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.

scholarly journals Pinch-off of non-axisymmetric vortex rings

2014 ◽  
Vol 740 ◽  
pp. 61-96 ◽  
Author(s):  
Clara O’Farrell ◽  
John O. Dabiri
Keyword(s):  
Aspect Ratio ◽  
Vortex Rings ◽  
Equivalent Diameter ◽  
Local Curvature ◽  
Cross Sectional ◽  
Piston Cylinder ◽  
Circular Arcs ◽  
Axisymmetric Vortex ◽  
Formation Number ◽  
Nozzle Geometries

AbstractThe formation and pinch-off of non-axisymmetric vortex rings is considered experimentally. Vortex rings are generated using a non-circular piston–cylinder arrangement, and the resulting velocity fields are measured using digital particle image velocimetry. Three different nozzle geometries are considered: an elliptical nozzle with an aspect ratio of two, an elliptical nozzle with an aspect ratio of four and an oval nozzle constructed from tangent circular arcs. The formation of vortices from the three nozzles is analysed by means of the vorticity and circulation, as well as by investigation of the Lagrangian coherent structures in the flow. The results indicate that, in all three nozzles, the maximum circulation the vortex can attain is determined by the equivalent diameter of the nozzle: the diameter of a circular nozzle of identical cross-sectional area. In addition, the time at which the vortex rings pinch off is found to be constant along the nozzle contours, and independent of relative variations in the local curvature. A formation number for this class of vortex rings is defined based on the equivalent diameter of the nozzle, and the formation number for vortex rings of the three geometries considered is found to lie in the range of 3–4. The implications of the relative shape and local curvature independence of the formation number on the study and modelling of naturally occurring vortex rings such as those that appear in biological flows is discussed.

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.

Navier-Stokes simulations of axisymmetric vortex rings

1988 ◽  
Author(s):  
S. STANAWAY ◽  
B. CANTWELL ◽  
P. SPALART
Keyword(s):  
Navier Stokes ◽  
Vortex Rings ◽  
Axisymmetric Vortex

Joint inversion of seismic traveltime and frequency-domain airborne electromagnetic data for hydrocarbon exploration

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. U9-U22 ◽  
Author(s):  
Jide Nosakare Ogunbo ◽  
Guy Marquis ◽  
Jie Zhang ◽  
Weizhong Wang
Keyword(s):  
Frequency Domain ◽  
Joint Inversion ◽  
Sedimentary Environment ◽  
Computational Cost ◽  
Velocity Model ◽  
Two Dimensions ◽  
Hydrocarbon Exploration ◽  
Three Dimensions ◽  
Data Sets ◽  
The One

Geophysical joint inversion requires the setting of a few parameters for optimum performance of the process. However, there are yet no known detailed procedures for selecting the various parameters for performing the joint inversion. Previous works on the joint inversion of electromagnetic (EM) and seismic data have reported parameter applications for data sets acquired from the same dimensional geometry (either in two dimensions or three dimensions) and few on variant geometry. But none has discussed the parameter selections for the joint inversion of methods from variant geometry (for example, a 2D seismic travel and pseudo-2D frequency-domain EM data). With the advantage of affordable computational cost and the sufficient approximation of a 1D EM model in a horizontally layered sedimentary environment, we are able to set optimum joint inversion parameters to perform structurally constrained joint 2D seismic traveltime and pseudo-2D EM data for hydrocarbon exploration. From the synthetic experiments, even in the presence of noise, we are able to prescribe the rules for optimum parameter setting for the joint inversion, including the choice of initial model and the cross-gradient weighting. We apply these rules on field data to reconstruct a more reliable subsurface velocity model than the one obtained by the traveltime inversions alone. We expect that this approach will be useful for performing joint inversion of the seismic traveltime and frequency-domain EM data for the production of hydrocarbon.

