• <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.

    黑人巨大精品欧美一区二区蜜桃 | 丝袜在线中文字幕| 免费人成在线观看视频色| 看免费成人av毛片| 国产黄频视频在线观看| 欧美精品国产亚洲| 日韩欧美精品免费久久| 亚洲欧美一区二区三区国产| 国产淫语在线视频| 亚洲精品aⅴ在线观看| 又大又黄又爽视频免费| 中文字幕av电影在线播放| 51国产日韩欧美| 极品少妇高潮喷水抽搐| 在线天堂最新版资源| 亚洲欧美精品专区久久| 国产亚洲5aaaaa淫片| 中国三级夫妇交换| 欧美少妇被猛烈插入视频| 人妻人人澡人人爽人人| 中文字幕亚洲精品专区| 国产在线视频一区二区| 日韩伦理黄色片| 丰满迷人的少妇在线观看| 精品人妻熟女av久视频| 欧美变态另类bdsm刘玥| 日日啪夜夜撸| 成人漫画全彩无遮挡| 午夜激情福利司机影院| 国产午夜精品一二区理论片| 22中文网久久字幕| 国产高清国产精品国产三级| 亚洲av综合色区一区| 日韩成人伦理影院| 国产一区二区在线观看日韩| 18禁在线无遮挡免费观看视频| 美女视频免费永久观看网站| 国产成人精品福利久久| 久久久久久久久大av| 六月丁香七月| 丝袜喷水一区| a级毛片在线看网站| 九色成人免费人妻av| 日韩亚洲欧美综合| 另类亚洲欧美激情| 国产精品无大码| 9色porny在线观看| 三级国产精品片| 国产精品人妻久久久久久| 男人舔奶头视频| 夫妻午夜视频| 亚洲色图综合在线观看| 一二三四中文在线观看免费高清| 欧美区成人在线视频| 国产精品一区二区在线观看99| 亚洲欧美精品自产自拍| 亚洲精品自拍成人| 黄片无遮挡物在线观看| 国产午夜精品久久久久久一区二区三区| 91aial.com中文字幕在线观看| 在线观看免费日韩欧美大片 | 久久免费观看电影| 一级,二级,三级黄色视频| 免费观看a级毛片全部| 看非洲黑人一级黄片| 69精品国产乱码久久久| 精品一区二区免费观看| 国产成人精品婷婷| 天美传媒精品一区二区| av不卡在线播放| 韩国高清视频一区二区三区| 国产精品一区二区三区四区免费观看| 日本wwww免费看| 男男h啪啪无遮挡| 国产深夜福利视频在线观看| 欧美三级亚洲精品| 丰满乱子伦码专区| 国产69精品久久久久777片| 亚洲国产精品999| 亚洲精品,欧美精品| 18禁在线播放成人免费| 亚洲精品乱码久久久v下载方式| 国产在线免费精品| 我的女老师完整版在线观看| 欧美精品亚洲一区二区| 十八禁网站网址无遮挡 | 97在线人人人人妻| 伊人亚洲综合成人网| 男女国产视频网站| 建设人人有责人人尽责人人享有的| 熟女av电影| 少妇人妻一区二区三区视频| 亚洲情色 制服丝袜| 青春草国产在线视频| 国产成人一区二区在线| 国产成人91sexporn| 亚洲欧美清纯卡通| 男女无遮挡免费网站观看| 成人毛片60女人毛片免费| 色哟哟·www| 久久人人爽人人片av| 欧美激情国产日韩精品一区| 亚洲国产av新网站| 久久久久精品性色| 午夜视频国产福利| 国产精品偷伦视频观看了| 观看美女的网站| 国产欧美日韩一区二区三区在线 | 七月丁香在线播放| 51国产日韩欧美| 亚洲无线观看免费| 亚洲欧洲国产日韩| 亚洲国产色片| 伊人久久精品亚洲午夜| 七月丁香在线播放| 99热6这里只有精品| 中文资源天堂在线| 日韩制服骚丝袜av| 日韩 亚洲 欧美在线| 亚洲精品一二三| 日本av免费视频播放| 啦啦啦视频在线资源免费观看| 