Fishes are very smart swimmers in water. Fishes are able to make full use of the flows around their bodies, saving forces, and obtaining the optimal hydrodynamic performance [1]. So far the man-made underwater vehicle is very difficult to swim in such a high efficiency like a fish. Humans still need to learn a lot form animals.

Fishlike swimming has been a classic hydrodynamic problem which attracts the attention of researchers for a long history[2–5]). Many works has been done, trying to explain the mechanism of swimming propulsion of single fish [6–8] and the reason of fish schooling [5, 9, 10]. The fishlike swimming problem also has many applications in the field of naval architecture and ocean Engineering. One remarkable application is in the propulsion of marine vehicles. The swimming propulsion or bionic propulsion can have higher efficiency than the using of screw propeller and can avoid the problem of hydroacoustic noise and cavitation erosion. Recently, with the rapid development in the research of underwater vehicles, many of them are designed to have a fishlike shape, use a swimming propulsion and therefore have superior stealth property.

例如：有机硅材料耐低温达到零下70度以上，耐高温达到250度以上，1969年美国宇航员阿姆斯特朗登月时穿的鞋就是有机硅材料的。航天、航空使用的密封材料都是有机硅的。有机硅在纺织品上使用，能增加5倍的强度，能增强纺织品的柔性，防尘防水，不用有机硅材料就没有高档的纺织品。在建筑上使用有机硅材料，是最高端的防水剂。所有的高档化妆品都离不开有机硅材料。在医院所有使用的人造器官、人造血管，都是有机硅材料的。有机硅材料是高分子领域，最优质的耐老化、耐紫外线耐臭氧的材料。总之，有机硅新材料在各行各业，无所不在。

In the early years, the study of fishlike swimming hydrodynamics are mainly based on experimental observations [3].Recently as the development of the computational fluid dynamics (CFD), the investigations based on the numerical models are also rapidly growing. One representative numerical method is the immersed boundary method (IBM) which uses a Lagrangian boundary to track the surface of the rigid or deformable structure with complex shapes [11]. With the hybrid of IBM and other Naiver–Stocks solvers, fishlike swimming problems have been modeled for both two dimensional (2D) [9, 10, 12] and three di-mensional (3D) cases [13].

To the best of our knowledge, there are still very few publish papers modeling fishlike swimming problems using mesh-free or particle methods. One of the most widely used particle methods in the study of fluid dynamics is the smoothed particle hydrodynamics (SPH) method [14, 15]. Similar to IBM method,SPH also has the advantage of solving fluid-structure interaction(FSI) problems characterized by moving boundaries with large deformations [16].

In the traditional works, when investigating the self-propulsive swimming bodies, the swimmers are fixed in an uniform incoming free stream with a fixed inflow velocity . The hydrodynamic forces on the swimming body are measured. When the streamwise force becomes negative, the fish is considered to be able to swim forward with a speed larger than the inflow velocity. This investigation method is named as Approach 1 in this work. Approach 1 has been adopted in Deng et al. [9] and Dong and Lu [10] to study the hydrodynamic performance of a single fish and the interactions between two fishes in different relative locations. However, strictly speaking, the hydrodynamic state of the flapping fish fixed in a stream is different to the one swimming freely in the still fluid (Approach 2). In the former case, the fish is constrained by a varying external force to make it remain in its location, while in the latter case, the fish stays in a situation that the propulsive force, drag force, and inertia force reach a dynamic balance.

The streamwise and transverse motions on the center of mass of the fish are both allowed in this case. Time evolutions of the swimming velocity in forward and lateral directions are plotted in Fig. 11. After a transitional stage, the swimming velocity of the fish reaches a steady state, i.e. the cruising velocity. The cruising velocity predicted by the SPH model is aboutwhich is closer to the experimental value than the numerical result as predicted by the FVM method [12]. The vortical structures shed behind the foil is depicted in Fig. 12. In this case, the Reynolds number is much higher than the cases and therefore the sizes of the vortices are smaller and their distribution is more chaotic.

