A hydrodynamical analysis of fish turning manoeuvres

1972 ◽  
Vol 182 (1066) ◽  
pp. 59-72 ◽  
Keyword(s):  
Present Theory ◽  
Inviscid Fluid ◽  
Centre Of Mass ◽  
Turning Process ◽  
Slender Body Theory ◽  
Turning Mechanism ◽  
Three Stages ◽  
Straight Lines ◽  
Body Theory ◽  
Good Agreement

Slender body theory, adapted here to the study of unsteady, curvilinear large amplitude movements in an inviscid fluid, is applied to the study of the turning mechanism in fishes. The vortex wake is represented by the circulation shed from the fins in the present theory. Examination of filmed sequences of turning fish show that the turning process includes three stages, distinguished by different movements of the centre of mass. In the first and third stages the centre of mass moves in straight lines in the initial and final directions of swimming while in the middle period it moves along an approximately circular connecting arc. The forces and moments acting on the fish, calculated by the present method are found to be in good agreement with these experimental observations.

On an Approximate Method of Calculating Pressures on Non-lifting Head Shapes at Supersonic Speeds

1955 ◽  
Vol 6 (1) ◽  
pp. 31-45
Author(s):  
H. K. Zienkiewicz
Keyword(s):  
Method Of Characteristics ◽  
Order Theory ◽  
Stagnation Pressure ◽  
Slender Body Theory ◽  
Pressure Losses ◽  
The Method Of Characteristics ◽  
Curvature Approximation ◽  
Body Theory ◽  
Theory And Experiment ◽  
Good Agreement

SummarySlender-body theory is used to derive the ogive of curvature approximation for very slender, pointed, convex head shapes at supersonic speeds. Results of application of this approximation, together with the λ-method for circular arc ogives, to a variety of non-slender head shapes show very good agreement with the method of characteristics, van Dyke's second-order theory and experiment. Good agreement with the method of characteristics and with experiment is obtained even in cases when the stagnation pressure losses across the nose shock wave are not negligible.

Slender-body theory for steady sheared plumes in very viscous fluid

2008 ◽  
Vol 612 ◽  
pp. 21-44 ◽  
Author(s):  
ROBERT J. WHITTAKER ◽  
JOHN R. LISTER
Keyword(s):  
Simple Model ◽  
Shear Flow ◽  
Viscous Fluid ◽  
Experimental Studies ◽  
Slender Body ◽  
Slender Body Theory ◽  
Dimensionless Parameters ◽  
Dynamical Regimes ◽  
Body Theory ◽  
Good Agreement

A simple model based on slender-body theory is developed to describe the deflection of a steady plume by shear flow in very viscous fluid of the same viscosity. The key dimensionless parameters measuring the relative strengths of the shear, diffusion and source flux are identified, which allows a number of different dynamical regimes to be distinguished. The predictions of the model show good agreement with many, but not all, observations from previous experimental studies. Possible reasons for the discrepancies are discussed.

Inhomogeneous distribution of a rigid fibre undergoing rectilinear flow between parallel walls at high Péclet numbers

2009 ◽  
Vol 630 ◽  
pp. 267-298 ◽  
Author(s):  
JOONTAEK PARK ◽  
JASON E. BUTLER
Keyword(s):  
Simple Shear Flow ◽  
Inhomogeneous Distribution ◽  
Slender Body Theory ◽  
Shear Rates ◽  
Net Migration ◽  
High Shear Rates ◽  
Fibre Suspensions ◽  
Parabolic Flow ◽  
Body Theory ◽  
Good Agreement

We use slender-body theory to simulate a rigid fibre within simple shear flow and parabolic flow at zero Reynolds number and high Péclet numbers (weak Brownian motion). Hydrodynamic interactions of bulk fibres with the bounding walls are included using previously developed methods (Harlen, Sundararajakumar & Koch, J. Fluid Mech., vol. 388, 1999, pp. 355–388; Butler & Shaqfeh, J. Fluid Mech., vol. 468, 2002, pp. 205–237). We also extend a previous analytic theory (Park, Bricker & Butler, Phys. Rev. E, vol. 76, 2007, 04081) predicting the centre-of-mass distribution of rigid fibre suspensions undergoing rectilinear flow near a wall to compare the steady and transient distributions. The distributions obtained by the simulation and theory are in good agreement at sufficiently high shear rates, validating approximations made in the theory which predicts a net migration of the rigid fibres away from the walls due to a hydrodynamic lift force. The effect of the inhomogeneous distribution on the effective stress is also investigated.

