A k-ε Turbulence Model for the Convective Atmosphere

A k-epsilon turbulence model for the stable atmosphere is extended for the convective atmosphere. The new model represents the buoyancy-induced increase in the kinetic energy and scale of eddies, and is consistent with the Monin-Obukhov similarity theory for convective atmospheric boundary layers (ABLs). After being incorporated into an ABL model with the Coriolis force, the model is tested by comparing the ABL model results with the Businger-Dyer (BD) relationship. ABL model simulations are carried out to reveal the sensitivity of the vertical wind profile to model parameters (e.g., the Obukhov length, friction velocity, and geostrophic wind). When the friction velocity is consistent with geostrophic wind speed (or the turbulence in the inner regime is in equilibrium with that in the outer regime), the modeled wind profile is close to the BD relationship near the ground surface. Otherwise, the modeled wind profile deviates from the BD relationship, resembling the hockey stick transition model.