Note on the swimming of an elongated body in a non-uniform flow

2013 ◽  
Vol 716 ◽  
pp. 616-637 ◽  
Author(s):  
Fabien Candelier ◽  
Mathieu Porez ◽  
Frederic Boyer
Keyword(s):  
Cross Sections ◽  
Potential Flow ◽  
Velocity Potential ◽  
Fluid Velocity ◽  
The Body ◽  
Curvilinear Coordinates ◽  
Elliptical Cross ◽  
Fish Locomotion ◽  
Pitch Bending ◽  
Body Theory

AbstractThis paper presents an extension of Lighthill’s large-amplitude elongated-body theory of fish locomotion which enables the effects of an external weakly non-uniform potential flow to be taken into account. To do so, the body is modelled as a Kirchhoff beam, made up of elliptical cross-sections whose size may vary along the body, undergoing prescribed deformations consisting of yaw and pitch bending. The fluid velocity potential is decomposed into two parts corresponding to the unperturbed potential flow, which is assumed to be known, and to the perturbation flow. The Laplace equation and the corresponding Neumann’s boundary conditions governing the perturbation velocity potential are expressed in terms of curvilinear coordinates which follow the body during its motion, thus allowing the boundary of the body to be considered as a fixed surface. Equations are simplified according to the slenderness of the body and the weakness of the non-uniformity of the unperturbed flow. These simplifications allow the pressure acting on the body to be determined analytically using the classical Bernoulli equation, which is then integrated over the body. The model is finally used to investigate the passive and the active swimming of a fish in a Kármán vortex street.

Line source distributions and slender-body theory

1963 ◽  
Vol 17 (2) ◽  
pp. 285-304 ◽  
Author(s):  
John P. Moran
Keyword(s):  
Potential Flow ◽  
Line Source ◽  
The Body ◽  
Successive Approximations ◽  
External Disturbances ◽  
Slender Body Theory ◽  
Bodies Of Revolution ◽  
Plane Flow ◽  
Body Theory

A systematic procedure is presented for the determination of uniformly valid successive approximations to the axisymmetric incompressible potential flow about elongated bodies of revolution meeting certain shape requirements. The presence of external disturbances moving with respect to the body under study is admitted. The accuracy of the procedure and its extension beyond the scope of the present study—e.g. to problems in plane flow - are discussed.

Calculation of Nonlifting Potential Flow About Arbitrary Three-Dimensional Bodies

1964 ◽  
Vol 8 (04) ◽  
pp. 22-44 ◽  
Author(s):  
John L. Hess ◽  
A. M. O. Smith
Keyword(s):  
Body Surface ◽  
Potential Flow ◽  
Fluid Velocity ◽  
Normal Component ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
The Body ◽  
Algebraic Equations ◽  
Source Density ◽  
Linear Algebraic Equations

A general method is described for calculating, with the aid of an electronic computer, the incompressible potential flow about arbitrary, nonlifting, three-dimensional bodies. The method utilizes a source density distribution on the surface of the body and solves for the distribution necessary to make the normal component of fluid velocity zero on the boundary. Plane quadrilateral surface elements are used to approximate the body surface, and the integral equation for the source density is replaced by a set of linear algebraic equations for the values of the source density on the quadrilateral elements. When this set of equations has been solved, the flow velocity both on and off the body surface is calculated. After the basic ideas and equations have been derived end discussed, the accuracy of the method is exhibited by means of comparisons with analytic solutions, and its usefulness is shown by comparing calculated pressure distributions with experimental data. Some of the design problems to which the method has been applied are also presented, to indicate the variety of flow situations that can be calculated by this approach.

scholarly journals Three-dimensional extension of Lighthill's large-amplitude elongated-body theory of fish locomotion

2011 ◽  
Vol 674 ◽  
pp. 196-226 ◽  
Author(s):  
FABIEN CANDELIER ◽  
FREDERIC BOYER ◽  
ALBAN LEROYER
Keyword(s):  
Cross Sections ◽  
Velocity Potential ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Neumann Boundary ◽  
The Body ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Curvature Effects ◽  
The Cross

