  Motivated by the need to characterize the spatio-temporal structure of
turbulence in wall-bounded flows, we study wavenumber-frequency spectra of the
streamwise velocity component based on large-eddy simulation (LES) data. The
LES data are used to measure spectra as a function of the two wall-parallel
wavenumbers and the frequency in the equilibrium (logarithmic) layer. We then
reformulate one of the simplest models that is able to reproduce the
observations: the random sweeping model with a Gaussian large-scale fluctuating
velocity and with additional mean flow. Comparison with LES data shows that the
model captures the observed temporal decorrelation, which is related to the
Doppler broadening of frequencies. We furthermore introduce a parameterization
for the entire wavenumber-frequency spectrum $E_{11}(k_1,k_2,\omega;z)$, where
$k_1$, $k_2$ are the streamwise and spanwise wavenumbers, $\omega$ is the
frequency and $z$ is the distance to the wall. The results are found to be in
good agreement with LES data.

Fluid Dynamics