Analysis of a stochastic backscatter model for the large-eddy simulation of wall-bounded flow

The stochastic backscatter model of Mason and Thomson (1992) has been analysed using direct numerical simulation databases of turbulent channel flow at Re δ =300. Backscatter is quantified using a number of different filters with cutoffs at wavenumbers corresponding to an inertial subrange at high Reynolds numbers. Since the model finds greatest application at meteorological Reynolds numbers, the implications of using low-Reynolds-number data are addressed. Probability distributions of the energy transfer obtained both directly from the DNS data and using the stochastic model are compared by matching the first moments and using a single tuneable constant to optimise agreement of the variances. It is found that the probability distributions essentially have the same shape, illustrating the model's ability to represent the backscatter correctly outside the viscous sublayer. However, the model consistently underestimates the non-Gaussian behaviour of the energy transfer and some suggestions have been made to remedy this. Probability distributions of the energy transfer conditional on the square of the resolved strain rate show that a range of values of transfer exist for one value of strain rate.