Unsteady motion: escape jumps in planktonic copepods,their kinematics and energetics

We describe the kinematics of escape jumps in three species of 0.3–3.0 mm-sized planktonic copepods. We find similar kinematics between species with periodically alternating power strokes and passive coasting and a resulting highly fluctuating escape velocity. By direct numerical simulations, we estimate the force and power output needed to accelerate and overcome drag. Both are very high compared with those of other organisms, as are the escape velocities in comparison to startle velocities of other aquatic animals. Thus, the maximum weight-specific force, which for muscle motors of other animals has been found to be near constant at 57 N (kg muscle)⁻¹, is more than an order of magnitude higher for the escaping copepods. We argue that this is feasible because most copepods have different systems for steady propulsion (feeding appendages) and intensive escapes (swimming legs), with the muscular arrangement of the latter probably adapted for high force production during short-lasting bursts. The resulting escape velocities scale with body length to power 0.65, different from the size-scaling of both similar sized and larger animals moving at constant velocity, but similar to that found for startle velocities in other aquatic organisms. The relative duration of the pauses between power strokes was observed to increase with organism size. We demonstrate that this is an inherent property of swimming by alternating power strokes and pauses. We finally show that the Strouhal number is in the range of peak propulsion efficiency, again suggesting that copepods are optimally designed for rapid escape jumps.     

The management of fluid and wave resistances by whirligig beetles

Whirligig beetles (Coleoptera: Gyrinidae) are semi-aquatic insects with a morphology and propulsion system highly adapted to their life at the air–water interface. When swimming on the water surface, beetles are subject to both fluid resistance and wave resistance.The purpose of this study was to analyse swimming speed, leg kinematics and the capillarity waves produced by whirligig beetles on the water surface in a simple environment. Whirligig beetles of the species Gyrinus substriatus were filmed in a large container, with a high-speed camera. Resistance forces were also estimated.These beetles used three types of leg kinematics, differing in the sequence of leg strokes: two for swimming at low speed and one for swimming at high speed. Four main speed patterns were produced by different combinations of these types of leg kinematics, and the minimum speed for the production of surface waves (23 cm s⁻¹) corresponded to an upper limit when beetles used low-speed leg kinematics. Each type of leg kinematics produced characteristic capillarity waves, even if the beetles moved at a speed below 23 cm s⁻¹. Our results indicate that whirligig beetles use low- and high-speed leg kinematics to avoid maximum drag and swim at speed corresponding to low resistances.     

Swimming of the semi-infinite strip revisited

Idealized mathematical models have been devised over the years for study of the fundamentals of the swimming of fishes. The two-dimensional flexible strip propelled by execution of transverse traveling-wave undulation is one of the most well-studied of the simple models. This model is redeveloped here, with the finding that higher propulsive efficiencies are theoretically available within the undulatory swimming mode than have been previously exposed. This is by configuring the displacement wave-form for continuously zero circulation over the body length with time, and thereby avoiding the shedding of a vortex wake and its attendant induced drag. The thrust is reactive, via acceleration processes, rather than inductive via relative velocity and lift. As in most of the classical work on fish propulsion, the analysis assumes high Reynolds number and a thin boundary layer, which provides the use of ideal-flow theory. The advance speed is assumed constant and the analysis is initially linearized, but both nonlinear and linear transient analysis are provided in supporting the basic “wakeless swimming” possibility.     

The fluid dynamics of swimming by jumping in copepods

Copepods swim either continuously by vibrating their feeding appendages or erratically by repeatedly beating their swimming legs, resulting in a series of small jumps. The two swimming modes generate different hydrodynamic disturbances and therefore expose the swimmers differently to rheotactic predators. We developed an impulsive stresslet model to quantify the jump-imposed flow disturbance. The predicted flow consists of two counter-rotating viscous vortex rings of similar intensity, one in the wake and one around the body of the copepod. We showed that the entire jumping flow is spatially limited and temporally ephemeral owing to jump-impulsiveness and viscous decay. In contrast, continuous steady swimming generates two well-extended long-lasting momentum jets both in front of and behind the swimmer, as suggested by the well-known steady stresslet model. Based on the observed jump-swimming kinematics of a small copepod Oithona davisae, we further showed that jump-swimming produces a hydrodynamic disturbance with much smaller spatial extension and shorter temporal duration than that produced by a same-size copepod cruising steadily at the same average translating velocity. Hence, small copepods in jump-swimming are in general much less detectable by rheotactic predators. The present impulsive stresslet model improves a previously published impulsive Stokeslet model that applies only to the wake vortex.     