陕西省不同级别医院药学人员的职业认同水平及其影响因素研究 ………………………………………… 施 昶等（14）：1877

In Eq. (3), a particle repositioning is performed at the end of each time step as [25]

Similar to Deng et al. [9], Dong and Lu [10], and Yang et al.[12], a NACA0012 foil is adopted to mimic the backbone undulation of a swimming fish. The midline of the NACA0012 foil is designed to undulate according to the following formula:

Time evolutions of the fish movement and the swimming velocity are plotted in Fig. 7. The swimming foil accelerates at the initial stage and then reaches a steady terminal velocity. As the phase speed is increased, the magnitude of the terminal velocity improves accordingly. The vorticity contours behind the swimming foil at the same time instants for the three phase speeds are depicted in Fig. 8. At a small phase speed, the reverse von Karman vortex street behind the foil has a regular structure. In each flapping period, two single vortices are shed(2S mode). As the phase speed is increased, the reverse von Karman vortex street starts to be disturbed and in each period, the number of vortices shed are increased.

where is the vertical oscillating magnitude and is the local horizontal coordinate starting form the foil head to the tail and therefore we have 0 ≤ x′≤ L where is the length of the foil.The wave number is where the wave length is equal to unless otherwise specified. The streamwise travelling wave propagates with a constant phase speed as is the phase angle of the wavy foil. A (x′) is the oscillating amplitude depending on the local horizontal coordinate on the foil. is usually determined by the swimming characters of different fishes [24].

Generally two approaches can be adopted to investigate the hydrodynamic performance of swimming bodies. In Approach 1,the swimming body flaps in a free stream but its location is constrained on a fixed position by an external force, see the left part of Fig. 1. The free stream with a steady velocity of enters from the left side of the fluid domain. The fluid domain is designed with the width of in order to avoid the blockage effect from the lateral walls on which a free-slip boundary condition is imposed. The fish is placed away from the in-flow boundary and the total length of the fluid domain is which is large enough to avoid the effect of the out-flow boundary. The hydrodynamic force on the swimming body is measured and if the drag force coefficient is negative, it means the swimmer can move forward with a speed larger than the inflow velocity.

In Approach 2, the swimming foil is able to move forward under the thrust force, see the right sketch in Fig. 1. According to the self-propulsion model proposed by Carling et al. [17] and further extended in Ref. [12], the governing equations of the fish motion can be written as

Fig. 1. Sketches for the fluid domain and the placement of the fishlike swimming foil in different investigation approaches. Plot a shows the concept of Approach 1, where the fish is fixed in an incoming free stream; plot b shows the concept of Approach 2, in which the fish is self-driven to swim forward in a still fluid field.

where and denote the mass and the instantaneous moment of inertia about the centre of mass (c.m., denoted by subscript ). and represent the linear and angular velocity with respect to c.m. and are the total external force and the total external torque with respect to c.m. Through the solving of Eq. (2), self-propulsive motions of the swimming body can be realized. In this case, the force balance can be reached among the drag force, the thrust force, the inertia force and so on. A comparative study for the results of Approach 1 and Approach 2 will be given later.

The recently developed scheme [20] is adopted to solve the physical problem described before. scheme avoids the problem of particle disorder and therefore allows a very smooth vorticity field in the numerical results [23]. The tensile instability is also prevented in this scheme thanks to the tensile instability control (TIC) [25].

The governing equations of the scheme are written as [20, 26, 27]:

The quantities , , , , and denote respectively the density, the mass, the volume, the velocity, and the position associated with the i-th particle.

The quantity W ij=W(|i-j|;h) represents the Wendland C2 kernel with where is the initial particle spacing. is the dynamic viscosity and where is the number of spacial dimensions of the problem. The artificial speed is set equal to where is the reference velocity. In this work, the inflow velocity has been used as the reference velocity in the simulations of both Approach 1 and Approach 2.is the reference density when the pressure is zero. is the body force which has been set as zero in the present study.

In Eq. (3), the forms of the diffusive term and the viscous term can be referred to Refs. [20, 26, 27]. Specifically, the parameter of is adopted in the density diffusion.

乍一听“平地一声雷”这个菜名，我满头雾水，同时也感到非常好奇：什么样的菜肴，会在餐桌上爆出雷一般的响动呢？而且还是“平地一声雷”——瞬间，便发生了奇异的变化！带着这个疑问，我和朋友进了南京一家知名的饭店，专门点了这道“平地一声雷”！

Generally in classic SPH models, is written as[15]. However, in order to completely prevent tensile instability, a switch correction named TIC proposed in Ref. [25] is adopted with being written as TIC is able to completely prevent the tensile instability when the pressure becomes negative and the PST presented later can help to reduce the non-conservation of momentum generated by TIC term [25].

