Autoregressive models for quantification of time-averaging uncertainties in turbulent flows

Abstract

Autoregressive models (ARMs) can be powerful tools for quantifying uncertainty in the time averages of turbulent flow quantities. This is because ARMs are efficient estimators of the autocorrelation function (ACF) of statistically stationary turbulence processes. In this study, we demonstrate a method for order selection of ARMs that uses the integral timescale of turbulence. A crucial insight into the operating principles of the ARM in terms of the time span covered by the product of model order and spacing between samples is provided, which enables us to develop computationally efficient implementations of ARM-based uncertainty estimators. This approach facilitates the quantification of uncertainty in downsampled time series and on a series of autocorrelated batch means with minimal loss of accuracy. Furthermore, a method for estimating uncertainties in second-order moments using first-order uncertainties is discussed. These techniques are applied to the time series data of turbulent flow a) through a plane channel and b) over periodic hills. Additionally, we illustrate the potential of ARMs in generating synthetic turbulence time series. Our study presents autoregressive models as intuitive and powerful tools for turbulent flows, paving the way for further applications in the field.