Analytical insights into optimality and resonance in fish swimming

This paper provides analytical insights into the hypothesis that fish exploit resonance to reduce the mechanical cost of swimming. A simple body–fluid fish model, representing carangiform locomotion, is developed. Steady swimming at various speeds is analysed using optimal gait theory by minimizing bending moment over tail movements and stiffness, and the results are shown to match with data from observed swimming. Our analysis indicates the following: thrust–drag balance leads to the Strouhal number being predetermined based on the drag coefficient and the ratio of wetted body area to cross-sectional area of accelerated fluid. Muscle tension is reduced when undulation frequency matches resonance frequency, which maximizes the ratio of tail-tip velocity to bending moment. Finally, hydrodynamic resonance determines tail-beat frequency, whereas muscle stiffness is actively adjusted, so that overall body–fluid resonance is exploited.     

Propulsive performance of a fish-like travelling wavy wall

Summary. A numerical simulation is performed to investigate the viscous flow over a smooth wavy wall undergoing transverse motion in the form of a streamwise travelling wave, which is similar to the backbone undulation of swimming fish. The objective of this study is to elucidate hydrodynamic features of the flow structure over the travelling wavy wall and to get physical insights to the understanding of fish-like swimming mechanisms in terms of drag reduction and optimal propulsive efficiency. The effect of phase speed, amplitude and Reynolds number on the flow structure over the wavy wall, the drag force acting on the wall, and the power consumption required for the propulsive motion of the wall is investigated. The phase speed and the amplitude, which are two important parameters in this problem, predicted based on the optimal propulsive efficiency agree well with the available data obtained for the wave-like swimming motion of live fish in nature.     

Choreographed swimming of copepod nauplii

Small metazoan paddlers, such as crustacean larvae (nauplii), are abundant, ecologically important and active swimmers, which depend on exploiting viscous forces for locomotion. The physics of micropaddling at low Reynolds number was investigated using a model of swimming based on slender-body theory for Stokes flow. Locomotion of nauplii of the copepod Bestiolina similis was quantified from high-speed video images to obtain precise measurements of appendage movements and the resulting displacement of the body. The kinematic and morphological data served as inputs to the model, which predicted the displacement in good agreement with observations. The results of interest did not depend sensitively on the parameters within the error of measurement. Model tests revealed that the commonly attributed mechanism of ‘feathering’ appendages during return strokes accounts for only part of the displacement. As important for effective paddling at low Reynolds number is the ability to generate a metachronal sequence of power strokes in combination with synchronous return strokes of appendages. The effect of feathering together with a synchronous return stroke is greater than the sum of each factor individually. The model serves as a foundation for future exploration of micropaddlers swimming at intermediate Reynolds number where both viscous and inertial forces are important.     

Fish responses to flow velocity and turbulence in relation to size,sex and parasite load

Riverine fish are subjected to heterogeneous flow velocities and turbulence and may use this to their advantage by selecting regions that balance energy expenditure for station holding while maximizing energy gain through feeding opportunities. This study investigated microhabitat selection by guppies Poecilia reticulata in terms of flow characteristics generated by hemisphere boulders in an open channel flume. Velocity and turbulence influenced the variation in swimming behaviour with respect to size, sex and parasite intensity. With increasing body length, fish swam further and more frequently between boulder regions. Larger guppies spent more time in the areas of high-velocity and low-turbulence regions beside the boulders, whereas smaller guppies frequented the low-velocity and high-turbulence regions directly behind the boulders. Male guppies selected the regions of low velocity, indicating possible reduced swimming ability owing to hydrodynamic drag imposed by their fins. With increasing Gyrodactylus turnbulli burden, fish spent more time in regions with moderate velocity and lowest turbulent kinetic energy which were the most spatially and temporally homogeneous in terms of velocity and turbulence. These findings highlight the importance of heterogeneous flow conditions in river channel design owing to the behavioural variability within a species in response to velocity and turbulence.     

Metachronal waves in the flagellar beating of Volvox and their hydrodynamic origin

Groups of eukaryotic cilia and flagella are capable of coordinating their beating over large scales, routinely exhibiting collective dynamics in the form of metachronal waves. The origin of this behaviour—possibly influenced by both mechanical interactions and direct biological regulation—is poorly understood, in large part due to a lack of quantitative experimental studies. Here we characterize in detail flagellar coordination on the surface of the multicellular alga Volvox carteri, an emerging model organism for flagellar dynamics. Our studies reveal for the first time that the average metachronal coordination observed is punctuated by periodic phase defects during which synchrony is partial and limited to specific groups of cells. A minimal model of hydrodynamically coupled oscillators can reproduce semi-quantitatively the characteristics of the average metachronal dynamics, and the emergence of defects. We systematically study the model''s behaviour by assessing the effect of changing intrinsic rotor characteristics, including oscillator stiffness and the nature of their internal driving force, as well as their geometric properties and spatial arrangement. Our results suggest that metachronal coordination follows from deformations in the oscillators'' limit cycles induced by hydrodynamic stresses, and that defects result from sufficiently steep local biases in the oscillators'' intrinsic frequencies. Additionally, we find that random variations in the intrinsic rotor frequencies increase the robustness of the average properties of the emergent metachronal waves.     