久久精品国产鲁丝片午夜精品| 欧美区成人在线视频| 一级片'在线观看视频| 少妇 在线观看| 欧美+日韩+精品| 成人国产麻豆网| 亚洲欧美清纯卡通| 80岁老熟妇乱子伦牲交| 久久精品久久久久久噜噜老黄| 午夜91福利影院| 在线观看一区二区三区激情| freevideosex欧美| 欧美日韩国产mv在线观看视频| 夜夜爽夜夜爽视频| 午夜av观看不卡| 国产成人a∨麻豆精品| 久久久a久久爽久久v久久| 久久久久久久久久久久大奶| 中文字幕av电影在线播放| 国产亚洲av片在线观看秒播厂| 在线看a的网站| 久久ye,这里只有精品| 在线免费观看不下载黄p国产| 高清视频免费观看一区二区| 亚洲真实伦在线观看| 一级a做视频免费观看| 人妻少妇偷人精品九色| 熟妇人妻不卡中文字幕| 久久热精品热| 中文字幕av电影在线播放| 免费黄频网站在线观看国产| 黄片无遮挡物在线观看| 国产精品熟女久久久久浪| 久久久欧美国产精品| 欧美日韩精品成人综合77777| 插阴视频在线观看视频| 欧美老熟妇乱子伦牲交| 各种免费的搞黄视频| 最近的中文字幕免费完整| 十八禁网站网址无遮挡 | 在线播放无遮挡| 久久精品国产自在天天线| 一区二区三区乱码不卡18| 国产免费又黄又爽又色| 精华霜和精华液先用哪个| 插阴视频在线观看视频| 内射极品少妇av片p| 七月丁香在线播放| 国产日韩欧美视频二区| 中文字幕人妻丝袜制服| 久久青草综合色| 精品亚洲成a人片在线观看| 欧美精品人与动牲交sv欧美| 少妇猛男粗大的猛烈进出视频| 欧美97在线视频| 国产亚洲5aaaaa淫片| 大片免费播放器 马上看| 成年女人在线观看亚洲视频| 又大又黄又爽视频免费| 国产日韩欧美视频二区| 久久人妻熟女aⅴ| 日韩强制内射视频| 老熟女久久久| a级毛片在线看网站| av在线播放精品| 国产成人精品一,二区| 亚洲精品,欧美精品| 99九九在线精品视频 | av在线播放精品| 精品久久久噜噜| 久久99蜜桃精品久久| 一区二区三区乱码不卡18| 国产又色又爽无遮挡免| 女人精品久久久久毛片| 超碰97精品在线观看| 美女脱内裤让男人舔精品视频| a级毛片免费高清观看在线播放| 亚洲国产成人一精品久久久| 大话2 男鬼变身卡| 精品少妇久久久久久888优播| 国产高清三级在线| 久久精品久久久久久噜噜老黄| 亚洲国产精品成人久久小说| .国产精品久久| 黑人猛操日本美女一级片| 18禁动态无遮挡网站| 免费观看在线日韩| 亚洲色图综合在线观看| 在线播放无遮挡| 女人精品久久久久毛片| 国产精品蜜桃在线观看| 日韩av不卡免费在线播放| 热re99久久国产66热| 欧美变态另类bdsm刘玥| 五月玫瑰六月丁香| 亚洲精品中文字幕在线视频 | 嫩草影院入口| 国产伦在线观看视频一区| 18禁裸乳无遮挡动漫免费视频| 国产亚洲一区二区精品| 男的添女的下面高潮视频| 国产免费视频播放在线视频| 伦精品一区二区三区| 亚洲精品乱久久久久久| 精品99又大又爽又粗少妇毛片| 男的添女的下面高潮视频| 午夜福利视频精品| 少妇被粗大的猛进出69影院 | 精品国产露脸久久av麻豆| 偷拍熟女少妇极品色| 丝袜喷水一区| 99久久精品热视频| 国产精品蜜桃在线观看| 国产黄频视频在线观看| 欧美xxxx性猛交bbbb| av天堂中文字幕网| 一区二区三区四区激情视频| 欧美老熟妇乱子伦牲交| 多毛熟女@视频| 极品少妇高潮喷水抽搐| 少妇被粗大猛烈的视频| 久久精品国产亚洲网站| 美女大奶头黄色视频| 18禁在线无遮挡免费观看视频| 在线播放无遮挡| 