品综合| 亚洲国产精品一区三区| 五月天丁香电影| 一级黄色大片毛片| 国产亚洲av高清不卡| 999精品在线视频| 精品人妻1区二区| 亚洲国产毛片av蜜桃av| 精品国产一区二区三区四区第35| 欧美在线黄色| 久久毛片免费看一区二区三区| 1024香蕉在线观看| www.999成人在线观看| 免费高清在线观看日韩| 国产成人精品无人区| 两性夫妻黄色片| 黄色片一级片一级黄色片| 精品久久蜜臀av无| 国产人伦9x9x在线观看| 啦啦啦在线免费观看视频4| 精品久久久精品久久久| 亚洲欧美激情在线| 好男人电影高清在线观看| 国产精品香港三级国产av潘金莲| 日本精品一区二区三区蜜桃| av网站免费在线观看视频| 一本色道久久久久久精品综合| 久久午夜综合久久蜜桃| 久久青草综合色| 在线观看免费高清a一片| 一二三四在线观看免费中文在| 精品亚洲成a人片在线观看| 欧美激情极品国产一区二区三区| 十八禁人妻一区二区| 一级片免费观看大全| 久久九九热精品免费| 男女高潮啪啪啪动态图| 99国产精品一区二区三区| 国产深夜福利视频在线观看| videos熟女内射| 99精品欧美一区二区三区四区| 嫁个100分男人电影在线观看| av天堂久久9| 九色亚洲精品在线播放| 精品视频人人做人人爽| 丝袜在线中文字幕| 搡老熟女国产l中国老女人| 岛国在线观看网站| 纯流量卡能插随身wifi吗| 巨乳人妻的诱惑在线观看| 老汉色av国产亚洲站长工具| 纵有疾风起免费观看全集完整版| 一区在线观看完整版| 熟女少妇亚洲综合色aaa.| 黄色怎么调成土黄色| 99热全是精品| 国产精品久久久人人做人人爽| 久久久久国内视频| 伦理电影免费视频| 精品福利观看| 美女中出高潮动态图| 国产精品av久久久久免费| 亚洲天堂av无毛| 国产精品 欧美亚洲| 一本大道久久a久久精品| 免费在线观看影片大全网站| 1024香蕉在线观看| 亚洲美女黄色视频免费看| 亚洲成人手机| 国产深夜福利视频在线观看| 免费高清在线观看日韩| 久久精品久久久久久噜噜老黄| 国产亚洲午夜精品一区二区久久| 99国产精品99久久久久| 欧美国产精品va在线观看不卡| 黑人巨大精品欧美一区二区mp4| 亚洲第一av免费看| 日本a在线网址| 婷婷丁香在线五月| 亚洲国产精品成人久久小说| 天天影视国产精品| 午夜福利免费观看在线| 1024视频免费在线观看| av网站在线播放免费| 热re99久久国产66热| 在线 av 中文字幕| 美女视频免费永久观看网站| 欧美日本中文国产一区发布| 亚洲av欧美aⅴ国产| 91麻豆av在线| 欧美激情久久久久久爽电影 | 狠狠婷婷综合久久久久久88av| 国产区一区二久久| 99国产精品99久久久久| 99国产极品粉嫩在线观看| 国产亚洲欧美在线一区二区| 免费看十八禁软件| 国产成人欧美在线观看 | 国产又爽黄色视频| 视频区欧美日本亚洲| 国产黄频视频在线观看| 久久久国产一区二区| 一本久久精品| 91字幕亚洲| 少妇被粗大的猛进出69影院| 男女之事视频高清在线观看| 久久久精品国产亚洲av高清涩受| 丰满迷人的少妇在线观看| 五月天丁香电影| tube8黄色片| 国产精品一区二区在线观看99| 在线观看免费日韩欧美大片| 欧美日韩亚洲国产一区二区在线观看 | 后天国语完整版免费观看| 成人18禁高潮啪啪吃奶动态图| 曰老女人黄片| 国产淫语在线视频| 人成视频在线观看免费观看| 别揉我奶头~嗯~啊~动态视频 | 国产野战对白在线观看| 一二三四社区在线视频社区8| 