In the present work, Yang's self-propulsion model [12] has been applied in the framework of a particle method. The recently developed -SPH model [20] is adopted to model the self-propulsive fishlike swimming problem and investigate the speedability of the swimming foil with different flapping parameters. In order to understand the mechanism of the thrust force generated in different swimming conditions, the vortical structures in the flow field can be detected by Eulerian definitions, e.g. vorticity or Q criterion. Finite-time Lyapunov exponent (FTLE), which is a Lagrangian definition used to reveal Lagrangian coherent structures (LCSs), can also be calculated and it helps understanding the flow physics in a Lagrangian way [21].Recently, 3D LCSs have been reveled by Kumar et al. [22] in the FTLE field and the latter has been shown to be a reliable tool to study the relationship between the thrust generation and the wake structure behind a pitching panel. As emphasized in Ref.[23], the Lagrangian nature of SPH method provides greater convenience than the Eulerian CFD solver in detecting LCSs through the calculation of FTLE field.

where is evaluated as

This formula is similar to the PST in Ref. [28] but in a weakly compressible form. PST is helpful to obtain a smoother vorticity field [23]. Here the number is 1.5 since the forth order Runge–Kutta time integration is adopted. is the Mach number equal to . The parameters and are used to obtain an efficient regularization of the particle distribution when the smoothing length is relatively large( ). The evaluation of the time step,, used in the forth order Runge-Kutta time integration, can be referred to Ref. [20].

In the present work, in order to accelerate the computational speed, the technique of adaptive particle refinement (APR) [29]has been adopted. Further, the improved version of APR [30] has been adopted here. In this technique, the distribution of the switched off particles has the possibility to be disordered since their velocities are interpolated from the fluid particles of the finest resolution using a Shepard kernel, but thanks to the PST nested in the scheme, the switched off particles are regularized in each time step. Therefore we can say, on one hand,APR improves the efficiency of scheme; on the other hand, scheme also improves the robustness of APR [31].

The inflow and outflow boundary conditions presented in Ref. [32] are adopted here to model the free stream condition when the Approach 1 is used. The particle packing algorithm proposed in Ref. [33] is adopted at the initial stage of the simulation, in order to uniformly arrange the fluid particles around the wavy foil.

Regarding the implementation of lateral solid wall boundaries, the "fixed ghost particle" technique presented in Refs. [26,34] is implemented in this work and a free-slip boundary condition is imposed. The flapping foil is modeled also using the"fixed ghost particle" but with a no-slip boundary condition applied. The ghost particles of the foil undulate according to Eq. (1)presented before. The pressure interpolation from the fluid to the ghost uses the Shepard interpolation as adopted in Ref. [35].

她没有请他们坐下来。她只是站在门口，静静地听着，直到发言的代表结结巴巴地说完，他们这时才听到那块隐在金链子那一端的挂表嘀嗒作响。

Regarding FSI algorithm, the conventional parallel staggered(CPS) algorithm presented in Ref. [36] is applied. Since here the time step for the weakly compressible SPH is relatively small, a satisfied numerical stability is allowed within this FSI coupling strategy. The forces on the foils are measured by summating the interacting forces between the fluid particles and ghost particles[37], [38]. The governing equations for the motion of the selfpropulsive wavy foil (see Eq. (2)) are also integrated using the Fourth order Runge–Kutta integration scheme.

Since the scheme has been full validated in Refs.[20, 25] for viscous flows around bluff bodies with different irregular shapes and in different Reynolds numbers, benchmark val-idations will not be presented. And it is noted that we only focus on the forward propulsive speed of the swimming foil and therefore the transversal and rotational motions of the foil are ignored. The transverse and angular velocities due to the tail flapping of the foil are left for the future studies.

In all the simulations, in the far field, the particle resolution is, and the particles are gradually refined when they approach the flapping foil and de-refined when they leave far away [20, 25]. In the presentation of the results, the inflow velocity , the fluid density , and the foil length are used to nondimensionalize the other variables. The mass of the foil in Approach 2 is set as M =0.12ρL2. The Reynolds numbers of all the cases are set as . In the numerical calculation,=1 m/s, = 1 kg/m2, and= 1 m are used in the present study.A linear ramp with a constant acceleration is used for gradually increasing the inflow velocity and the oscillating amplitudeuntil the preconcerted values in order to avoid an impulsive start of the velocity field.

