Title:

Local energy transfer theory in forced and decaying isotropic turbulence

In mathematical analyses of the turbulence phenomenon, averaging the governing equation of fluid flow leads to an impasse at which the number of equations is outweighed by the number of unknowns. This difficulty is often described as the 'closure problem'. A 'closure hypothesis' is an additional ingredient, typically comprising a set of mathematical assumptions based on some physical insights. This is artificially introduced into the problem an extra relation, and hence match the number of equations and unknowns. Many such closure hypotheses have been proposed and range from simple empirical rules to complex mathematical treatments. The 'Local Energy Transfer' (LET) theory [W. D. McComb, M. J. Filipiak and V. Shanmugasundaram, J. Fluid Mech, 245, 279 (1992)] is a closure hypothesis based on renormalized perturbation theory (RPT). This theory has enjoyed much success in predicting the behaviour of freely decaying, isotropic, homogeneous turbulence. LET is the only timedependent Eulerian RPT closure which is compatible with Kolmogorov's k^{} ^{5}/_{3} law. In this research, we begin by reviewing the mathematical background of turbulence theory. We then consider the derivation of LET, surveying the evolution of the theory and its relation with other RPT closure hypotheses. Computer software for numerically solving the LET equations is then developed and tested. This is used to generate quantitative forecasts for the behaviour of freely decaying turbulent flows. To investigate the accuracy of these predictions, comprehensive, detailed, purposerun comparisons between LET output and Direct Numerical Simulation (DNS) data are performed for the first time. These demonstrate that LET theory can provide reasonably accurate numerical estimates for the time evolution of a range of spectral measures and integral parameters in freely decaying turbulence.