免费在线观看黄色视频的| 一级毛片精品| 97在线人人人人妻| 在线看a的网站| 色综合欧美亚洲国产小说| 午夜日韩欧美国产| 新久久久久国产一级毛片| 亚洲一码二码三码区别大吗| 国产亚洲午夜精品一区二区久久| 国产日韩欧美视频二区| 在线精品无人区一区二区三| 国产av又大| 精品一区二区三区av网在线观看 | 日本vs欧美在线观看视频| 精品国产国语对白av| 精品亚洲成a人片在线观看| 亚洲七黄色美女视频| 亚洲综合色网址| 欧美精品啪啪一区二区三区 | 国产av一区二区精品久久| 欧美精品人与动牲交sv欧美| 成人三级做爰电影| 国产精品久久久久成人av| 国产一区有黄有色的免费视频| 久久人妻福利社区极品人妻图片| 精品久久久久久电影网| 搡老熟女国产l中国老女人| 男人舔女人的私密视频| 精品人妻熟女毛片av久久网站| 亚洲av男天堂| 久久人人爽人人片av| 岛国毛片在线播放| 日韩大片免费观看网站| 国产日韩欧美视频二区| 国产av一区二区精品久久| 亚洲精品日韩在线中文字幕| 50天的宝宝边吃奶边哭怎么回事| 12—13女人毛片做爰片一| 视频区欧美日本亚洲| 亚洲欧美日韩高清在线视频 | 热re99久久国产66热| 国产淫语在线视频| 日本av免费视频播放| 丰满少妇做爰视频| 人妻 亚洲 视频| 超色免费av| 窝窝影院91人妻| 在线观看人妻少妇| 少妇裸体淫交视频免费看高清 | 在线十欧美十亚洲十日本专区| 国产av一区二区精品久久| 汤姆久久久久久久影院中文字幕| 午夜免费鲁丝| 伊人久久大香线蕉亚洲五| 免费观看人在逋| 国产激情久久老熟女| 久久人人爽人人片av| 五月开心婷婷网| 777米奇影视久久| 一二三四在线观看免费中文在| 日韩欧美一区二区三区在线观看 | 菩萨蛮人人尽说江南好唐韦庄| 在线观看免费高清a一片| 久久久精品免费免费高清| 在线精品无人区一区二区三| 一级a爱视频在线免费观看| 欧美黄色片欧美黄色片| 免费不卡黄色视频| 亚洲精品一卡2卡三卡4卡5卡 | 亚洲国产毛片av蜜桃av| 亚洲精品自拍成人| 91大片在线观看| 三上悠亚av全集在线观看| 国产成人精品久久二区二区91| 午夜久久久在线观看| 欧美日韩黄片免| 狠狠狠狠99中文字幕| 久久久久久久久免费视频了| 男人添女人高潮全过程视频| 美女主播在线视频| 动漫黄色视频在线观看| 亚洲精品自拍成人| 真人做人爱边吃奶动态| 极品少妇高潮喷水抽搐| 超色免费av| 女人爽到高潮嗷嗷叫在线视频| 久久中文看片网| 久久久精品国产亚洲av高清涩受| 亚洲国产精品成人久久小说| 另类亚洲欧美激情| 久久久国产成人免费| 一区二区三区四区激情视频| 丝瓜视频免费看黄片| 天堂中文最新版在线下载| 国产精品 欧美亚洲| 另类精品久久| 日韩,欧美,国产一区二区三区| 日本wwww免费看| 国产精品久久久久久精品电影小说| 他把我摸到了高潮在线观看 | 亚洲av电影在线进入| 中文字幕色久视频| 欧美日韩精品网址| 国产一区二区三区综合在线观看| 老司机午夜十八禁免费视频| 在线十欧美十亚洲十日本专区| 国产又色又爽无遮挡免| 99香蕉大伊视频| 一本大道久久a久久精品| 80岁老熟妇乱子伦牲交| 日本wwww免费看| 妹子高潮喷水视频| 国产精品自产拍在线观看55亚洲 | 少妇粗大呻吟视频| 中文字幕另类日韩欧美亚洲嫩草| 天堂8中文在线网| 丝瓜视频免费看黄片| 久久99一区二区三区| 69av精品久久久久久 | 丝袜人妻中文字幕| 国产高清国产精品国产三级| 