A. Governing equations of the model   b. Turbulence model
A.b.ii. Surface flux parameterization Surface momentum and heat fluxes are given by the bulk formulae of Louis (1979). The bulk coefficient for heat transport and momentum is equivalent. In this study, surface fluxes must be treated with care since diurnal change is taken into consideration and since focus is placed on the magnitude of surface stress estimated by the surface momentum flux. Surface fluxes significantly change with atmospheric stability. The surface flux parameterization presented by Louis (1979) can be used to easily represent the dependence of surface flux on atmospheric stability. are the horizontal wind and temperature at the lowest level of the model atmosphere . is the surface temperature. The bulk coefficient is calculated as follows. where, and is the Karman constant (= 0.35), is the roughness length. The roughness length is 1 cm ( Sutton et al., 1978). is the bulk Richardson number, which is given as follows. where are the potential temperature and horizontal mean potential temperature at the lowest level of the model atmosphere. is the potential temperature of ground surface (=).
A Numerical Simulation of Thermal Convection in the Martian Lower Atmosphere with a Two-Dimensional Anelastic Model