Realizing turbulent statistics

How to design an artificial inflow condition in simulations of the Navier-Stokes equation that is already fully turbulent? This is the turbulent inflow problem. This first question is followed by: How much of the true turbulence must be reproduced at the inflow? We present a technique able to produce a random field with the exact two-point two-time covariance of a given reference turbulent flow. It is obtained as the output of a linear filter fed with white noise. The method is illustrated on the simulation of a turbulent free shear layer. The filter coefficients are obtained from the solution of the Yule-Walker equation, and the computation can be performed efficiently using a recursive solution procedure. The method should also be useful in the study of flow receptivity, when the processes of transition to turbulence are sensitive to the perturbation environment.