球头体逆向喷流减阻的数值模拟研究

为研究逆向喷流对超声速球头体减阻的影响,该文结合标准k-ε湍流模型,通过求解轴对称和三维Navier-Stokes方程,数值模拟了超声速球头体逆向冷喷流流场,着重分析了喷口总压、喷口尺寸及攻角对流场模态和减阻效果的影响。计算结果显示:喷流能使球头体受到的阻力明显减小;随着喷流总压的增大,在不同喷口尺寸和攻角下,流场均先后经历长射流和短射流穿透模态;存在最大减阻临界喷流总压值,该值与喷口尺寸比呈近似的线性关系,在所研究参数范围内最大减阻可达54.7%;随着攻角的增大,流场的不对称性加强,减阻效果下降。该文的研究对超声速钝体减阻技术在工程上的应用具有一定的参考价值。     

Hydrodynamics of the double-wave structure of insect spermatozoa flagella

In addition to conventional planar and helical flagellar waves, insect sperm flagella have also been observed to display a double-wave structure characterized by the presence of two superimposed helical waves. In this paper, we present a hydrodynamic investigation of the locomotion of insect spermatozoa exhibiting the double-wave structure, idealized here as superhelical waves. Resolving the hydrodynamic interactions with a non-local slender body theory, we predict the swimming kinematics of these superhelical swimmers based on experimentally collected geometric and kinematic data. Our consideration provides insight into the relative contributions of the major and minor helical waves to swimming; namely, propulsion is owing primarily to the minor wave, with negligible contribution from the major wave. We also explore the dependence of the propulsion speed on geometric and kinematic parameters, revealing counterintuitive results, particularly for the case when the minor and major helical structures are of opposite chirality.     

LSM control of Maglev vehicle ride quality

The ride quality of a high speed repulsion type magnetically levitated vehicle using linear synchronous motor (LSM) propulsion has been studied. Vehicle motion is dependent upon the active LSM forces, the passive magnetic lift and drag forces, the aerodynamic drag force, and the technique employed for control. Derivations of the passive lift and drag forces and of the active heave and propulsion control forces are presented. For a balanced three phase LSM, it is shown that harmonic force pulsations disappear, except for the sixth harmonic and its multiples. A control technique which stabilizes the surge motion and provides needed damping in heave to guarantee acceptable ride quality has been simulated. Transient responses, for a vehicle traveling at 120 m/s show stable well damped motion. At this velocity, sixth harmonic effects are completely negligible. Stochastic results show that the heave motion power spectral density response to a moderately rough guideway, i.e., A = 1.34 × 10^-5m, more than satisfies the UMTA ride quality specification.     

Passive elastic mechanism to mimic fish-muscle action in anguilliform swimming

Swimmers in nature use body undulations to generate propulsive and manoeuvring forces. The anguilliform kinematics is driven by muscular actions all along the body, involving a complex temporal and spatial coordination of all the local actuations. Such swimming kinematics can be reproduced artificially, in a simpler way, by using the elasticity of the body passively. Here, we present experiments on self-propelled elastic swimmers at a free surface in the inertial regime. By addressing the fluid–structure interaction problem of anguilliform swimming, we show that our artificial swimmers are well described by coupling a beam theory with the potential flow model of Lighthill. In particular, we show that the propagative nature of the elastic wave producing the propulsive force is strongly dependent on the dissipation of energy along the body of the swimmer.     

全向移动机器人驱动轮同步转向机构设计

针对现有轮式全向移动机器人在工程实际应用中存在的驱动轮同步转向能力差的问题,设计了驱动轮同步转向机构。首先,基于虚拟样机技术分析了该同步转向机构的工作原理,并将它应用于轮式全向移动机器人。然后,利用运动学原理对加入同步转向机构机器人进行运动学分析,得到了电机输入转速与驱动轮转向速度之间的关系。最后,根据系统结构参数研制了一款主要应用于工厂物料搬运工作的产品样机并进行实验验证。机器人横向移动实验结果表明,该机器人可以通过不同方式进行全向移动,验证了该机器人的全向移动功能。研究表明同步转向机构的应用降低了轮式全向移动机器人控制难度,实现了机器人高速、高精度、高稳定性全向移动。     

