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Title: A study of the renormalization group as a model for large-eddy simulations of turbulence
Author: Johnston, Craig
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2000
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This thesis presents a Renormalization Group approach for the modelling of homogeneous, isotropic and statistically stationary turbulence. The general problem is described and, following a discussion of various alternative approaches, it is outlined in general how the Renormalization Group may be used to reduce the number of degrees of freedom needed to accurately describe turbulence. A critical discussion of the various Renormalization Group theories is then made before the new approach is introduced. This is based upon the two-field theory of McComb and Watt [Phys. Rev. A 46, 4797 (1992)], and in particular the idea of a formal conditional average [W. D. McComb, W. Roberts & A. G. Watt, Phys. Rev A 45, 3507 (1992)]. First, the formalism of the conditional average is redefined in terms of an ensemble of time-dependent realizations. This resolves one problem, present in the two-field theory, regarding the order in which operations are performed. Second, a hypothesis which enables us to split conditional averages into low and high wavenumber velocity modes is introduced and discussed. It is then shown how the conditional average and hypothesis may be used together to eliminate from the system a finite band of high wavenumber modes, the effects of the eliminated modes being represented by an enhanced viscosity acting upon the remaining scales. The mode elimination procedure is then used as the basis for a Renormalization Group calculation. This calculation is found to reach a fixed point, that is a point at which the equation of motion exhibits form-invariance under the Renormalization Group transformation. Using the effective viscosity at this fixed point, a value for the Kolmogorov constant of α » 1.62 is obtained.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available