Characterizing Energy Transfer in Restricted Nonlinear Wall-Bounded Turbulence

The computational expense of resolving all scales of turbulence in wall-bounded flows is impractical for engineering applications, prompting the development of reduced-order models. Numerical and experimental evidence showing the existence of structures elongated in the streamwise direction of turbulent shear flows motivates the exploration of a streamwise coherent modeling framework. The restricted nonlinear (RNL) modeling paradigm takes such an approach by omitting the streamwise varying part of the perturbation-perturbation nonlinearity in the Navier-Stokes equations, thereby reducing the number of active streamwise Fourier modes in order to reduce computational cost. This model has shown promise in reproducing first- and second-order statistics with as few as one nonzero streamwise mode. Despite the promise of this approach, certain aspects of the dynamics have yet to be fully understood. Here we focus on the production, dissipation, and transport of energy on these restricted modes. Spectra and energy budgets from the RNL system supported by its natural set and selected set of streamwise modes are compared to DNS data in the low-to-moderate Reynolds number range.