各种免费的搞黄视频| 极品教师在线视频| 男人舔奶头视频| 最近手机中文字幕大全| 三级经典国产精品| 亚洲欧洲精品一区二区精品久久久 | 九色成人免费人妻av| 丝瓜视频免费看黄片| 国产亚洲5aaaaa淫片| 久久国内精品自在自线图片| 成人亚洲精品一区在线观看| 嫩草影院新地址| 精品视频人人做人人爽| 国产成人91sexporn| 超碰97精品在线观看| 男的添女的下面高潮视频| 午夜91福利影院| 亚洲久久久国产精品| 国产国拍精品亚洲av在线观看| 特大巨黑吊av在线直播| 黑丝袜美女国产一区| 看非洲黑人一级黄片| 制服丝袜香蕉在线| 日韩不卡一区二区三区视频在线| 久久 成人 亚洲| 国产深夜福利视频在线观看| 国产高清不卡午夜福利| 啦啦啦在线观看免费高清www| 国产精品一区www在线观看| 丝袜喷水一区| 亚洲国产精品一区二区三区在线| 亚洲av男天堂| 曰老女人黄片| 精品视频人人做人人爽| 中文欧美无线码| 国产成人免费无遮挡视频| 国产在线一区二区三区精| 女人久久www免费人成看片| 最新中文字幕久久久久| 国产中年淑女户外野战色| 一级毛片黄色毛片免费观看视频| 国产精品久久久久久av不卡| 免费大片黄手机在线观看| 欧美国产精品一级二级三级 | 极品人妻少妇av视频| 如何舔出高潮| 日本av免费视频播放| 国产黄色视频一区二区在线观看| 永久免费av网站大全| 精品少妇内射三级| 亚洲中文av在线| 在线观看美女被高潮喷水网站| 久久久精品免费免费高清| 日韩中文字幕视频在线看片| 欧美精品高潮呻吟av久久| 亚洲欧洲国产日韩| 自线自在国产av| 日韩av在线免费看完整版不卡| 丰满迷人的少妇在线观看| 日本黄色片子视频| 成人美女网站在线观看视频| 国产精品一区二区性色av| 国产亚洲最大av| 三级国产精品片| 久久精品国产亚洲av涩爱| 亚洲一区二区三区欧美精品| 国产日韩一区二区三区精品不卡 | 免费大片18禁| 成年av动漫网址| 国产精品久久久久久久电影| 国国产精品蜜臀av免费| 亚洲精品第二区| 欧美人与善性xxx| 日韩精品有码人妻一区| 丰满少妇做爰视频| 国产免费又黄又爽又色| 日日啪夜夜撸| 久久99热这里只频精品6学生| 亚洲精品一区蜜桃| 国产精品一区二区性色av| 青春草亚洲视频在线观看| 亚洲av不卡在线观看| 丝袜喷水一区| 高清不卡的av网站| 秋霞伦理黄片| 一区二区av电影网| 秋霞在线观看毛片| 熟女电影av网| 多毛熟女@视频| 美女视频免费永久观看网站| 免费观看av网站的网址| 国产综合精华液| 精品亚洲成a人片在线观看| 国产精品福利在线免费观看| 亚洲精品日本国产第一区| 波野结衣二区三区在线| 亚洲欧洲精品一区二区精品久久久 | 寂寞人妻少妇视频99o| 啦啦啦中文免费视频观看日本| 中文字幕久久专区| 欧美日韩精品成人综合77777| 亚洲av免费高清在线观看| 久久久精品免费免费高清| 成人黄色视频免费在线看| 精品国产国语对白av| 男女无遮挡免费网站观看| 日韩伦理黄色片| 欧美精品亚洲一区二区| av福利片在线观看| 国产男人的电影天堂91| 丰满饥渴人妻一区二区三| 大陆偷拍与自拍| 久久午夜综合久久蜜桃| 新久久久久国产一级毛片| 亚洲精品乱码久久久久久按摩| 男男h啪啪无遮挡| 久久毛片免费看一区二区三区| 美女国产视频在线观看| 免费看av在线观看网站| 国产成人精品久久久久久| 嫩草影院新地址| 99re6热这里在线精品视频| 一级二级三级毛片免费看| 熟女av电影| 亚洲情色 制服丝袜| 