A stochastic dynamic model for space-time energy spectra in turbulent shear flows

Space-time energy spectra describe the distribution of energy density over space and time scales, which are fundamental to studying dynamic coupling at spatial and temporal scales and turbulence-generated noise. We develop a dynamic autoregressive (DAR) random forcing model for space-time energy spectra in turbulent shear flows. This model includes the two essential mechanisms of statistical decorrelation: the convection proposed by Taylor's model and the random sweeping proposed by the Kraichnan-Tennekes model. The new development is that DAR random forcing is introduced to represent the random sweeping effect. The resulting model can correctly reproduce the convection velocity and spectral bandwidths, while a white-in-time random forcing model makes erroneous predictions on spectral bandwidths. The DAR model is further combined with linear stochastic estimation (LSE) to reconstruct the near-wall velocity fluctuations of the desired space-time energy spectra. Direct numerical simulation (DNS) of turbulent channel flows is used to validate the DAR model and evaluate the Werner-Wengle wall model and the LSE approach. Both the wall model and LSE incorrectly estimate the spectral bandwidths.