SIMPLIFIED EQUATIONS FOR THE INTERACTION OF NEARLY PARALLEL VORTEX FILAMENTS

被引：81
作者：
KLEIN, R
MAJDA, AJ
DAMODARAN, K
机构：
[1] PRINCETON UNIV,DEPT MATH,PRINCETON,NJ 08544
[2] PRINCETON UNIV,PROGRAM APPL & COMPUTAT MATH,PRINCETON,NJ 08544
[3] UNIV CAMBRIDGE,DEPT APPL MATH & THEORET PHYS,CAMBRIDGE CB3 9EW,ENGLAND
来源：
JOURNAL OF FLUID MECHANICS | 1995年 / 288卷
关键词：
D O I：
10.1017/S0022112095001121
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
New simplified asymptotic equations for the interaction of nearly parallel vortex filaments are derived and analysed here. The simplified equations retain the important physical effects of linearized local self-induction and nonlinear potential vortex interaction among different vortices but neglect other non-local effects of self-stretching and mutual induction. These equations are derived systematically in a suitable distinguished asymptotic limit from the Navier-Stokes equations. The general Hamiltonian formalism and conserved quantities for the simplified equations are developed here. Properties of these asymptotic equations for the important special case involving nearly parallel pairs of interacting filaments are developed in detail. In particular, strong evidence is presented that for any filament pair with a negative circulation ratio, there is finite-time collapse in a self-similar fashion independent of the perturbation but with a structure depending on the circulation ratio. On the other hand, strong evidence is presented that no finite-time collapse is possible for perturbations of a filament pair with a positive circulation ratio. The present theory is also compared and contrasted with earlier linear and nonlinear stability analyses for pairs of filaments.
引用
收藏
页码：201 / 248
页数：48
相关论文
共 34 条
  • [21] KLEIN R., KNIO O.M., Asymptotic vorticity structure and numerical simulation of slender vortex filaments, J. Fluid Mech., 284, pp. 275-321, (1995)
  • [22] KLEIN R., MAJDA A., a Self-stretching of a perturbed vortex filament I. The asymptotic equations for deviations from a straight line, Physica, D 49, pp. 323-352, (1991)
  • [23] KLEIN R., MAJDA A., Self-stretching of perturbed vortex filaments II. Structure of solutions, Physica, D 53, pp. 267-294, (1991)
  • [24] KLEIN R., MAJDA A., An asymptotic theory for the nonlinear instability of anti-parallel pairs of vortex filaments, Phys. Fluids, A 5, pp. 369-387, (1993)
  • [25] KLEIN R., MAJDA A.J., MCLAUGHLIN R.M., Asymptotic equations for the stretching of vortex filaments in a background flow field, Phys. Fluids, A 4, pp. 2271-2281, (1992)
  • [26] LAMB H., Hydrodynamis, (1932)
  • [27] LOGAN J.D., Applied Mathematics - A Contemporary Approach., (1987)
  • [28] MELANDER M.V., ZABUSKY N., Interaction and Reconnection of Vortex Tubes via Direct Numerical Simulations, Proceedings IUTAM Symposium on Fundamental Aspects of Vortex Motion, (1987)
  • [29] MEIRON D., SHELLEY M., ASHURST W., ORSZAG S., Mathematical Aspects of Vortex Dynamics, pp. 183-194, (1989)
  • [30] MOORE D.W., SAFFMAN P.G., The motion of a vortex filament with axial flow, Phil. Trans. R. Soc. Lond., A 272, (1972)
1234