A family of steady vortex rings

1973 ◽  
Vol 57 (3) ◽  
pp. 417-431 ◽  
Author(s):  
J. Norbury
Keyword(s):  
Theoretical Work ◽  
Vortex Rings ◽  
Small Cross Section ◽  
The Core ◽  
Axisymmetric Vortex ◽  
Recent Theoretical Work ◽  
The Family ◽  
Core Boundary ◽  
Spherical Vortex ◽  
Axis Of Symmetry

Axisymmetric vortex rings which propagate steadily through an unbounded ideal fluid at rest at infinity are considered. The vorticity in the ring is proportional to the distance from the axis of symmetry. Recent theoretical work suggests the existence of a one-parameter family, [npar ]2 ≥ α ≥ 0 (the parameter α is taken as the non-dimensional mean core radius), of these vortex rings extending from Hill's spherical vortex, which has the parameter value α = [npar ]2, to vortex rings of small cross-section, where α → 0. This paper gives a numerical description of vortex rings in this family. As well as the core boundary, propagation velocity and flux, various other properties of the vortex ring are given, including the circulation, fluid impulse and kinetic energy. This numerical description is then compared with asymptotic descriptions which can be found near both ends of the family, that is, when α → [npar ]2 and α → 0.

scholarly journals Perturbation response and pinch-off of vortex rings and dipoles

2012 ◽  
Vol 704 ◽  
pp. 280-300 ◽  
Author(s):  
Clara O’Farrell ◽  
John O. Dabiri
Keyword(s):  
Vortex Formation ◽  
Three Dimensions ◽  
Vortex Rings ◽  
Two Dimensional ◽  
Vortex Pairs ◽  
The Core ◽  
Axisymmetric Vortex ◽  
Prolate Shape ◽  
The Family ◽  
Spherical Vortex

AbstractThe nonlinear perturbation response of two families of vortices, the Norbury family of axisymmetric vortex rings and the Pierrehumbert family of two-dimensional vortex pairs, is considered. Members of both families are subjected to prolate shape perturbations similar to those previously introduced to Hill’s spherical vortex, and their response is computed using contour dynamics algorithms. The response of the entire Norbury family to this class of perturbations is considered, in order to bridge the gap between past observations of the behaviour of thin-cored members of the family and that of Hill’s spherical vortex. The behaviour of the Norbury family is contrasted with the response of the analogous two-dimensional family of Pierrehumbert vortex pairs. It is found that the Norbury family exhibits a change in perturbation response as members of the family with progressively thicker cores are considered. Thin-cored vortices are found to undergo quasi-periodic deformations of the core shape, but detrain no circulation into their wake. In contrast, thicker-cored Norbury vortices are found to detrain excess rotational fluid into a trailing vortex tail. This behaviour is found to be in agreement with previous results for Hill’s spherical vortex, as well as with observations of pinch-off of experimentally generated vortex rings at long formation times. In contrast, the detrainment of circulation that is characteristic of pinch-off is not observed for Pierrehumbert vortex pairs of any core size. These observations are in agreement with recent studies that contrast the formation of vortices in two and three dimensions. We hypothesize that transitions in vortex formation, such as those occurring between wake shedding modes and in vortex pinch-off more generally, might be understood and possibly predicted based on the observed perturbation responses of forming vortex rings or dipoles.

The formation of ‘optimal’ vortex rings, and the efficiency of propulsion devices

2001 ◽  
Vol 427 ◽  
pp. 61-72 ◽  
Author(s):  
P. F. LINDEN ◽  
J. S. TURNER
Keyword(s):  
Energy Input ◽  
Physical Mechanism ◽  
Vortex Rings ◽  
The Core ◽  
Aspect Ratios ◽  
Axisymmetric Vortex ◽  
Single Ring ◽  
Spherical Vortex ◽  
Limiting Case ◽  
Limiting Value

The formation of an axisymmetric vortex ring by forcing uid impulsively through a pipe is examined. An idealized model of the circulation, impulse and energy provided by the injected plug is developed, and these quantities are equated to the corresponding properties of the class of rings with finite cores described by Norbury (1973). It is shown that, as the length-to-diameter aspect ratio L/D of the plug increases, the size of the core increases in comparison with all the fluid carried along with the ring, until the limiting case of Hill's spherical vortex is reached. For aspect ratios larger than a certain value it is not possible to produce a single ring while conserving circulation, impulse, volume and energy. This implies that the limiting vortex is ‘optimal’ in the sense that it has maximum impulse, circulation and volume for a given energy input. While this matching calculation makes the physical mechanism clear, the L/D ratio that can be achieved in practice is more appropriately taken from the direct experimental measurements of Gharib et al. (1998) who concluded that the limiting value is L/D = 4. This is close to the value found in our calculation.

