Model-based spectral coherence analysis enhanced by scale-dependent eddy dissipation and anisotropic forcing terms

The eddy-viscosity enhanced linearized Navier-Stokes equations have been shown to capture the geometric scaling of wall-coherent structures in the logarithmic layer of turbulent wall-bounded flows. Together with a source of white- or colored-in-time stochastic excitation, the eddy-viscosity term is used to compensate for the absence of nonlinear terms and their role in the production and dissipation of energy among various scales of motion. In this work, we explore the efficacy of two recently proposed enhancements to theses classes of low-complexity models, namely, the entrainment of scale-dependence in the magnitude of the dissipation term and anisotropy in the stochastic forcing term. We show the benefits of using such models in capturing the energy spectrum of turbulent channel flow at different Reynolds numbers. We also show that while their resulting linear coherence spectrum fails to demonstrate the anticipated wall-distance scaling, it excels in extracting components of the energy spectra that are attributed to active self-similar motions. Our results support the utility of such enhancements as a computationally efficient alternative to the entrainment of colored-in-time stochastic forcing models in capturing the structural features of high-Reynolds number wall-bounded flows.