Vortices and boundaries
Authors:
S. J. Chapman, B. J. Hunton and J. R. Ockendon
Journal:
Quart. Appl. Math. 56 (1998), 507-519
MSC:
Primary 76B47; Secondary 76A25, 76D17, 82D55
DOI:
https://doi.org/10.1090/qam/1637052
MathSciNet review:
MR1637052
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Abstract: This paper develops a framework in which vortex/boundary interactions can be analysed for the cases of inviscid fluid dynamics and type II superconductors. Comments are made concerning the possibility of reconnection, defined as an interaction in which an initially single-component vortex eventually emerges with two components.
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M. V. Melander and F. Hussain, Cross-linking of two antiparallel vortex tubes, Phys. Fluids A1 (4), 633–636 (1989)
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E. D. Siggia and A. Pumir, Vortex dynamics and the existence of solutions to the Navier-Stokes equations, Phys. Fluids 30 (6), 1606–1626 (1987)
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V. E. Zakharov, Wave collapse, Usp. Fiz. Nauk. 155, 529–533 (1988)
W. T. Ashurst and D. I. Meiron, Numerical study of vortex reconnection, Phys. Rev. Lett. 58 (16), 1632–1635 (1987)
G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, 1967
L. P. Bernal and J. T. Kwon, Vortex ring dynamics beneath a free surface, Phys. Fluids A 1 (3), 449–451 (1989)
A. Callegari and L. Ting, Motion of a curved vortex filament with decaying vortical core and axial velocity, SIAM J. Appl. Math. 35 (1), 148–175 (1978)
S. J. Chapman and G. W. Richardson, Motion of vortices in type II superconductors, SIAM J. Appl. Math. 55 (5), 1275–1296 (1995)
W. Craig and B. J. Hunton, Modulated waves on a vortex filament beneath a fluid surface, Appl. Math. Lett. 8 (3), 7–11 (1995)
W. Craig, C. Sulem, and P. L. Sulem, Nonlinear modulation of gravity waves: A rigorous approach, Nonlinearity 6, 497–522 (1992)
S. C. Crow, Stability theory for a pair of trailing vortices, A.I.A.A.A. Journal 8 (12), 2172–2179 (1970)
H. Hasimoto, A soliton on a vortex filament, J. Fluid Mech. 51, 477–485 (1972)
J. P. Hirth and J. Lothe, Theory of Dislocations, second edition, John Wiley and Sons, New York, 1982
B. J. Hunton, Vortex Dynamics, D. Phil. thesis, Oxford University, 1994
A. S. Joseph and W. T. Tomasch, Experimental evidence for delayed entry of flux into a type II superconductor, Phys. Rev. Lett. 12 (9), 219–222 (1964)
R. M. Kerr, Evidence for a singularity of the three-dimensional, incompressible Euler equations, Phys. Fluids A5 (7), 1725–1746 (1993)
S. Kida and M. Takaoka, Bridging in vortex reconnection, Phys. Fluids 30 (10), 2911–2914 (1987)
R. Klein, A. J. Majda, and K. Damodaran, Simplified equations for the interaction of nearly parallel vortex filaments, J. Fluid Mech. 288, 201–248 (1995)
R. Klein and L. Ting, Theoretical and experimental studies of slender vortex filaments, Appl. Math. Lett. 8 (2), 45–50 (1995)
J. Koeplik and H. Levine, Vortex reconnection in superfluid helium, Phys. Rev. Lett. 71 (9), 1375–1378 (1993)
M. D. Kruskal and H. Segur, Asymptotics beyond all orders in a model of crystal growth, Stud. Appl. Math. 85, 129–181 (1991)
J. B. McLeod, private communication, 1995
D. I. Meiron, M. Shelley, W. T. Ashurst, and S. Orzsag, Numerical studies of vortex reconnection, in Mathematical Aspects of Vortex Dynamics, 1989, pp. 183–194
M. V. Melander and F. Hussain, Cross-linking of two antiparallel vortex tubes, Phys. Fluids A1 (4), 633–636 (1989)
D. W. Moore and P. G. Saffman, The motion of a vortex filament with axial flow, Phil. Trans. 272, 403–429 (1972)
P. G. Saffman, A model of vortex reconnection, J. Fluid Mech. 212, 395–402 (1990)
P. G. Saffman, Vortex Dynamics, Cambridge University Press, 1992
M. J. Shelley, D. I. Meiron, and S. A. Orszag, Dynamic aspects of vortex reconnection of perturbed anti-parallel vortex tubes, J. Fluid Mech. 246, 613–652 (1993)
E. D. Siggia, Collapse and amplification of a vortex filament, Phys. Fluids 28 (3), 794–805 (1985)
E. D. Siggia and A. Pumir, Vortex dynamics and the existence of solutions to the Navier-Stokes equations, Phys. Fluids 30 (6), 1606–1626 (1987)
J. G. Skifstead, Numerical treatment of line singularities for modelling a jet in a low speed cross flow. In: Analysis of a jet in a subsonic crosswind, NASA SP-218
L. Ting and R. Klein, Viscous Vortical Flows, Lecture Notes in Physics, Vol. 374, Springer-Verlag, Berlin, 1991
N. J. Zabusky and M. V. Melander, Three-dimensional vortex tube reconnection-morphology for orthogonally-offset tubes, Physica D 37, 555–562 (1989)
V. E. Zakharov, Wave collapse, Usp. Fiz. Nauk. 155, 529–533 (1988)
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Article copyright:
© Copyright 1998
American Mathematical Society