We consider a wavy liquid film flow, which is partly laminar and partly turbulent. Such a situation may
occur for the large-amplitude solitary wave regime which develops at Reynolds numbers in the range
100 to 300, which corresponds precisely to the operational conditions of current chemical devices. We
propose to model the onset of turbulence by a simple eddy-viscosity formulation using the Van Driest
mixing length formula. A simplified two equation model is then derived within the framework of the
weighted residual method in terms of the local flow rate q(x, t) and the film thickness h(x, t). The model
is consistent with the asymptotic long-wave expansion, which guarantees that instability thresholds are
correctly captured, and accounts for surface tension and elongational viscosity. Each coefficient of
the model is a function of the local Reynolds number, |q(x, t)|/ν and has been tabulated numerically.
Preliminary comparisons to the experimental data by Brock [3] for roll waves in the full turbulent regime
prove to be satisfactory. In particular, the values of the coefficient of the Chezy law proposed to model
the wall shear stress using Brock's experiments are recovered without adjusting parameters.