Numerical simulations of wall-turbulence using the restricted nonlinear (RNL) model generate realistic mean velocity profiles in plane Couette and channel flow at low Reynolds numbers. The results are less accurate at higher Re, and while a logarithmic region is observed, its von-Kármán constant is not consistent with the standard logarithmic law. In half-channel flow we show that limiting the streamwise-varying wavenumber support of RNL turbulence to one or few empirically determined modes improves its predictions considerably. In particular, the mean velocity profiles obtained with the band-limited RNL model follow standard logarithmic behavior for the higher Reynolds numbers in this study.
A new approach to the reduced-order modeling of wind farms based on the recently formulated restricted nonlinear large eddy simulation (RNL-LES) framework is introduced. The approach has been shown to accurately reproduce mean flow distributions and turbulence statistics in wall-bounded flows at a fraction of the cost of traditional LES, making it a potentially attractive reduced-order model for studying wind farm behavior over a range of conditions. An appropriately altered version of the actuator disk turbine model is used to evaluate the ability of the RNL-LES framework to simulate very large wind farms in the fully developed regime through comparisons with the standard LES of wind farms under a variety of conditions. Then, the low computational cost of the RNL-LES approach is exploited to conduct a parametric study of several vertically staggered wind farm configurations.
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