A simple spectral model for the modification of turbulence in flow over gentle hills

A model is presented which calculates the changes of the velocity variances and stress <(u'w')over bar> in flow over gentle isolated hills. At intermediate frequencies spectra of the velocity components are modified according to rapid distortion theory. At low frequencies spectral densities change in proportion to the square of the mean wind.

The inner and outer layer of the flow are distinguished. Streamline curvature effects are accounted for in the vertical velocity variance and the covariance. The sensitivity of the model to several parameters is investigated. Then, its results are compared with measurements of turbulent flow over various hills and an escarpment.

The model is able to simulate the structure of the modified variance and covariance fields although larger differences occur at individual positions. The calculated modified spectra compare well with observed spectra.