Инд. авторы:	Grebenev V.N., Oberlack M.
Заглавие:	A geometry of the correlation space and a nonlocal degenerate parabolic equation from isotropic turbulence
Библ. ссылка:	Grebenev V.N., Oberlack M. A geometry of the correlation space and a nonlocal degenerate parabolic equation from isotropic turbulence // ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. - 2012. - Vol.92. - Iss. 3. - P.179-195. - ISSN 0044-2267. - EISSN 1521-4001.
Внешние системы:	DOI: 10.1002/zamm.201100021; РИНЦ: 17976539; SCOPUS: 2-s2.0-84856827783; WoS: 000300425200004;
Реферат:	eng: Considering the metric tensor ds2(t), associated with the two-point velocity correlation tensor field (parametrized by the time variable t) in the space kappa 3of correlation vectors, at the first part of the paper we construct the Lagrangian system (Mt,ds2(t)) in the extended space kappa(3) x R+ for homogeneous isotropic turbulence. This allows to introduce into the consideration common concept and technics of Lagrangian mechanics for the application in turbulence. Dynamics in time of (Mt,ds2(t)) (a singled out fluid volume equipped with a family of pseudo-Riemannian metrics) is described in the frame of the geometry generated by the 1-parameter family of metrics ds2(t) whose components are the correlation functions that evolve according to the von Karman-Howarth equation. This is the first step one needs to get in a future analysis the physical realization of the evolution of this volume. It means that we have to construct isometric embedding of the manifold Mt equipped with metric ds2(t) into R3 with the Euclidean metric. In order to specify the correlation functions, at the second part of this paper we study in details an initial-boundary value problem to the closure model [19,26] for the von Karman-Howarth equation in the case of large Reynolds numbers limit.
Издано:	2012
Физ. характеристика:	с.179-195