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.

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.

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.

Vortex growth in jets

1970 ◽  
Vol 44 (1) ◽  
pp. 97-112 ◽  
Author(s):  
Gordon S. Beavers ◽  
Theodore A. Wilson
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Computer Experiments ◽  
Vortex Rings ◽  
Periodic Flow ◽  
Two Dimensional ◽  
Vortex Sheets ◽  
Vortex Pairs ◽  
Symmetric Pattern ◽  
Circular Orifice

Observations are reported on the growth of vortices in the vortex sheets bounding the jet emerging from a sharp-edged two-dimensional slit and from a sharp-edged circular orifice. A regular periodic flow is observed near the orifice for both configurations when the Reynolds number of the jet lies between about 500 and 3000. The two-dimensional jet produces a symmetric pattern of vortex pairs with a Strouhal number of 0·43. Vortex rings are formed in the circular jet with a Strouhal number of 0·63. Computer experiments show that a growing pair of vortices in two parallel vortex sheets produces a symmetric pattern of vortices upstream from the original disturbance.

Vortex formation out of two-dimensional orifices

2010 ◽  
Vol 655 ◽  
pp. 198-216 ◽  
Author(s):  
GIANNI PEDRIZZETTI
Keyword(s):  
Shear Layer ◽  
Formation Process ◽  
Vortex Formation ◽  
Formation Time ◽  
Inviscid Limit ◽  
Small Scale ◽  
Two Dimensional ◽  
Single Vortex ◽  
Vortex Model ◽  
Vortex Pairs

The understanding of the vortex formation process is currently driving a novel attempt to evaluate the performance of fluid dynamics in biological systems. The concept of formation time, developed for axially symmetric orifices, is here studied in two-dimensional flows for the generation of vortex pairs. The early stage of the formation process is studied with the single vortex model in the inviscid limit. Within this framework, the equation can be written in a universal form in terms of the formation time. The single vortex model properly represents the initial circular spiralling vortex sheet and its acceleration for self-induced motion. Then, an analysis is performed by numerical simulation of the two-dimensional Navier–Stokes equations to cope with the spatially extended vortex structure. The results do not show the pinch-off phenomenon previously reported for vortex rings. The two-dimensional vortex pair tends to a stably growing structure such that, while it translates and extends longitudinally, it remains connected to the sharp edge by a shear layer whose velocity is always about twice that of the leading vortex. At larger values of the Reynolds number the instability of the shear layer develops small-scale vortices capable of destabilizing the coherent vortex growth. The absence of a critical formation number for two-dimensional vortex pairs suggests further considerations for the development of concepts of optimal vortex formation from orifices with variable curvature or of a tapered shape.

scholarly journals Nested contour dynamics models for axisymmetric vortex rings and vortex wakes

2014 ◽  
Vol 748 ◽  
pp. 521-548 ◽  
Author(s):  
Clara O’Farrell ◽  
John O. Dabiri
Keyword(s):  
Vortex Formation ◽  
Computational Cost ◽  
Small Region ◽  
Two Dimensions ◽  
Vortex Rings ◽  
Contour Dynamics ◽  
Piston Cylinder ◽  
Axisymmetric Vortex ◽  
Contour Models ◽  
Perturbation Size

AbstractInviscid models for vortex rings and dipoles are constructed using nested patches of vorticity. These models constitute more realistic approximations to experimental vortex rings and dipoles than the single-contour models of Norbury and Pierrehumbert, and nested contour dynamics algorithms allow their simulation with low computational cost. In two dimensions, nested-contour models for the analytical Lamb dipole are constructed. In the axisymmetric case, a family of models for vortex rings generated by a piston–cylinder apparatus at different stroke ratios is constructed from experimental data. The perturbation response of this family is considered by the introduction of a small region of vorticity at the rear of the vortex, which mimics the addition of circulation to a growing vortex ring by a feeding shear layer. Model vortex rings are found to either accept the additional circulation or shed vorticity into a tail, depending on the perturbation size. A change in the behaviour of the model vortex rings is identified at a stroke ratio of three, when it is found that the maximum relative perturbation size vortex rings can accept becomes approximately constant. We hypothesise that this change in response is related to pinch-off, and that pinch-off might be understood and predicted based on the perturbation responses of model vortex rings. In particular, we suggest that a perturbation response-based framework can be useful in understanding vortex formation in biological flows.

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.

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.

‘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 BMS field theories and Weyl anomaly

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Arjun Bagchi ◽  
Sudipta Dutta ◽  
Kedar S. Kolekar ◽  
Punit Sharma
Keyword(s):  
Three Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Two Dimensional ◽  
Speed Of Light ◽  
Asymptotically Flat ◽  
Weyl Invariance ◽  
Flat Spacetimes ◽  
Liouville Action ◽  
Null Surfaces

Abstract Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier.

Dynamic Contrast-Enhanced MRI and Fractal Characteristics of Percolation Clusters in Two-Dimensional Tumor Blood Perfusion

1999 ◽  
Vol 121 (5) ◽  
pp. 480-486 ◽  
Author(s):  
O. I. Craciunescu ◽  
S. K. Das ◽  
S. T. Clegg
Keyword(s):  
Tumor Tissue ◽  
Blood Perfusion ◽  
Percolation Cluster ◽  
Three Dimensions ◽  
Invasion Percolation ◽  
Two Dimensional ◽  
Tumor Perfusion ◽  
Dynamic Contrast Enhanced ◽  
Contrast Enhanced ◽  
Fractal Characteristics

Dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool is used to study tumor tissue perfusion. The results are then analyzed using percolation models. Percolation cluster geometry is depicted using the wash-in component of MRI contrast signal intensity. Fractal characteristics are determined for each two-dimensional cluster. The invasion percolation model is used to describe the evolution of the tumor perfusion front. Although tumor perfusion can be depicted rigorously only in three dimensions, two-dimensional cases are used to validate the methodology. It is concluded that the blood perfusion in a two-dimensional tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. For all the cases studied, the front starts to grow from the periphery of the tumor (where the feeding vessel was assumed to lie) and continues to grow toward the center of the tumor, accounting for the well-documented perfused periphery and necrotic core of the tumor tissue.

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