By L. Ting, R. Klein, O. M. Knio (auth.), E. Krause, K. Gersten (eds.)
The selection of the overall meeting of the foreign Union of Theoretical and utilized Mechanics to arrange a Symposium on Dynamics of slim Vortices used to be greeted with nice enthusiasm. The popularity of the notion, forwarded by means of the Deutsches Komitee fiir Mechanik (DEKOMECH) signalized, that there has been a necessity for discussing the subject selected within the body the IUTAM Symposia provide. additionally the site of the symposium used to be definitely selected: It was once determined to carry the symposium on the RWTH Aachen, the place, years in the past, Theodore von Karman had labored on difficulties with regards to these to be mentioned now anew. It was once transparent from the start of the making plans, that the symposium might purely be held within the von Karman-Auditorium ofthe Rheinisch-Westfalische Technische Hochschule Aachen, a construction named after him. The symposium was once together geared up through the editors of this quantity, strongly supported by way of the neighborhood organizing committee. The invites of the clinical committee introduced jointly scientists actively engaged in examine at the dynamics of narrow vortices. It used to be the purpose of the committee to have the cutting-edge summarized and in addition to have the newest result of particular difficulties investigated communicated to the contributors of the symposium. the subjects selected have been asymptotic theories, numerical equipment, vor tices in shear layers, interplay of vortices, vortex breakdown, vortex sound, and plane and helicopter vortices.
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Additional resources for IUTAM Symposium on Dynamics of Slender Vortices: Proceedings of the IUTAM Symposium held in Aachen, Germany, 31 August – 3 September 1997
1018~1027. Klein, R. and Knio, O. M. (1995) Asymptotic vorticity structure and numerical simulation of slender vortex filaments, 1. Fluid Meeh. 284, pp. 275~321. Klein, R. and Majda, A. J. (1991) Self-stretching of a perturbed vortex filament. I. The asymptotic equation for deviations from a straight line, Physiea D 49, pp. 323~352. Moffatt, H. , and Ohkitani, K (1994) Stretched vortices ~ the sinews of turbulence; large-Reynolds-number asymptotics, J. Fluid Meeh. 259, pp. 241~264. Moore, D. W.
33) (Widnall et al. 1971). However a difficulty arises when the discrete distribution is replaced by a continuous one, because the continuity condition is no longer of help. To make matters worse, both cg> and c~~) admit arbitrary time dependence as long as we stick to the matching condition (30). This is true also for the discrete model, and therefore (33) is merely one possibility. MOTION OF A VISCOUS VORTEX RING 29 We can show that cW and cW serve as the parameters placing the circular core in the moving frame, to an accuracy of O(t) in terms of the inner spatial scale.
K. MOFFATT flow which decays rapidly with distance from the core center. Thus we are led to inner and outer expansions (Tung and Ting 1967). The inner region has length scale of order the core radius ~ and there we seek the solution of the Navier-Stokes equations matched to the outer solution given by (6). It is expedient to choose a coordinate frame moving with the core center (R(t), Z(t)) in which we introduce local cylindrical coordinates (r,9) such that p = R(t) z = Z(t) + rsin9. + rcos9, (7) Introduce dimensionless variables: r* = r/Ello, = = = (/ Rff2' t* t/~ '.
IUTAM Symposium on Dynamics of Slender Vortices: Proceedings of the IUTAM Symposium held in Aachen, Germany, 31 August – 3 September 1997 by L. Ting, R. Klein, O. M. Knio (auth.), E. Krause, K. Gersten (eds.)