Renormalization Methods Applied to Turbulence Theory
In these notes the turbulence problem is interpreted as one in many-body physics. We consider the many-body problem, along with the concept of renormalization, and show how the methods of renormalized perturbation theory have been applied to turbulence. Then a review and assessment of the two-point, two-time closures which arise from renormalized perturbation theory is given. After that, renormalization group is introduced as a more limited but potentially more rigorous way of applying perturbation methods to turbulence with particular relevance to the sub-grid modelling problem. We conclude with a brief discussion of the possible application of these methods to more realistic problems in shear flows.
KeywordsPartition Function Dissipation Rate Ising Model Isotropic Turbulence Perturbation Expansion
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- Allen, J. (1963). Formulation of the theory of turbulent shear flow. Ph.D. Dissertation, Victoria University of Manchester.Google Scholar
- Bertoglio, J.-P., and Jeandel, D. (1987). A simplified spectral closure for inhomogeneous turbulence applicable to the boundary layer. In Durst, F., ed., Turbulent Shear Flows 5, 323. Berlin: Springer-Verlag.Google Scholar
- Burden, A. D. (1991). Towards an EDQNM-Closure for inhomogeneous turbulence. In Johansson, A. V., and Alfredsson, P. H., eds., Advances in Turbulence 3, 387. Berlin: Springer-Verlag.Google Scholar
- Herring, J., and Kraichnan, R. (1972). Comparison of some approximations for isotropic turbulence Lecture Notes in Physics, volume 12. Springer, Berlin. chapter Statistical Models and Turbulence, 148.Google Scholar
- Johnston, C., and McComb, W. (2000). Renormalized expression for the turbulent energy dissipation rate. Phys. Rev E 63: 015304.Google Scholar
- Leslie, D. (1973). Developments in the theory of modern turbulence. Clarendon Press, Oxford.Google Scholar
- McComb, W. D., and Johnston, C. (1999). Conditional mode elimination with asymptotic freedom for isotropic turbulence at large Reynolds numbers. In Vassilicos, J., ed., Turbulence Structure and Vortex Dynamics, Proceedings of the Symposium at the Isaac Newton Institute Cambridge. CUP.Google Scholar
- McComb, W., Yang, T.-J., Young, A., and Machiels, L. (1997). Investigation of renormalization group methods for the numerical simulation of isotropic turbulence. In Proc. Eleventh Symposium on Turbulent Shear Flows.Google Scholar
- McComb, W. (1990). The Physics of Fluid Turbulence. Oxford University Press.Google Scholar
- Oberlack, M., McComb, W., and Quinn, A. (2001). Solution of functional equations and reduction of dimension in the local energy transfer theory of incompressible, three-dimensional turbulence. Phys. Rev. E 63: 026308–1.Google Scholar
- Quinn, A. P. (2000). Local Energy Transfer theory in forced and decaying isotropic turbulence. Ph.D. Dissertation, University of Edinburgh.Google Scholar
- Reichl, L. (1980). A modern course in statistical physics. Edward Arnold, London.Google Scholar