An investigation of renormalization group methods in the study of fluid turbulence, and their development for large eddy simulations

• Main Author: Hunter, Adrian
• Published: University of Edinburgh 2000
• Subjects: 530.1
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.652736

Turbulence is a problem of chaotic motion involving many length and time scales. When the Navier-Stokes equation is Fourier transformed, it comes to resemble a many-body problem in statistical physics, and as such is amenable to treatment by the Renormalization Group (RG) to reduce the number of degrees of freedom. The work of this thesis builds upon the RG approach due to McComb and Watt [Phys. Rev. A 46, 4797 (1992)], referred to as Two-field theory. After presenting a brief introduction to turbulence in general and other theories, we review the Two-field approach. An extension of the idea of <i>conditional averaging, </i>central to Two-field theory, is made to the contrasting RG theory of Forster, Nelson and Stephen [Phys. Rev. A 16, 732 (1977)] to emphasize how it there addresses the question of deterministic connection of turbulent modes, resolving a long-standing criticism of that work relatively simple means. The results of Two-field theory, in the form of an eddy viscosity, are tested <i>a posteriori</i> in a high resolution large eddy simulation (LES) for the first time. The results are reviewed with the aim of pursuing further investigations into Two-field theory treatment of turbulent dynamics. In particular the effect of the cross-term <i>u^-u⁺</i> is important since Two-field theory deals with this term less well at the momentum equation level. These investigations are carried out by theoretical and numerical means. Theoretically, we try to account for some of the cross term by the use of graded spectral filtering within the RG procedure, which may have some relevance to work on graded filters used in the mixed modelling presented later. The results are also tested briefly in a numerical simulation.