Examples of steady vortex rings of small cross-section in an ideal fluid

1972 ◽  
Vol 51 (1) ◽  
pp. 119-135 ◽  
Author(s):  
L. E. Fraenkel
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Existence Theory ◽  
Vortex Rings ◽  
Small Cross Section ◽  
The Core ◽  
A Value ◽  
Asymptotic Formulae ◽  
Core Boundary ◽  
Two Parameter

The existence theory for steady vortex rings of small cross-section is used to derive asymptotic formulae that describe the shape and overall properties of such rings. A certain two-parameter family of rings is studied in detail, to a first approximation; for members of this family, the ratio ω/r(of vorticity to cylindrical radius) falls from a positive maximum at a central point of the core cross-section to a value at the core boundary that can be substantially smaller or even negative. The case of uniform ω/ris considered to a higher order of approximation, and the formulae given for this case appear to be useful for quite substantial cross-sections.

On steady vortex rings of small cross-section in an ideal fluid

1970 ◽  
Vol 316 (1524) ◽  
pp. 29-62 ◽  
Keyword(s):  
Cross Section ◽  
Propagation Speed ◽  
Vortex Rings ◽  
Uniform Density ◽  
Inviscid Fluid ◽  
Small Cross Section ◽  
Cross Sectional ◽  
The Core ◽  
Ring Radius ◽  
Explicit Formulae

This paper is concerned with vortex rings, in an unbounded inviscid fluid of uniform density, that move without change of form and with constant velocity when the fluid at infinity is at rest. The work is restricted to rings whose cross-sectional area is small relative to the square of a mean ring radius. An existence theorem is proved for distributions of vorticity in the core that are arbitrary, apart from the condition imposed by the equation of motion and certain smoothness requirements. The method of proof relies on the nearly plane, or two-dimensional, nature of the flow in the neighbourhood of a small cross-section, and leads to approximate but explicit formulae for the propagation speed and shape of the vortex rings in question.

Some steady axisymmetric vortex flows past a sphere

2001 ◽  
Vol 433 ◽  
pp. 315-328 ◽  
Author(s):  
ALAN ELCRAT ◽  
BENGT FORNBERG ◽  
KENNETH MILLER
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stream Function ◽  
Vortex Rings ◽  
Vortex Flows ◽  
Partial Differential ◽  
Axisymmetric Vortex ◽  
Spherical Vortex ◽  
Attached Vortex ◽  
Vortex Tubes

Steady, inviscid, axisymmetric vortex flows past a sphere are obtained numerically as solutions of a partial differential equation for the stream function. The solutions found include vortex rings, bounded vortices attached to the sphere and infinite vortex tubes. Four families of attached vortices are described: vortex wakes behind the sphere, spherically annular vortices surrounding the spherical obstacle (which can be given analytically), bands of vorticity around the sphere and symmetric pairs of vortices fore and aft of the sphere. Each attached vortex leads to a one-parameter family of vortex rings, analogous to the connection between Hill's spherical vortex and the vortex rings of Norbury.

A steady vortex ring close to Hill's spherical vortex

1972 ◽  
Vol 72 (2) ◽  
pp. 253-284 ◽  
Author(s):  
J. Norbury
Keyword(s):  
Vortex Ring ◽  
Stream Surface ◽  
Approximate Description ◽  
The Core ◽  
Spherical Vortex ◽  
Axis Of Symmetry ◽  
Unbounded Fluid

AbstractThe existence of a steady vortex ring close to Hill's spherical vortex is established, and an approximate description of its boundary is given. The vorticity in the ring is proportional to the distance from the axis of symmetry. The core propagates steadily in an unbounded fluid at rest at infinity. The boundary of the vortex ring is close to an interior stream surface of Hill's vortex.

