A. Governing equations of the model   b. Turbulence parameterization
A.b.i. Subgrid turbulent mixing parameterization The turbulent diffusion coefficient is evaluated by using turbulent kinetic energy following Klemp and Wilhelmson (1978). The value of turbulent diffusion coefficient for heat is equal to that for momentum. The turbulence parameterization scheme presented by Klemp and Wilhelmson (1978) succeeds in representing subgrid scale turbulent mixing in numerical simulation of cumulus convection in the terrestrial atmosphere. We suppose that the turbulence parameterization can be applied for the turbulent in the Martian atmosphere. The prognostic equation of turbulent kinetic energy is as follows. . BP and SP are generation terms of the turbulent kinetic energy associated with buoyancy force and wind shear, respectively. where is the mixing length which is the smaller value of either vertical grid interval or altitude. The last term in left hand side of (A.9) represents the dissipation rate of turbulent kinetic energy. By using this term, in equation (A.4) is given as follows.
A numerical simulation of thermal convection in the Martian lower atmosphere.