Институт вычислительной математики и математической геофизики СОРАН

Тезисы докладов

Статистическое моделирование и методы Монте-Карло

A new geometric view of homogeneous isotropic turbulence is contemplated employing the two-point velocity correlation tensor of the velocity fluctuations. We show that this correlation tensor generates a family of pseudo-Riemannian metrics. This enables us to specify the geometry of a singled out Eulerian fluid volume in a statistical sense. We expose the relationship of some geometric constructions with statistical quantities arising in turbulence. Moreover, we investigate how terms of this family of pseudo-Riemannian metrics influence the length scales of turbulent motion and demonstrate that the action of the two-parametric scaling group admitted by the von Karman-Howarth equation in the limit of infinite Reynolds numbers and the one-parametric scaling group in the case of finite Reynolds numbers on the semi-reducible pseudo-Riemannian manifold constructed leads to the conformal invariance of the corresponding manifolds.

Примечание. Тезисы докладов публикуются в авторской редакции

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