Model-based spectral coherence analysis for high-Reynolds number turbulent shear flows

We evaluate the predictive capability of the eddy-viscosity enhanced and data-enhanced variants of the stochastically forced linearized Navier-Stokes equations in capturing the geometric self-similarity of turbulent flow structures in high-Reynolds number channel flows. To this end, we use the linear coherence spectrum to quantify the wall-normal coherence of turbulent eddies, which is computed as the cross-correlation of the velocity field between two wall-normal locations normalized by the respective one-point correlations. The coherence spectrum can be used to construct spectral filters that decompose the energy spectrum of the inertial layer into contributions from wall-attached motions that are either self-similar or non-self-similar. We examine the ability of our model-based spectral filters in decomposing the energy spectrum and uncovering the inner-scaling of wall-attached self-similar motions at various Reynolds numbers. We also build on the wall-distance scaling of such spectral filters to propose analytical representations for their spectral parameterization. We demonstrate the Reynolds number independence of such parametric representations that can be leveraged for predicting coherent motions in higher Reynolds number flows.