Realizing turbulent statistics

Abstract

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.