Model of the motion of fishes and snakes

Lavrentʹev, Mikhail Alekseevich

doi:10.1007/bf01200671

Cited by 3 publications

(3 citation statements)

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“…The velocity depends largely on the relation between the friction force component (the parameter e). The result confirms Lavrent'ev's idea on the necessity of taking into account the viscous properties of the fluid [9]. Figure 2 gives the configurations of the elastic axis at various times.…”

Section: Analysis Of the Solutionsupporting

confidence: 90%

Reptation Motion of Large Animals in a Fluid

Шаповалов

2006

J Appl Mech Tech Phys

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An asymptotic analysis of the plane problem of reptation motion of animals in a fluid is performed in a long-wave approximation. Turbulent motion is considered. Asymptotic estimates are obtained for the axial and shear forces, expended energy, and motion trajectory. Results of numerical analysis are given.In [1,2], the problem in question was analyzed using the principle formulated by Lavrent'ev [3]. According to Lavrent'ev's principle, the animal's body is treated as an elastic rod placed in a solid channel of variable curvature. The environment surrounding the body plays the role of the solid walls of the channel. For motion in a fluid, the fluid plays the role of the channel walls because under rapid action for a time during which the organism moves a considerable distance, the fluid remains nearly motionless relative to the initial position by virtue of its inertia.Kuznetsov et al.[2] considered irrotational motion in an ideal fluid, which is equivalent to motion in a freely moving solid channel whose mass depends on the shape. For transverse flow around a cylinder, the potential was determined by the method of plane sections. The axial friction force was ignored since in an ideal fluid the shear stress on the body surface is equal to zero.Shapovalov [4] studied the laminar reptation motion of animals. The results obtained applies to the motion of microorganisms. The present paper extends the approach of [4] to the turbulent motion of animals. This is true for animals of large sizes, such as eel, moray, etc.The problem of plane reptation motion of large animals in a fluid is formulated and solved in a long-wave approximation. The energy, force, and kinematic characteristics of the motion are determined. The results of numerical analysis are given.1. Formulation of the Problem. We consider a developed turbulent regime that corresponds to the quadratic resistance law.We study the motion of animals whose body is prolate enough (eels, water snakes, etc.) to satisfy the condition l d (l and d are the length of the body in the prolate state and its diameter). The elastic axis passes along the backbone. The backbone can be treated as a hinged system of rods. The number of vertebras is considered infinite, and the elastic axis is treated as a monotonic smooth curve. The central nervous system sends command signals to the body muscles, so that a nearly sinusoidal traveling wave is formed. The number of muscles is considered infinite, and the command signal is a continuous monotonic function.The Archimedean force is ignored since the density of the animal's body is close to the density of the surrounding fluid. The cross section of the body is constant along its length. If the surrounding fluid is conditionally considered motionless, the dissipation of mechanical energy is localized in a region commensurable with the crosssectional dimensions of the animal, i.e., in the hydrodynamic boundary layer.The longitudinal and transverse friction forces (dP and dF , respectively) act on an elementary segment of the body of leng...

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Section: Analysis Of the Solutionsupporting

confidence: 90%

Reptation Motion of Large Animals in a Fluid

Шаповалов

2006

J Appl Mech Tech Phys

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“…Models of fish motion were developed, based on models of motion of bodies in a vortex-free flow of an inviscid fluid. Such a model of motion due to finite deformations of the body in a fluid was proposed in [1].The general features of motion of deformable bodies in an ideal fluid from the state at rest were summarized in [2]. The possibility of motion of the body in an ideal fluid due to body deformations and changes in the mass distribution inside the body was verified in [3].…”

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Inertial motion of a body in an ideal fluid from the state at rest

Voinov

2008

J Appl Mech Tech Phy

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UDC 532; 533 O. V. VoinovThe motion of a body in an ideal incompressible fluid flow without vortices in the absence of external forces is considered. It is demonstrated that the body can move inertially from the state at rest if its shape satisfies certain conditions. Key words: ideal incompressible fluid, vortex-free flow, motion of a body in a fluid, inertia.Introduction. The first studies of motion of various bodies in fluids under the action of internal forces were performed with modeling the motion of living organisms in water. Models of fish motion were developed, based on models of motion of bodies in a vortex-free flow of an inviscid fluid. Such a model of motion due to finite deformations of the body in a fluid was proposed in [1].The general features of motion of deformable bodies in an ideal fluid from the state at rest were summarized in [2]. The possibility of motion of the body in an ideal fluid due to body deformations and changes in the mass distribution inside the body was verified in [3]. Examples of motion of a pulsing sphere and an ellipsoid with a variable eccentricity and examples of motion of a body due to small deformations defined by two parameters were also given in [3].The motion of a deformable body in a fluid can be described by the Lagrangian equations. Based on these equations, axisymmetric and plane flows around bodies were studied, and conditions were found, which restrict the possibility of body motion for arbitrary given laws of variation of the body shape and changes in the mass distribution inside the body [4].A problem of motion of a nondeformable body with variable internal characteristics in an ideal fluid was considered in [5]. It follows from the known solutions that the body displacement in a fluid can be provided by periodic changes in parameters determining the body shape. The motion is nonuniform: the translational velocity is not constant, and the body stops if internal forces cease to act and deformation is terminated (in the case of a deformable body). Until now, the theory of self-induced motion of a body in a fluid predicted that it is impossible to reach uniform motion on the basis of available solutions of the problem of self-induced motion of the body [3]. It is demonstrated below that a body, being at rest at the initial time, can uniformly move in an ideal fluid under the action of internal forces.1. Shape of the Body that can Ensure its Inertial Motion in a Fluid from the State at Rest. Let us consider the motion of a body in an unbounded ideal incompressible fluid with the state at rest at infinity. The fluid motion does not contain vortices, and there are no external forces. The motion in the gravity field with neutral buoyancy of the body also refers to this case. The body is at rest at the initial time.Let us find the body shape that can ensure inertial motion of the body from the state at rest. We consider arbitrary symmetric shapes. The symmetry of the body surface is necessary for solutions of dynamic equations corresponding to straight-line motion o...

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