scholarly journals Analysis of Steady Vortex Rings Using Contour Dynamics Method for the Stream Function

2020 ◽  
Vol 34 (2) ◽  
pp. 89-96
Author(s):  
Yoon-Rak Choi
Keyword(s):  
Stream Function ◽  
Vortex Rings ◽  
Contour Dynamics ◽  
Dynamics Method

Finite-core hetons: stability and interactions

2000 ◽  
Vol 423 ◽  
pp. 127-154 ◽  
Author(s):  
M. A. SOKOLOVSKIY ◽  
J. VERRON
Keyword(s):  
Parameter Space ◽  
The Other ◽  
Geometrical Parameters ◽  
Stationary States ◽  
Contour Dynamics ◽  
Surgery Technique ◽  
Special Case ◽  
Dynamics Method

The dynamics of vertically compensated two-layer vortices (hetons) with finite cores are examined within the context of the quasi-geostrophic approximation on the f-plane. The two-layer version of the contour dynamics method is used, and complemented by the so-called contour surgery technique. Special attention is paid to two-heton interactions when the initial locations of the vortex patches are symmetrical. A classification of the different regimes observed is made according to external parameters, namely geometrical parameters and stratification. In this parameter space, novel quasi-stationary states resulting from collisions between two hetons may be observed: (i) formation of a configuration consisting of two-layer vortices moving in opposite directions and, as a special case, a configuration analogous to the ‘klapstoss’ billiard shot, (ii) absorption of one heton by the other and subsequent movement of a new dipole, (iii) formation of two-layer dipoles, larger than the original hetons, associated with rotating peripheral satellite eddies in their wakes. Some of these results may have implications for the analysis of mesoscale vortices in the ocean.

On the existence of localized rotational disturbances which propagate without change of structure in an inviscid fluid

1986 ◽  
Vol 173 ◽  
pp. 289-302 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Euler Equations ◽  
Stream Function ◽  
Wide Class ◽  
Magnetic Relaxation ◽  
Topological Invariant ◽  
Vortex Rings ◽  
Inviscid Fluid ◽  
Arbitrary Signature ◽  
Axisymmetric Solutions ◽  
Uniform Stream

A wide class of solutions of the steady Euler equations, representing localized rotational disturbances imbedded in a uniform stream U0 is inferred by considering the process of magnetic relaxation to analogous magnetostatic equilibria. These solutions, which may be regarded as generalizations of vortex rings, are characterized by their streamline topology, distinct topologies giving rise to distinct solutions.Particular attention is paid to the class of axisymmetric solutions described by Stokes stream function ψ(s, z). It is argued that the appropriate topological ‘invariant’ characterizing the flow is the function Vψ representing the volume inside toroidal surfaces ψ = const, in the region of closed streamlines where ψ > 0. This function is described as the ‘signature’ of the flow, and it is shown that in a certain sense, flows with different signatures are topologically distinct. The approach yields a method by which flows of arbitrary signature V(ψ) may in principle be found, and the corresponding vorticity ωφ = sFψ calculated.

Simulation of the instability of axisymmetric vortices using the contour dynamics method

1985 ◽  
Vol 20 (1) ◽  
pp. 28-34 ◽  
Author(s):  
V. F. Kozlov ◽  
V. G. Makarov
Keyword(s):  
Contour Dynamics ◽  
Dynamics Method

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.

scholarly journals Axisymmetric contour dynamics for buoyant vortex rings

2020 ◽  
Vol 887 ◽  
Author(s):  
Ching Chang ◽  
Stefan G. Llewellyn Smith
Keyword(s):  
Vortex Rings ◽  
Contour Dynamics ◽  
Image Position ◽  
Buoyant Vortex Rings

scholarly journals Cyclostrophic vortices in polar regions of rotating planets

2001 ◽  
Vol 8 (4/5) ◽  
pp. 301-311 ◽  
Author(s):  
V. Goncharov ◽  
V. Pavlov
Keyword(s):  
Temperature Field ◽  
Time Dependent ◽  
Polar Regions ◽  
Two Dimensional ◽  
Contour Dynamics ◽  
Inviscid Incompressible Fluid ◽  
Stationary Observer ◽  
Contour Curvature ◽  
Dynamics Method

Abstract. Multi-petal, rotating vortices can form in two-dimensional flows consisting of an inviscid incompressible fluid under certain conditions. Such vortices are principally nonlinear thermo-hydrodynamical structures. The proper rotation of these structures which leads to time-dependent variations of the associated temperature field can be enregistred by a stationary observer. The problem is analyzed in the framework of the contour dynamics method (CDM). An analytical solution of the reduced equation for a contour curvature is found. We give a classification of the solutions and compare the obtained results with observational data.

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