麻豆成人av视频| 久久人人爽av亚洲精品天堂| 欧美日本中文国产一区发布| 大片免费播放器 马上看| 看十八女毛片水多多多| videossex国产| 99视频精品全部免费 在线| 丰满少妇做爰视频| 日本黄大片高清| 欧美 亚洲 国产 日韩一| 全区人妻精品视频| av女优亚洲男人天堂| 午夜福利网站1000一区二区三区| 侵犯人妻中文字幕一二三四区| 国产黄色免费在线视频| 欧美亚洲日本最大视频资源| 三级毛片av免费| 亚洲av成人不卡在线观看播放网 | 亚洲第一av免费看| 精品久久蜜臀av无| 久热这里只有精品99| 80岁老熟妇乱子伦牲交| 亚洲情色 制服丝袜| 99国产精品免费福利视频| 日本av手机在线免费观看| 一二三四社区在线视频社区8| 一区二区三区四区激情视频| 国产精品自产拍在线观看55亚洲 | 国精品久久久久久国模美| av有码第一页| 亚洲专区字幕在线| 亚洲黑人精品在线| 一二三四在线观看免费中文在| 亚洲精品自拍成人| 老汉色∧v一级毛片| 亚洲人成电影免费在线| 国产亚洲精品第一综合不卡| 午夜激情久久久久久久| 91麻豆精品激情在线观看国产 | 国产欧美日韩精品亚洲av| 亚洲 欧美一区二区三区| av有码第一页| 无限看片的www在线观看| 亚洲七黄色美女视频| 精品福利观看| 久久九九热精品免费| 午夜视频精品福利| 国产区一区二久久| 午夜免费观看性视频| 欧美精品av麻豆av| 国产欧美亚洲国产| 日韩免费高清中文字幕av| 满18在线观看网站| 日韩中文字幕欧美一区二区| 99热国产这里只有精品6| 午夜免费成人在线视频| 午夜激情久久久久久久| 宅男免费午夜| 日本av手机在线免费观看| 亚洲av日韩精品久久久久久密| 王馨瑶露胸无遮挡在线观看| 亚洲av日韩在线播放| 亚洲专区国产一区二区| 久9热在线精品视频| 韩国精品一区二区三区| 老司机福利观看| 他把我摸到了高潮在线观看 | 国产高清视频在线播放一区 | 他把我摸到了高潮在线观看 | 18禁观看日本| 一本—道久久a久久精品蜜桃钙片| 国产又爽黄色视频| 国产日韩一区二区三区精品不卡| 国产精品.久久久| 亚洲欧美一区二区三区久久| 大型av网站在线播放| 麻豆乱淫一区二区| 日韩有码中文字幕| 亚洲欧美色中文字幕在线| 黑人猛操日本美女一级片| 日本精品一区二区三区蜜桃| 色播在线永久视频| 欧美精品一区二区大全| 婷婷色av中文字幕| 桃花免费在线播放| 考比视频在线观看| 日日摸夜夜添夜夜添小说| 精品国产一区二区三区久久久樱花| 久久久久网色| 两性夫妻黄色片| 黑人巨大精品欧美一区二区蜜桃| 一级片'在线观看视频| 欧美老熟妇乱子伦牲交| 一级毛片精品| 男女免费视频国产| 另类精品久久| 性少妇av在线| 日韩视频在线欧美| 国产一区二区 视频在线| 亚洲国产看品久久| 久久久久精品国产欧美久久久 | 正在播放国产对白刺激| www.av在线官网国产| 一本久久精品| 亚洲一区二区三区欧美精品| 好男人电影高清在线观看| 日韩中文字幕视频在线看片| 亚洲国产精品999| 精品少妇内射三级| 久久久久久久久久久久大奶| 每晚都被弄得嗷嗷叫到高潮| 可以免费在线观看a视频的电影网站| 日韩欧美一区二区三区在线观看 | 国产一区二区在线观看av| 久久狼人影院| 50天的宝宝边吃奶边哭怎么回事| 国内毛片毛片毛片毛片毛片| 国产视频一区二区在线看| 操出白浆在线播放| 美女中出高潮动态图| 我的亚洲天堂| 91av网站免费观看| 亚洲中文字幕日韩| 操美女的视频在线观看| 亚洲视频免费观看视频| 精品卡一卡二卡四卡免费| 欧美精品一区二区大全| 女人被躁到高潮嗷嗷叫费观| 中文精品一卡2卡3卡4更新| 午夜福利,免费看| 丰满少妇做爰视频| 汤姆久久久久久久影院中文字幕| 国产在线一区二区三区精| 熟女少妇亚洲综合色aaa.