The oscillating amplitude is written as

where,, and are three different coefficients solved from the kinematic data of a steadily swimming fish [24]. In the determination of the oscillating amplitude of the foil,, and are adopted in order to ensure. The phase speed is set as c p=2U where U is the inflow velocity as stated before. The numerical results for the simulation of fishlike swimming problems are modeled using both Approach 1 and Approach 2.(1) In Approach 1, the swimming foil is fixed in a free stream(2) In Approach 2, the swimming foil is self-driven to move forward under the thrust force.

In Ref. [25], a numerical validation has been conducted for the viscous flow past wavy foil at Reynolds number using Approach 1. The hydrodynamics forces on the foil were proven to agree fairly well with the solution by a Naiver-Stocks solver [10]. Here the results solved by Approach 2 are shown firstly and will be compared with the results of Approach 1.

Firstly, four different particles resolutions on the foil are adopted for the simulation to check the convergence of the results in Approach 2. Time evolutions of the fish movement and the swimming velocity are plotted in Fig. 2. In the presentation of SPH results, x and y denote the horizontal and vertical positions of the fish and the subscript stands for the initial positions at . The minus sign means the foil swims from the right side to the left. As the particle resolution is refined, the terminal velocity converges to u terminal=-1.23U. After a compromise between computational costs and numerical accuracy, in the following part of the paper, the particle resolution L/Δx=200 on the foil will be used for the other numerical investigations.

As shown in Fig. 3, the vorticity contours at three different time instants are depicted. During the accelerating stage, the vorticity generated by the flapping foil deflects to the upper part of the flow region. After the swimming velocity reaches the terminal stage, the distribution of vorticity locates in a straight line behind the foil.

In the following part, the numerical results solved by Approach 1 and Approach 2 will be compared. Firstly, the drag force coefficients () where is the drag force measured on the foil) are compared. Results from both Approach 1 and Approach 2 are plotted in Fig. 4. In Approach 1,during the steady stage, the drag force is almost always below zero, that means under such a phase speed and flapping amplitude, the foil can reach a terminal speed larger than . In Approach 2, after a transitional stage, the drag force oscillates around zero. That is due to the magnitude of the terminal velocity uterminal=-1.23U is larger that , the magnitude of the thrust force and the drag force reaches a dynamic balance.

The vorticity contours behind the foil solved by the two approaches at are compared in Fig. 5. Further, LCSs are reveled through the calculation of FTLE field [23] in the SPH results. The ridges of the FTLE field clearly show the boundaries of the vortices. The setting up of a threshold to locate these boundaries (as in the vorticity field) is not necessary in FTLE field. The convenience in detecting the LCSs is one of the superiorities of SPH compared with other Eulerian CFD models. The vortex structures, presenting a shape of the reverse von Karman vortex street, are similar in the two approaches, which means that both the two methods are applicable for the investigation of the flow features in this kind of problem.

Fig. 2. Time evolutions of the fish movement and the swimming velocity of the fishlike swimming foil in four different particle resolutions.

In conclusion, Approach 2 is easier to give the terminal swimming velocity, while for Approach 1, several numerical trials are generally needed to adjust the inflow velocity , ensure the drag force oscillating around zero and then obtain an accurate prediction of the terminal swimming velocity. In the rest of the paper, Approach 2 will be only adopted to investigate the propulsive performance of the fishlike swimming foil in different flapping parameters.

The vorticity contours behind the foil at the time instantare depicted in Fig. 10. With the increase of the amplitudes, the vortex street distributes in a wider region. In each period, the number of vortices shed from the tail is increased. In a higher flapping magnitude, the swimming wake behind the foil tends to be more chaotic.

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信息技术和生物技术革命仍处于初级阶段，它们对当前的自由主义危机究竟要负多大的责任，这值得商榷。伯明翰、伊斯坦布尔、圣彼得堡和孟买的大多数人只是模糊地意识到人工智能的兴起及其对他们生活的潜在影响。然而，毫无疑问，技术革命正在加速发展，在今后几十年中，人类将面临迄今所遇到的最严峻考验。

The 2D fish body is modeled by the NACA0012 foil as stated before, but the amplitude (see Eq. (1)) in the undulation motion of the foil's centreline is written as [12]

Fig. 3. Vorticity contours at three different time instants during which the fishlike swimming foil undergoes an acceleration firstly and then reaches a steady velocity.

