Composition of resolvents enhanced by random sweeping for large-scale structures in turbulent channel flows

A composition of sweeping-enhanced resolvents, referred to as the R²-model, is proposed to predict the space-time statistics of large-scale structures in turbulent channel flows. This model incorporates two key mechanisms: (i) eddy damping is introduced to represent random-sweeping decorrelation caused by nonlinear forcing, leading to a sweeping-enhanced resolvent R; and (ii) the sweeping-enhanced resolvent R² is composited into its iterations R² to yield nonvanishing Taylor time microscales. The resulting R²-model can correctly predict the frequency spectra and two-point cross-spectra of large-scale structures. This model is numerically compared with eddy-viscosity-enhanced resolvent models. The latter is designed to represent energy transfer instead for time decorrelation and thus under-predicts the characteristic decay timescales. The R²-model correctly yields the characteristic decay timescales over the channel.