The goal of this paper is to derive expressions for the pressure forces and moments acting on an elongated body swimming in a quiescent fluid. The body is modelled as an inextensible and unshearable (Kirchhoff) beam, whose cross-sections are elliptic, undergoing prescribed deformations, consisting of yaw and pitch bending. The surrounding fluid is assumed to be inviscid, and irrotational everywhere, except in a thin vortical wake. The Laplace equation and the corresponding Neumann boundary conditions are first written in terms of the body coordinates of a beam treating the body as a fixed surface. They are then simplified according to the slenderness of the body and its kinematics. Because the equations are linear, the velocity potential is sought as a sum of two terms which are linked respectively to the axial movements of the beam and to its lateral movements. The lateral component of the velocity potential is decomposed further into two sub-components, in order to exhibit explicitly the role of the two-dimensional potential flow produced by the lateral motion of the cross-section, and the role played by the curvature effects of the beam on the cross-sectional flow. The pressure, which is given by Bernoulli's equation, is integrated along the body surface, and the expressions for the resultant and the moment are derived analytically. Thereafter, the validity of the force and moment obtained analytically is checked by comparisons with Navier–Stokes simulations (using Reynolds-averaged Navier–Stokes equations), and relatively good agreements are observed.

scholarly journals Saint-Venant’s torsion of thin-walled nonhomogeneous open elliptical cross section

2021 ◽  
Vol 11 (5) ◽  
pp. 151-158
Author(s):  
István Ecsedi ◽  
Ákos József Lengyel ◽  
Attila Baksa ◽  
Dávid Gönczi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Torsional Rigidity ◽  
Elliptical Cross Section ◽  
Curvilinear Coordinates ◽  
Torsion Problem ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Thin Walled ◽  
The One

This paper deals with the Saint-Venant’s torsion of thin-walled isotropic nonhomogeneous open elliptical cross section whose shear modulus depends on the one of the curvilinear coordinates which define the cross-sectional area of the beam. The approximate solution of torsion problem is obtained by variational method. The usual simplification assumptions are used to solve the uniform torsion problem of bars with thin-walled elliptical cross-sections. An example illustrates the application of the derived formulae of shearing stress and torsional rigidity.

The Drift Force and Moment on Ships in Waves

1967 ◽  
Vol 11 (01) ◽  
pp. 51-60 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Velocity Potential ◽  
The Body ◽  
Horizontal Force ◽  
Regular Waves ◽  
Slender Body Theory ◽  
Kochin Function ◽  
Field Velocity ◽  
Drift Force ◽  
The Waves ◽  
Body Theory

The second-order steady horizontal force and vertical moment are derived for a freely floating ship in regular waves. The fluid is assumed to be ideal and the motion is linearized. Momentum relations are used to derive general results for an arbitrary ship or other body, in terms of the Kochin function or far-field velocity potential of the body. Explicit results are derived for slender ships, based upon the assumptions of slender body theory. Computations are made for a Series 60 hull and are compared with experiments. The analysis of the vertical moment permits the prediction of stable heading angles in oblique waves, and it is shown that unless the waves are very short, the ship will be stable only in beam waves.

The formation of elliptical wakes

1967 ◽  
Vol 27 (2) ◽  
pp. 353-360 ◽  
Author(s):  
Yung-Huang Kuo ◽  
Lionel V. Baldwin
Keyword(s):  
Strouhal Number ◽  
Cross Sections ◽  
Major Axis ◽  
Turbulent Energy ◽  
Minor Axis ◽  
The Body ◽  
Wake Flow ◽  
Mean Velocity ◽  
Elliptical Cross ◽  
Number Range

The wakes formed behind sharp-edged, bluff, elliptical bodies have elliptical cross-sections, but the major axis of the wake is aligned with the minor axis of the body. This effect was observed in both mean velocity and turbulent intensity data in wakes throughout the range of the experiment, from several body diameters to distances of 250 diameters downstream of the body. The turbulent energy in the wake flow near the body displayed a periodicity which was correlated using a Strouhal number. Over the Reynolds-number range from 8 × 103to 7 × 104, the Strouhal number depended only on the body eccentricity.

scholarly journals Experimental verification of an Oseen flow slender body theory

2010 ◽  
Vol 654 ◽  
pp. 271-279 ◽  
Author(s):  
E. CHADWICK ◽  
H. M. KHAN ◽  
M. MOATAMEDI ◽  
M. MAPPIN ◽  
M. PENNEY
Keyword(s):  
Cross Section ◽  
Semimajor Axis ◽  
Major Axis ◽  
The Body ◽  
Slender Body ◽  
Radius Of Curvature ◽  
Slender Body Theory ◽  
Elliptical Cross ◽  
Oseen Flow ◽  
Body Theory

Consider uniform flow past four slender bodies with elliptical cross-section of constant ellipticity along the length of 0, 0.125, 0.25 and 0.375, respectively, for each body. Here, ellipticity is defined as the ratio of the semiminor axis of the ellipse to the semimajor axis. The bodies have a pointed nose which gradually increases in cross-section with a radius of curvature 419 mm to a mid-section which then remains constant up to a blunt end section with semimajor axis diameter 160 mm, the total length of all bodies being 800 mm. The bodies are side-mounted within a low-speed wind tunnel with an operational wind speed of the order 30 m s−1. The side force (or lift) is measured within an angle of attack range of −3° to 3° such that the body is rotated about the major axis of the ellipse cross-section. The lift slope is determined for each body, and how it varies with ellipticity. It is found that this variance follows a straight line which steadily increases with increasing ellipticity. It is shown that this result is predicted by a recently developed Oseen flow slender body theory, and cannot be predicted by either inviscid flow slender body theory or viscous crossflow theories based upon the Allen and Perkins method.

