The angular momentum equation for a finite element of a fluid: A new representation and application to turbulent modeling

• Published in: Physics of fluids (1994) 2002-08, Vol.14 (8), p.2673-2682
• Main Authors: Iovieno, M., Tordella, D.
• Format: Article
• Language: English
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.1485765

The equation for the intrinsic moment of momentum averaged over small volumes of linear dimension δ has been considered. A representation of it is given as an infinite sequence of independent equations using a series expansion in terms of δ 2 . The equations of different orders are obtained through linear antisymmetric operators—with a structure that is similar to that of the curl—acting on the momentum equation. The first-order term of the sequence is the Helmholtz equation; the remaining terms can be considered as balances for a kind of higher-orders vorticity. It has been shown that the coupling between the momentum and the angular momentum equation, based on a supposed antisymmetrical part of the stress tensor—which has sometimes been assumed by authors who deal with turbulent flow of a homogeneous fluid—is devoid of physical rationale. A different form of coupling is proposed that may be used to describe a turbulent flow of a homogeneous medium, using a large eddy simulation technique. In the authors model the coupling is given by a functional dependence of the turbulent eddy diffusivity over the angular momentum of a finite volume of a fluid.