| 亚洲成av片中文字幕在线观看| 久久 成人 亚洲| 国产免费现黄频在线看| 啦啦啦视频在线资源免费观看| 亚洲一区中文字幕在线| 日韩,欧美,国产一区二区三区| 精品第一国产精品| 两个人免费观看高清视频| 少妇人妻久久综合中文| 18禁观看日本| 操出白浆在线播放| 久久久久久人人人人人| 国产av又大| 每晚都被弄得嗷嗷叫到高潮| 欧美人与性动交α欧美精品济南到| 国产精品一二三区在线看| 1024视频免费在线观看| 一级黄色大片毛片| 日韩人妻精品一区2区三区| 亚洲精品一卡2卡三卡4卡5卡 | 日本vs欧美在线观看视频| videos熟女内射| 亚洲免费av在线视频| 精品亚洲成a人片在线观看| 18禁裸乳无遮挡动漫免费视频| 国产在线观看jvid| 中文精品一卡2卡3卡4更新| 精品一品国产午夜福利视频| 欧美国产精品一级二级三级| 热99久久久久精品小说推荐| 久久热在线av| 亚洲精品美女久久av网站| 久久国产亚洲av麻豆专区| 久久女婷五月综合色啪小说| 人妻人人澡人人爽人人| 日韩大码丰满熟妇| 97在线人人人人妻| 两个人看的免费小视频| 天堂中文最新版在线下载| 啦啦啦啦在线视频资源| 爱豆传媒免费全集在线观看| 精品人妻熟女毛片av久久网站| 五月天丁香电影| av福利片在线| 精品人妻在线不人妻| 一区二区三区四区激情视频| 伊人亚洲综合成人网| 日韩制服丝袜自拍偷拍| 国产精品一区二区在线不卡| 久久人妻福利社区极品人妻图片| 不卡一级毛片| 美女扒开内裤让男人捅视频| 午夜福利免费观看在线| 秋霞在线观看毛片| 亚洲成国产人片在线观看| www.999成人在线观看| 国产老妇伦熟女老妇高清| av福利片在线| 在线永久观看黄色视频| 午夜福利影视在线免费观看| 成人黄色视频免费在线看| 亚洲国产看品久久| 免费一级毛片在线播放高清视频 | 久久综合国产亚洲精品| 亚洲国产精品一区二区三区在线| 999久久久国产精品视频| 男女高潮啪啪啪动态图| 国产有黄有色有爽视频| 悠悠久久av| 午夜久久久在线观看| 午夜福利免费观看在线| 国产精品一二三区在线看| 精品久久蜜臀av无| av有码第一页| 日韩一区二区三区影片| 狂野欧美激情性xxxx| 亚洲精品国产精品久久久不卡| 欧美精品亚洲一区二区| 亚洲免费av在线视频| 老汉色av国产亚洲站长工具| av免费在线观看网站| 制服人妻中文乱码| 久久人妻福利社区极品人妻图片| 飞空精品影院首页| 一级毛片电影观看| 中文字幕另类日韩欧美亚洲嫩草| 成人av一区二区三区在线看 | 视频区欧美日本亚洲| 国产日韩欧美视频二区| 国产男人的电影天堂91| 国产精品一区二区在线观看99| 韩国高清视频一区二区三区| 午夜激情久久久久久久| 国产一区二区三区在线臀色熟女 | 精品一区二区三区四区五区乱码| 亚洲视频免费观看视频| 欧美性长视频在线观看| 热99re8久久精品国产| 久久亚洲国产成人精品v| 两性午夜刺激爽爽歪歪视频在线观看 | 下体分泌物呈黄色| 日韩一卡2卡3卡4卡2021年| 在线精品无人区一区二区三| 老司机深夜福利视频在线观看 | 久久狼人影院| netflix在线观看网站| 亚洲天堂av无毛| 热99久久久久精品小说推荐| 欧美精品啪啪一区二区三区 |