Vortex rings and plasma toroidal vortices in homogeneous unbounded media. II. The study of vortex formation process

2011 ◽  
Vol 38 (9) ◽  
pp. 275-282 ◽  
Author(s):  
U. Yusupaliev ◽  
N. P. Savenkova ◽  
Yu. V. Troshchiev ◽  
S. A. Shuteev ◽  
S. A. Skladchikov ◽  
...  
Keyword(s):  
Formation Process ◽  
Vortex Formation ◽  
Vortex Rings ◽  
Toroidal Vortices ◽  
Unbounded Media

scholarly journals Circulation and formation number of laminar vortex rings

1998 ◽  
Vol 376 ◽  
pp. 297-318 ◽  
Author(s):  
MOSHE ROSENFELD ◽  
EDMOND RAMBOD ◽  
MORTEZA GHARIB
Keyword(s):  
Velocity Profile ◽  
Time Scale ◽  
Vortex Generator ◽  
Formation Time ◽  
Vortex Rings ◽  
Axisymmetric Vortex ◽  
Parabolic Velocity Profile ◽  
Formation Number ◽  
Experimental Findings ◽  
Good Agreement

The formation time scale of axisymmetric vortex rings is studied numerically for relatively long discharge times. Experimental findings on the existence and universality of a formation time scale, referred to as the ‘formation number’, are confirmed. The formation number is indicative of the time at which a vortex ring acquires its maximal circulation. For vortex rings generated by impulsive motion of a piston, the formation number was found to be approximately four, in very good agreement with experimental results. Numerical extensions of the experimental study to other cases, including cases with thick shear layers, show that the scaled circulation of the pinched-off vortex is relatively insensitive to the details of the formation process, such as the velocity programme, velocity profile, vortex generator geometry and the Reynolds number. This finding might also indicate that the properly scaled circulation of steady vortex rings varies very little. The formation number does depend on the velocity profile. Non-impulsive velocity programmes slightly increase the formation number, while non-uniform velocity profiles may decrease it significantly. In the case of a parabolic velocity profile of the discharged flow, for example, the formation number decreases by a factor as large as four. These findings indicate that a major source of the experimentally found small variations in the formation number is the different evolution of the velocity profile of the discharged flow.

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 Advective balance in pipe-formed vortex rings

2017 ◽  
Vol 836 ◽  
pp. 773-796
Author(s):  
Karim Shariff ◽  
Paul S. Krueger
Keyword(s):  
Reynolds Numbers ◽  
Vortex Rings ◽  
Quadratic Term ◽  
Axisymmetric Vortex ◽  
Order Of Magnitude ◽  
Cylindrical Diffusion ◽  
Type Boundary ◽  
The One ◽  
Type Boundary Condition ◽  
Edge Layer

Vorticity distributions in axisymmetric vortex rings produced by a piston–pipe apparatus are numerically studied over a range of Reynolds numbers, $Re$, and stroke-to-diameter ratios, $L/D$. It is found that a state of advective balance, such that $\unicode[STIX]{x1D701}\equiv \unicode[STIX]{x1D714}_{\unicode[STIX]{x1D719}}/r\approx F(\unicode[STIX]{x1D713},t)$, is achieved within the region (called the vortex ring bubble) enclosed by the dividing streamline. Here $\unicode[STIX]{x1D701}\equiv \unicode[STIX]{x1D714}_{\unicode[STIX]{x1D719}}/r$ is the ratio of azimuthal vorticity to cylindrical radius, and $\unicode[STIX]{x1D713}$ is the Stokes streamfunction in the frame of the ring. Some, but not all, of the $Re$ dependence in the time evolution of $F(\unicode[STIX]{x1D713},t)$ can be captured by introducing a scaled time $\unicode[STIX]{x1D70F}=\unicode[STIX]{x1D708}t$, where $\unicode[STIX]{x1D708}$ is the kinematic viscosity. When $\unicode[STIX]{x1D708}t/D^{2}\gtrsim 0.02$, the shape of $F(\unicode[STIX]{x1D713})$ is dominated by the linear-in-$\unicode[STIX]{x1D713}$ component, the coefficient of the quadratic term being an order of magnitude smaller. An important feature is that, as the dividing streamline ($\unicode[STIX]{x1D713}=0$) is approached, $F(\unicode[STIX]{x1D713})$ tends to a non-zero intercept which exhibits an extra $Re$ dependence. This and other features are explained by a simple toy model consisting of the one-dimensional cylindrical diffusion equation. The key ingredient in the model responsible for the extra $Re$ dependence is a Robin-type boundary condition, similar to Newton’s law of cooling, that accounts for the edge layer at the dividing streamline.

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