An estimate of the Kelvin impulse of a transient cavity

1994 ◽  
Vol 261 ◽  
pp. 75-93 ◽  
Author(s):  
J. P. Best ◽  
J. R. Blake
Keyword(s):  
Velocity Potential ◽  
Fluid Velocity ◽  
The Body ◽  
Jet Formation ◽  
Rigid Boundary ◽  
Bodies Of Revolution ◽  
Cavity Collapse ◽  
Submerged Sphere ◽  
Body Shapes ◽  
Collapse Phase

The Lagally theorem is used to obtain an expression for the Bjerknes force acting on a bubble in terms of the singularities of the fluid velocity potential, defined within the bubble by analytic continuation. This expression is applied to transient cavity collapse in the neighbourhood of boundaries, allowing analytical estimates to be made of the Kelvin impulse of the cavity. The known result for collapse near a horizontal rigid boundary is recovered, and the Kelvin impulse of a cavity collapsing in the neighbourhood of a submerged and partially submerged sphere is estimated. A numerical method is developed to deal with more general body shapes and in particular, bodies of revolution. Noting that the direction of the impulse at the end of the collapse phase generally indicates the direction of the liquid jet that may form, the behaviour of transient cavities in these geometries is predicted. In these examples the concept of a zone of attraction is introduced. This is a region around the body, within which the Kelvin impulse at the time of collapse, and consequent jet formation, is expected to be directed towards the body. Outside this zone the converse is true.

Gender determination of caucasoid hair using image analysis

1993 ◽  
Vol 51 ◽  
pp. 216-217
Author(s):  
T.B. Ball ◽  
W.M. Hess
Keyword(s):  
Image Analysis ◽  
Cross Sections ◽  
Scalp Hair ◽  
The Body ◽  
Equivalent Diameter ◽  
Cross Sectional ◽  
Hair Samples ◽  
Length Width ◽  
Morphological Differences

It has been demonstrated that cross sections of bundles of hair can be effectively studied using image analysis. These studies can help to elucidate morphological differences of hair from one region of the body to another. The purpose of the present investigation was to use image analysis to determine whether morphological differences could be demonstrated between male and female human Caucasian terminal scalp hair.Hair samples were taken from the back of the head from 18 caucasoid males and 13 caucasoid females (Figs. 1-2). Bundles of 50 hairs were processed for cross-sectional examination and then analyzed using Prism Image Analysis software on a Macintosh llci computer. Twenty morphological parameters of size and shape were evaluated for each hair cross-section. The size parameters evaluated were area, convex area, perimeter, convex perimeter, length, breadth, fiber length, width, equivalent diameter, and inscribed radius. The shape parameters considered were formfactor, roundness, convexity, solidity, compactness, aspect ratio, elongation, curl, and fractal dimension.

A body without a head

2020 ◽  
Author(s):  
Ali Chavoshian ◽  
Sophia Park
Keyword(s):  
Liberation Theology ◽  
The Body ◽  
Women's Spirituality ◽  
Passive Condition ◽  
Sexual Identities ◽  
Logical Square ◽  
The Social ◽  
Feminine Sexuality ◽  
Body Shapes ◽  
Body Theory

Along with the recent development of various theories of the body, Lacan’s body theory aligns with postmodern thinkers such as Michael Foucault and Maurice Merlot-Ponti, who consider body social not biological. Lacan emphasizes the body of the Real, the passive condition of the body in terms of formation, identity, and understanding. Then, this condition of body shapes further in the condition of bodies of women and laborers under patriarchy and capitalism, respectively. Lacan’s ‘not all’ position, which comes from the logical square, allows women to question patriarchy’s system and alternatives of sexual identities. Lacan’s approach to feminine sexuality can be applied to women’s spirituality, emphasizing multiple narratives of body and sexual identities, including gender roles. In the social discernment and analysis in the liberation theology, we can employ the capitalist discourse, which provides a tool to understand how people are manipulated by late capitalist society, not knowing it. Lacan’s theory of ‘a body without a head’ reflects the current condition of the human body, which manifests lack, yet including some possibilities for transforming society.

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