In a fixed phase speed, the amplitude of the oscillation on the tail of the foil also has significant effect on the propulsive performance. Based on the same phase speed of , four different oscillating amplitudes are considered on the foil tail.andare fixed for all the four cases and andare tested respectively. The parameters for determining the tail oscillating amplitudes (see Eq. (7)) are summarized in Table 1.

Fig. 4. Time evolutions of the drag force coefficients on the wavy foil solved using both Approach 1 and Approach 2.

Time evolutions of the fish movement and the swimming velocity in the four tail flapping amplitudes are plotted in Fig. 9. As the flapping amplitude is increased, the terminal velocity also increases. But the incasement reduces in a high flapping amplitude. That implies there exists a proper amplitude which is most efficient for the propulsion.

The thrust force generated by the flapping motion of the foil is tightly related to the phase speed . The effect of the phase speed on the terminal swimming speed is investigated. Results of three different phase speeds , , andare compared. In all the cases, parameters, and , which lead to, and , are adopted in the determination of the oscillating amplitude.

A typical case regarding the saithe swimming from rest to cruise is simulated using Approach 2 within the -SPH framework. The SPH result will be compared against the numerical result obtained in Ref. [12] and the experimental result obtained in Ref. [24].

2.增强实践能力。实践是检验真理的唯一标准。当代大学生应充分利用自己的课余时间和假期到企事业进行实践学习，增强实践能力，还可以通过加入学校的社团、参加学校举行的比赛和活动。在每一次实践过程中，都认真做好记录，而不是完成任务，要切实把自己在工作中遇到的问题全面记录下来，请教领导或老师，研究解决问题的方法，在这个过程中不断提高自己的能力和水平。 现在很多的用人单位在招聘时关注的是学历，但更为关注是大学生的实践经验和实践能力。所以大学生只有拥有实际的工作能力，才能为社会创造价值。

This formula represents a kind of caudal fin propulsion where the lateral displacement of the front part of the body is zero and only the posterior part performs a wavy motion. According to the experimental data [24], the fish length is0.37 m, the cycle of undulation s, the wavelength , the phase speed m/s, the maximum wavy amplitude. The density of fluid and the fish body are both equal to kg/m3 and dynamics viscosity These parameters lead to a Reynolds number for this problem as R e= ρcpL/μ =5×105 [12].

系统在ArcGIS for Silverlight下使用天地图服务。天地图服务使用缓存数据[5]，所以ArcGIS Server中需要创建自定义图层类，这个类要继承Tiled Map Service Layer类；自定义图层中需要定义以下4个属性和方法：①切图的范围Full Extent；②空间参考系Spatial Reference；③地图切片信息Tile Info，包括切片的大小、级数，以及每级的空间分辨率；④还需要重写Get Tile Url方法。当地图控件的范围改变时，需要获取到当前范围的信息，并将范围内的所有切片全部按顺序显示出来。

Fig. 5. Vorticity fields behind the wavy foils at the same time instant tU/L = 9.9. Results of Approach 1 and Approach 2 are compared.

Fig. 6. Lagrangian coherent structures behind the wavy foils at the same time instant tU/L = 9.9. Results of Approach 1 and Approach 2 are compared.

Fig. 7. Time evolutions of the fish movement and the swimming velocity of the fishlike swimming foil with three different phase speeds in Approach 2.

The theoretical model of the real self-propulsion under Newton's law has been proposed from the end of last century by Carling et al. [17]. In that work, 2D anguilliform swimming was modeled using the finite difference method (FEM) and advantages of allowing for acceleration and deceleration of the swimmer's body were demonstrated. Yang et al. [12] extended the theoretical model of Carling et al. [17] and 2D simulations in the framework of finite volume method (FVM) were performed. This model has been further extended into 3D problems regarding the fast-start swimming and fish's body-shape optimization by Xin and Wu [18, 19].

Fig. 8. Vorticity contours behind the fishlike swimming foil at for three different phase speeds,, andin Approach 2.

Table 1 Parameters for the determination of oscillating amplitudes on the tail of the wavy foil.

