Инд. авторы:	Grebenev V.N., Oberlack M.
Заглавие:	A geometric interpretation of the second-order structure function arising in turbulence
Библ. ссылка:	Grebenev V.N., Oberlack M. A geometric interpretation of the second-order structure function arising in turbulence // Mathematical Physics, Analysis and Geometry. - 2009. - Vol.12. - Iss. 1. - P.1-18. - ISSN 1385-0172. - EISSN 1572-9656.
Внешние системы:	DOI: 10.1007/s11040-008-9049-4; РИНЦ: 13609505; SCOPUS: 2-s2.0-61349127806; WoS: 000263419300001;
Реферат:	eng: We primarily deal with homogeneous isotropic turbulence and use a closure model for the von Karman-Howarth equation to study several geometric properties of turbulent fluid dynamics. We focus our attention on the application of Riemannian geometry methods in turbulence. Some advantage of this approach consists in exploring the specific form of a closure model for the von Karman-Howarth equation that enables to equip a model manifold (a cylindrical domain in the correlation space) by a family of inner metrics (length scales of turbulent motion) which depends on time. We show that for large Reynolds numbers (in the limit of large Reynolds numbers) the radius of this manifold can be evaluated in terms of the second-order structure function and the correlation distance. This model manifold presents a shrinking cylindrical domain as time evolves. This result is derived by using a selfsimilar solution of the closure model for the von Karman-Howarth equation under consideration. We demonstrate that in the new variables the selfsimilar solution obtained coincides with the element of Beltrami surface (or pseudo-sphere): a canonical surface of the constant sectional curvature equals -aEuro parts per thousand 1.
Издано:	Springer, 2009
Физ. характеристика:	с.1-18