Modification of two-equation models to account for plant drag

A modification of the most popular two-equation (E-phi) models, taking into account the plant drag, is proposed. Here E is the turbulent kinetic energy (TKE) and phi is any of the following variables: El (product of E and the mixing length l), epsilon (dissipation rate of TKE), and omega (specific dissipation of TKE, omega = epsilon/E). The proposed modification is due to the fact that the model constants estimated experimentally for 'free-air' flow do not allow for adequate reconstruction of the ratio between the production and dissipation rates of TKE in the vegetation canopy and have to be adjusted. The modification is universal, i.e. of the same type for all E-phi models considered. The numerical experiments carried out for both homogeneous and heterogeneous plant canopies with E-phi models (and with the E-l model taken as a kind of reference) show that the modification performs well. They also suggest that E-epsilon and E-omega schemes are more promising than the E-El scheme for canopy flow simulation since they are not limited by the need to use a wall function. In addition, a new parameterization for enhanced dissipation within the plant canopy is derived. It minimizes the model sensitivity to C mu, the key parameter for two-equation schemes, and whose estimates unfortunately vary considerably from experiment to experiment. The comparison of results of new modified E-epsilon and E-omega models with observations from both field and wind-tunnel experiments shows that the proposed parameterization is quite robust. However, because of uncertainties with the turbulence Prandtl and Schmidt numbers for the E-epsilon model within the canopy, the E-omega model is recommended for future implementation, with the suggested modifications.