Reliable quantification of uncertainty in time averages of turbulence simulations*

Estimation of uncertainties in time-averaged quantities of turbulence simulations requires statistical tools that take into account the temporal correlation within the data. This is the key result in our validation of the commonly used uncertainty estimators for turbulence time averages i.e., batch-means methods and autoregressive model (ARM) based estimators. The validation enabled us to derive novel guidelines for the choice of the hyperparameters intrinsic to these methods, such as the batch size in the batch-means methods and the order of the ARM model, in terms of turbulence timescales. Our study also revealed that the ARM estimator could be made to retain information through the autocorrelation exactly up to a given point in time by the combination of the model order and covered time lag. This property preserved the accuracy of the estimator even upon downsampling or batching the time series, thereby allowing computationally efficient implementations. We also address the need for including expected values of nonlinear components in the uncertainty quantification (UQ) of higher-order statistics, an aspect often neglected in the UQ/turbulence literature. The UQ analyses are performed using the time series of turbulent channel and periodic hill flow.