Local Energy Transfer Theory

Local Energy Transfer (LET) is a closure to the infinite hierarchy of moment equations which arise when one averages the Navier Stokes Equation. Mathematically, it is a form of "renormalized perturbation theory". It is, at present, the only Eulerian time-dependent closure to admit the Kolmogorov Spectrum as a solution in the limit of infinite Reynolds number.

The theory proposes that there exists an energy balance which is local in k-space (but not in x-space!). LET is then based on the premise that the turbulent response of a system can be determined via a propagator function which relates the correlation attatched to a wavenumber mode k to itself at a different time.

In essence, LET comprises a compact set of 3 integro-differential equations in 3 unknowns. These can be numerically solved to arbitrary accuracy to allow the time evolution of a turbulent system's energy spectrum to be determined.

LET has been applied to freely decaying, isotropic, homogeneous systems over a substantial range of Reynolds numbers and has continually produced compelling results which agree well with both experiments and a range of computer simulations.

Current research into LET in the group includes

• the parallelization of the LET numerical codes across a multi-processor CRAY machine to speed-up calculations and allow investigation of higher Reynolds number (and more computationally intensive) problems.
• the application of LET to stirred (and hence stationary) turbulence. The introduction of stirring forces introduces a new term into the governing equation, and this has to be incorporated into the existing numerical scheme.
• LET as a subgrid model for large eddy simulations (whereby a direct numerical simulation of the Navier Stokes equation is used to step out solutions for wavenumbers less than a certain cutoff value, and LET is employed to deal with the effects of wavenumbers above this cutoff).

Here you can see some example output from the LET code

• animation showing the free decay of an energy spectrum (33K)

1. Anthony Quinn
2. Alistair Young