Variational properties of steady fall in Stokes flow

1972 ◽  
Vol 52 (2) ◽  
pp. 321-344 ◽  
Author(s):  
H. F. Weinberger
Keyword(s):  
Stokes Flow ◽  
Variational Principles ◽  
Vertical Axis ◽  
The Body ◽  
Centre Of Mass ◽  
Slender Body Theory ◽  
First Approximation ◽  
Slender Bodies ◽  
Settling Speed ◽  
Body Theory

It is shown that for a given body and a given orientationgthere is always a position of the centre of mass which produces a stable falling motion in a very viscous fluid withgvertical and, in general, with a spin about the vertical axis. The corresponding terminal settling speed is bounded by means of several variational principles.Relations between the terminal speeds for falls with different downward directions and between the terminal speed and the geometry of the body are deduced. In particular, it is proved that for a large class of slender bodies the first approximation to the drag obtained from the slender-body theory of Burgers (1938) is correct. It follows that the ratio of the terminal speeds for falls with the long axis vertical and horizontal is near two.

scholarly journals Software development for subsonic aircraft’s unsteady longitudinal stability derivatives calculation

2005 ◽  
Vol 32 (4) ◽  
pp. 319-340 ◽  
Author(s):  
Nikola Maricic
Keyword(s):  
Method Of Images ◽  
Lattice Method ◽  
Aerodynamic Stability ◽  
Slender Body Theory ◽  
Stability Derivatives ◽  
Doublet Lattice Method ◽  
Body Theory ◽  
General Configuration ◽  
Finite Element Methodology ◽  
Good Agreement

Subsonic general configuration aircrafts? unsteady longitudinal aerodynamic stability derivatives can be estimated using finite element methodology based on the Doublet Lattice Method (DLM), the Slender Body Theory (SBT) and the Method of Images (MI). Applying this methodology, software DERIV is developed. The obtained results from DERIV are compared to NASTRAN examples HA21A and HA75H. A good agreement is achieved.

Note on the swimming of slender fish

1960 ◽  
Vol 9 (2) ◽  
pp. 305-317 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Swimming Speed ◽  
Critical Value ◽  
Slender Body ◽  
Vortex Wake ◽  
Frictional Drag ◽  
Slender Body Theory ◽  
Propulsive Efficiency ◽  
Deformable Bodies ◽  
Work Done ◽  
Body Theory

The paper seeks to determine what transverse oscillatory movements a slender fish can make which will give it a high Froude propulsive efficiency, $\frac{\hbox{(forward velocity)} \times \hbox{(thrust available to overcome frictional drag)}} {\hbox {(work done to produce both thrust and vortex wake)}}.$ The recommended procedure is for the fish to pass a wave down its body at a speed of around $\frac {5} {4}$ of the desired swimming speed, the amplitude increasing from zero over the front portion to a maximum at the tail, whose span should exceed a certain critical value, and the waveform including both a positive and a negative phase so that angular recoil is minimized. The Appendix gives a review of slender-body theory for deformable bodies.

Slender-body theory for slow viscous flow

1976 ◽  
Vol 75 (4) ◽  
pp. 705-714 ◽  
Author(s):  
Joseph B. Keller ◽  
Sol I. Rubinow
Keyword(s):  
Integral Equation ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Unit Length ◽  
The Body ◽  
Slender Body ◽  
Slow Flow ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Body Theory

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

Sign in / Sign up

Export Citation Format

Share Document