Exposure of protein VP7 on the surface of bluetongue virus

1990 ◽  
Vol 48 (3) ◽  
pp. 600-601
Author(s):  
A.D. Hyatt
Keyword(s):  
Bluetongue Virus ◽  
Structural Proteins ◽  
Major Constituent ◽  
Outer Coat ◽  
Virus Particles ◽  
Antibody Recognition ◽  
The Core ◽  
The Family ◽  
Electron Microscopical ◽  
Physical Accessibility

Bluetongue virus (BTV) is the type species os the genus orbivirus in the family Reoviridae. The virus has a fibrillar outer coat containing two major structural proteins VP2 and VP5 which surround an icosahedral core. The core contains two major proteins VP3 and VP7 and three minor proteins VP1, VP4 and VP6. Recent evidence has indicated that the core comprises a neucleoprotein center which is surrounded by two protein layers; VP7, a major constituent of capsomeres comprises the outer and VP3 the inner layer of the core . Antibodies to VP7 are currently used in enzyme-linked immunosorbant assays and immuno-electron microscopical (JEM) tests for the detection of BTV. The tests involve the antibody recognition of VP7 on virus particles. In an attempt to understand how complete viruses can interact with antibodies to VP7 various antibody types and methodologies were utilized to determine the physical accessibility of the core to the external environment.

The light-scattering Mueller matrices for Rayleigh and Rayleigh-Gans-Debye approximation

1990 ◽  
Vol 55 (12) ◽  
pp. 2889-2897
Author(s):  
Jaroslav Holoubek
Keyword(s):  
Light Scattering ◽  
Theoretical Work ◽  
Matrix Elements ◽  
Elastic Light Scattering ◽  
Yield Information ◽  
Recent Theoretical Work ◽  
Particle Parameters ◽  
Complete Set ◽  
Single Matrix ◽  
Scattering Matrix Elements

Recent theoretical work has shown that the complete set of polarized elastic light-scattering studies should yield information about scatterer structure that has so far hardly been utilized. We present here calculations of angular dependences of light-scattering matrix elements for spheres near the Rayleigh and Rayleigh-Gans-Debye limits. The significance of single matrix elements is documented on examples that show how different matrix elements respond to changes in particle parameters. It appears that in the small-particle limit (Rg/λ < 0.1) we do not loose much information by ignoring "large particle" observables.

‘To wise for a woman’

2018 ◽  
Author(s):  
Nicola Clark
Keyword(s):  
Marital Problems ◽  
The Core ◽  
The Family ◽  
Made In ◽  
The Way

While there were clear strategic aims in the way that marriages were made in the Howard dynasty during this period, the family was only unusual in that it operated at the very top of the aristocratic hierarchy and was therefore able to use marital alliances to successfully recover and bolster both status and finances. Where they were different, however, was in the experience of some of these women within marriage. By and large, the marriages made by and for members of the family, including women, seem to have been as successful as others of their class. However, three women close to the core of the dynasty experienced severe marital problems, even ‘failed’ marriages, almost simultaneously during the 1520s and 1530s. The records generated by these episodes tell us about the way in which the family operated as a whole, and the agency of women in this context, and this chapter therefore reconstructs these disputes for this purpose.

scholarly journals Magnetospheric Structure of Rotation-Powered Neutron Stars

1992 ◽  
Vol 128 ◽  
pp. 56-77 ◽  
Author(s):  
Jonathan Arons
Keyword(s):  
Radio Emission ◽  
Gamma Radiation ◽  
Heavy Ions ◽  
Theoretical Work ◽  
Future Research ◽  
Observational Constraints ◽  
Polar Caps ◽  
Recent Theoretical Work ◽  
Density Flow ◽  
Promising Avenue

AbstractI survey recent theoretical work on the structure of the magnetospheres of rotation-powered pulsars, within the observational constraints set by their observed spindown, their ability to power synchrotron nebulae and their ability to produce beamed collective radio emission, while putting only a small fraction of their energy into incoherent X- and gamma radiation. I find no single theory has yet given a consistent description of the magnetosphere, but I conclude that models based on a dense outflow of pairs from the polar caps, permeated by a lower density flow of heavy ions, are the most promising avenue for future research.

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