Spectral analogue of the law of the wall

We use a recently-proposed spectral model (Gioia et al., PRL, 2010) of the Reynolds shear stress in smooth wall-bounded, uniform turbulent flows to derive a scaling relation for the turbulent energy spectra. This scaling relation is the spectral analogue of Prandtl's scaling relation for the mean velocity profiles (the ``law of the wall''). To test the scaling relation for the turbulent energy spectra, we use data from direct numerical simulations of channel flow.