Oscillating amplitude on the tail C1 C2 C3 A(L) = 0.05L 0.02 –0.0700 0.1000 A(L) = 0.10L 0.02 –0.0825 0.1625 A(L) = 0.15L 0.02 –0.0950 0.2250 A(L) = 0.20L 0.02 –0.1075 0.2875

In the present work, fishlike swimming problems are modeled using a particle method. It is demonstrated that the recently developed scheme is very suitable in solving this kind of problem. The problems of high computational costs and tensile numerical instability are avoided in scheme since APR and TIC have been implemented.

航空航天技术的发达与否是一个国家国力的综合表现之一，在航空航天领域有着大量的先进科研技术应用，由于对航空产业结构优化方法的不断更新，航空领域的产品更新换代速率也非常迅猛，在追逐世界一流科研成果的道路上不能迟疑。航空航天科技的更新关乎到一个国家的方方面面，大到国防力量小到日常民生，这些都离不开航空航天技术，对航空航天产业的结构优化是当今相关科研人员的重中之重，这对国家安全性与人民群众的日常生活有着至关重要的作用。只要重视结构优化方法在航空航天领域发挥的作用，就能让我国能在航空航天领域越飞越高。

The fish-swimming motion can be well modeled within the framework of the particle method. The fish body undergoes large deformations and it can swim to anywhere in the flow field,avoiding the problem of mesh distortion or re-mesh in meshbased methods. Two investigation approaches are adopted for this topic. It shows that within SPH method, both of the two investigation approaches can be realized conveniently. But for a self-propulsive problem, the result by Approach 2 seems to be closer to the real status of the fish swimming. The accuracy of the SPH results are validated by comparing with other numerical results or experimental data in the literature.

Thanks to the Lagrangian nature of SPH method, LCSs can be conveniently detected through the calculation of FTLE field and help to provide a Lagrangian way in visualizing the vortical structures and understanding the flow physics.

Fig. 9. Time evolutions of the fish movement and the swimming velocity of the fishlike swimming foil with four different oscillating amplitudes on the fish tail.

Fig. 10. Vorticity contours behind the fishlike swimming foil at for four different oscillating amplitudes on the fish tail.

Fig. 11. Modeling of a saithe swimming from rest to cruise: time evolutions of the swimming velocity in forward and lateral directions.

In the future studies, the present scheme is straightforward to be extended in the fishlike swimming problems in 3D.Complex interactions among more than two fishes in different positions can be investigated, in order to further explain the mechanism of fish schooling in nature. In addition, since SPH is very good at modelling free-surface flows, the study of the interaction between fish and free-surface can also be carried out.

教师要加强对学生们身心修养的培养。高中生正处步入大学的学习阶段，由于学习的压力，出现的心理问题比较多，这样就会影响到学生们的正常学习以及健康成长，同时学生们还会产生逆反心理和厌学心理。例如教师在进行品德教育过程当中要从学生们的心理问题抓起，安排相应的心理健康咨询讲解课，同时在班会教育上对学生们的心理问题进行辅导，普及心理健康教育知识，加强学生们心理健康水平。教师及教育工作者要建设相应的心理健康教育管理机制，建立起心理健康辅导机构，充分运行其机制体系，发挥各级心理健康机构的作用，切实提升大学生心理健康水平。

Acknowledgements

This work was funded by the National Natural Science Foundation of China (U1430236) and the PhD Student Research and Innovation Fund of the Fundamental Research Funds for the Central Universities (HEUGIP201701), to which the authors are most grateful.

为了最大化EOS 5DS及EOS 5DS R在像素方面的领先优势，两款新品也应用了诸多新功能。在EOS 5DS及EOS 5DS R的照片风格模式中，增加了全新的“精致细节”模式，进一步展现了约5060万有效像素在图像细节刻画方面的卓越能力。通过M1（约3930万有效像素）JPEG、M2（约2210万有效像素）等丰富的图像文件尺寸，带给用户更灵活的拍摄选择，同时在实时取景拍摄模式下，画面放大倍率提升至6x或16x，拍摄者可以轻松观察到更细微的画面细节，有助于进一步判断对焦的精确度。

Fig. 12. Modeling of a saithe swimming from rest to cruise: the vorticity contour behind the swimming saithe at t/T = 23.

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