Trapping of water waves by moored bodies

Certain types of floating bodies are known to support trapped modes, with oscillatory fluid motion near the body and no energy radiation in the far field. Previous work has considered either fixed bodies, where the boundary conditions are homogeneous, or bodies which are freely floating and moving without any exciting force. For a fixed body the existence of a trapped mode implies that there is no unique solution of the boundary-value problem for the velocity potential with a prescribed body motion. For a free body which supports a trapped mode, the solution of the coupled problem for the motions of the fluid and body does not have a unique solution. A more general case is considered here, of a body with a linear restoring force such as an elastic mooring. The limiting cases of a fixed and free body correspond to infinite or zero values of the corresponding spring constant. A variety of body shapes are found including cylinders in two dimensions and axisymmetric bodies in three dimensions, which illustrate this more general case of trapping and provide a connection between the fixed and free cases.     

The slow stationary flow of incompressible micropolar fluid past a spheroid

The paper examines the slow stationary flow of incompressible micropolar fluid past a spheroid (prolate and oblate) adopting the Stokesian approximation, so that the inertial terms in the momentum equation and the bilinear terms in the balance of first stress moments are neglected. The flow over the space outside the body is analyzed and the velocity, microrotation, stress and couple stress are obtained analytically in infinite series form. The drag on the body is determined and it is observed that there is no couple exerted on the body. Numerical studies are undertaken to see the variation of the drag with respect to the geometric as well as the physical flow parameters. These have been presented in the form of figures. Micropolarity of the fluid has an augmenting effect on the drag. In an Appendix, an alternative method of determining the drag is indicated.     

A Method of Body Shape Optimization for Decreasing the Aerodynamic Drag Force in Gas Flow

Aerodynamic flow past bodies of various geometrical shapes was studied, and the aerodynamic drag force was reduced through optimization of the body shape using a specially proposed method. The resulting drag force was compared to that for bodies formed by revolution of the profiles of well-known standard series. The study was performed using the Ansys Fluent software for isothermal laminar steady-state flows of incompressible fluid with constant density in a velocity range of 0–10 m/s. It is shown that the aerodynamic drag force for a body with the optimized shape is lower than analogous values for the bodies of revolution with Su-26 and NASA-0006 reference profiles. In comparison to the aerodynamic-drag-force level of 100% for the body of revolution with NASA-0006 profile, the drag force for Su-26 profile at airflow velocity of 10 m/s is 89.4%, while that for the proposed optimized body shape is 89.2%.     

Numerical solutions of one-dimensional self-similar problems of gas motion in a porous medium for a quadratic drag law

Computations are performed of the pressure and velocity of gas motion in a porous medium for self-similar one-dimensional (plane, axisymmetric, and spherically symmetric) problems for a quadratic drag law.     

Leg stiffness of sprinters using running-specific prostheses

Running-specific prostheses (RSF) are designed to replicate the spring-like nature of biological legs (bioL) during running. However, it is not clear how these devices affect whole leg stiffness characteristics or running dynamics over a range of speeds. We used a simple spring–mass model to examine running mechanics across a range of speeds, in unilateral and bilateral transtibial amputees and performance-matched controls. We found significant differences between the affected leg (AL) of unilateral amputees and both ALs of bilateral amputees compared with the bioL of non-amputees for nearly every variable measured. Leg stiffness remained constant or increased with speed in bioL, but decreased with speed in legs with RSPs. The decrease in leg stiffness in legs with RSPs was mainly owing to a combination of lower peak ground reaction forces and increased leg compression with increasing speeds. Leg stiffness is an important parameter affecting contact time and the force exerted on the ground. It is likely that the fixed stiffness of the prosthesis coupled with differences in the limb posture required to run with the prosthesis limits the ability to modulate whole leg stiffness and the ability to apply high vertical ground reaction forces during sprinting.     

一种新型可重构5R机构的运动学分析

目的提出一种新型可重构5R机构,改变5R机构机架的尺寸和位置,提高基于5R机构设计的折箱设备和对不同加工作业的适应性。方法使用螺旋副提供驱动而改变定平台的位置和等效尺寸,从而实现机构的重构,得到一种新型的5R并联机构。使用旋量理论对此机构进行速度分析。结果得到了这种新型5R机构的输入-输出速度关系表达式,使用矢量法和旋量工具,进行了对比验证,两者结果一致。结论旋量理论在进行速度分析时,物理意义明确,求解模式统一,使用方便。通过对此新型并联机构进行运动学分析,可为该机构的优化设计、尺度综合、动力学分析提供理论基础。