By L. Ting, R. Klein, O. M. Knio (auth.), E. Krause, K. Gersten (eds.)
The determination of the overall meeting of the foreign Union of Theoretical and utilized Mechanics to arrange a Symposium on Dynamics of narrow Vortices used to be greeted with nice enthusiasm. The attractiveness 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 supply. additionally the positioning of the symposium was once definitely selected: It used to be determined to carry the symposium on the RWTH Aachen, the place, years in the past, Theodore von Karman had labored on difficulties relating to these to be mentioned now anew. It used to be transparent from the start of the making plans, that the symposium might in simple terms be held within the von Karman-Auditorium ofthe Rheinisch-Westfalische Technische Hochschule Aachen, a construction named after him. The symposium was once together equipped through the editors of this quantity, strongly supported via the neighborhood organizing committee. The invites of the clinical committee introduced jointly scientists actively engaged in examine at the dynamics of narrow vortices. It was once 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 info for IUTAM Symposium on Dynamics of Slender Vortices: Proceedings of the IUTAM Symposium held in Aachen, Germany, 31 August – 3 September 1997
The leading order term in (11) with respect to A depends only on the local solution, i. , in the length scale A « I. This fact renders the analysis local, avoiding using the periodicity condition of s with period So = 0(£). In our asymptotic analysis, we treated In(l/ f) to be 0(1). If 1/ In(l/ f) is treated as the small parameter A, then the leading term in (11) is b[fx:/41l']ln(l/f), depend- ASYMPTOTIC THEORY 19 ing only on the local geometry of C. Thus a simple theory for small amplitude short wavelength distortion of a nearly straight filament was obtained (Klein & Majda, (1991)), generalizing the analysis of Hasimoto (1972).
Interaction of three coaxial vortex rings. Initial configuration is coplanar. special cases of the interaction problems. In general, the problem depends on six parameters, or initial data, for example, Rj, Zj and r j , j 2,3, with ZI 0 and RI = £ = 1 and r l = 1. In addition there are three parameters, the initial core sizes, assuming that the cores have similarity profiles. We need some guidance in the selection or classification of the initial data in order to begin a systematic numerical investigation of the interaction problem.
267-294. , Majda, A. and Damodaran, K. (1995) Simplified Equations for the Interaction of Nearly Parallel Vortex Filaments, J. , 288, pp. 201-248. Klein, R. and Ting, L, (1992) Vortex Filament with Axial Core Structure Variation, Appl. Math. Letters, 5, pp. 99-103. Klein, R. and Ting, L. (1995) Theoretical and Experimental Studies of Slender Vortex Filaments, Appl. Math. Letters, 8, pp. 45-50. Kleinstein, G. and Ting, L. (1971) Optimum Solutions for Heat Conduction Problems, ZaMM, 51, pp. 1-16.
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.)