## FP7 Marie Curie Re-Integration Grant 228389

rapid distortion theory

In the framework of Rapid distortion theory (RDT) the analysis of the linearized equations of motion is used to explain some of the significant kinematical and dynamical aspects of the statistical properties of the eddy structure of the turbulence. The theory is valid for all kinds of rapidly changing turbulent flows, when the distortion is applied for a time that is short compared to the “turn-over” time scales of the energy-containing eddies. RDT uses linearized equations to describe the changes to a given velocity field uo(x, t) when it is subject to a rapid distortion. The basic idea of RDT is that, if the strain or rotation rate is rapid enough, the Navier-Stokes equations can be approximated by their linearized form and then solved for the evolution of a single Fourier mode. When these equations are solved, ensemble averaging can be used to calculate the development of the energy spectrum tensor, two-point correlations and other statistical quantities of interest. The necessary requirement for the applicability of RDT on a flow field is that the time scale of the energy containing turbulence q^2/ε must be much larger than the time scales of the mean strain, S, or mean rotation, Ω. Therefore the non-linear terms in the governing turbulence equations involving products of fluctuation quantities are neglected, and so the RDT equations for the fluctuating quantities are linear. RDT is a closed theory for twopoint correlations or spectra, but the one-point governing equations are, in general, not closed due to the non-locality of the pressure fluctuations.

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