Standard logarithmic mean velocity distribution in a band-limited restricted nonlinear model of turbulent flow in a half-channel

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-K\'arm\'an 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.