丰满人妻熟妇乱又伦精品不卡| 日韩欧美一区二区三区在线观看 | 国产一卡二卡三卡精品| 亚洲成人免费电影在线观看| 手机成人av网站| 丰满少妇做爰视频| 亚洲三区欧美一区| 老司机影院成人| 嫩草影视91久久| 午夜免费成人在线视频| 婷婷成人精品国产| 蜜桃国产av成人99| 在线观看免费视频网站a站| 精品久久久久久久毛片微露脸 | 国产精品成人在线| av天堂久久9| 久久久久久人人人人人| 女人久久www免费人成看片| 色婷婷av一区二区三区视频| 91精品伊人久久大香线蕉| 婷婷成人精品国产| 中文字幕人妻丝袜制服| 精品久久蜜臀av无| 国产成人欧美| 国产成人精品久久二区二区91| 成年女人毛片免费观看观看9 | 中文字幕人妻丝袜一区二区| 老司机午夜福利在线观看视频 | 国产日韩一区二区三区精品不卡| 国产精品一区二区精品视频观看| 久久亚洲国产成人精品v| 欧美日韩成人在线一区二区| 精品一区二区三区av网在线观看 | 亚洲av欧美aⅴ国产| 美女扒开内裤让男人捅视频| 欧美性长视频在线观看| 亚洲精品一二三| 操出白浆在线播放| 色播在线永久视频| 国产精品麻豆人妻色哟哟久久| 国产精品一区二区在线观看99| 国产一区二区在线观看av| 女人爽到高潮嗷嗷叫在线视频| 久久国产精品男人的天堂亚洲| 99精国产麻豆久久婷婷| 国产亚洲欧美精品永久| 亚洲国产精品成人久久小说| 久久精品aⅴ一区二区三区四区| 人成视频在线观看免费观看| 久久久久精品国产欧美久久久 | 国产免费av片在线观看野外av| 麻豆国产av国片精品| 免费在线观看日本一区| 午夜精品国产一区二区电影| 纵有疾风起免费观看全集完整版| 欧美人与性动交α欧美软件| 久久影院123| 国产99久久九九免费精品| 亚洲精品成人av观看孕妇| 啦啦啦 在线观看视频| 三级毛片av免费| 99九九在线精品视频| 国产在线一区二区三区精| 女人久久www免费人成看片| 在线观看免费午夜福利视频| 91精品国产国语对白视频| 黄色 视频免费看| 日韩,欧美,国产一区二区三区| 丝袜人妻中文字幕| 啦啦啦视频在线资源免费观看| 精品亚洲乱码少妇综合久久| 精品福利永久在线观看| 国产精品一区二区免费欧美 | 高清欧美精品videossex| 精品亚洲成a人片在线观看| 免费观看人在逋| 91大片在线观看| 狠狠精品人妻久久久久久综合| 欧美老熟妇乱子伦牲交| 1024视频免费在线观看| 午夜日韩欧美国产| 欧美激情久久久久久爽电影 | 国产亚洲一区二区精品| 亚洲中文字幕日韩| 日韩中文字幕欧美一区二区| 久久久久国产精品人妻一区二区| 黄色视频在线播放观看不卡| 亚洲精品国产区一区二| 叶爱在线成人免费视频播放| 人人澡人人妻人| 少妇精品久久久久久久| 大香蕉久久网| 精品国产一区二区三区久久久樱花| 中文欧美无线码| 欧美乱码精品一区二区三区| 久久久国产欧美日韩av| 成人手机av| 777久久人妻少妇嫩草av网站| 国产伦理片在线播放av一区| 各种免费的搞黄视频| 水蜜桃什么品种好| 人妻 亚洲 视频| 两性夫妻黄色片| 美女福利国产在线| 日韩视频在线欧美| 精品熟女少妇八av免费久了| 黄色 视频免费看| 亚洲人成电影免费在线| 蜜桃国产av成人99| 最近最新免费中文字幕在线| 免费在线观看视频国产中文字幕亚洲 | 国产精品免费视频内射| 国产免费现黄频在线看| 久久综合国产亚洲精品| 亚洲国产精品999| 淫妇啪啪啪对白视频 | 久久国产精品大桥未久av| 国产av国产精品国产| 久久久欧美国产精品|