Turbulence modeling near the free surface in an open channel flow

The velocity data from a direct numerical simulation of low Reynolds number turbulence in an open channel have been used to compute the terms in the budget equations for the turbulence kinetic energy, the dissipation of turbulence kinetic energy and the Reynolds stresses. The budget data show that the dissipation rates of the horizontal components of the turbulence are reduced near the surface while the dissipation of the vertical component remains approximately constant. The data also show that the pressure-strain term is the dominant producing term for the spanwise component of energy in the near surface region. A model for this behavior valid for flows exhibiting homogeneity in the spanwise and streamwise directions is proposed and tested against the data. In general the model is found to work well but wider testing is necessary.