3. Results: Dust-Free Case
3.d. Intensity of Convection (2): Conduction Layer The vertical gradient of potential temperature below approximately 50 m is in good agreement with that described by turbulent diffusion. where is heat flux. In evaluating Equation (2) , we have adopted ≈ 30 W m-2 which was obtained from the total amount of infrared radiative heating and sensible heat flux at around 12:00 LT. = 2×10-2 kg m-3, = 734.9 J kg-1 K-1, and $K$ = 15 m2 sec-1 were obtained from the turbulent diffusion coefficient calculated in our numerical model. The region below ~50 m in the thermal boundary layer can be referred to as the conduction layer. Provided that the temperature structure of the conduction layer is given by Equation (2), let us estimate the depth of conduction layer and potential temperature difference of the layer. The flux Rayleigh number of the conduction layer is given as where is thermal expansion coefficient, is gravitational acceleration, is temperature flux (), and are thermal diffusion coefficient and kinematic viscosity, respectively. Convective instability is expected to appear when the flux Rayleigh number exceeds the critical value. Supposing that $\kappa =\nu=K$ and , the depth of conduction layer can be estimated by using Equation (2) as According to linear stability analysis, the order of magnitude of the critical Rayleigh number for fixed heat flux boundary condition is 100 (Sasaki, 1970). Substituting this, we obtain ≈ 57 m, and from Equation (2), we have ≈ 8K. Although the values of conduction layer thickness and potential temperature difference at 14:00 LT shown in Figure. 7 ( < 50 m, ≈ 6K) are slightly smaller than those obtained above, they are fairly acceptable as order estimations.
A numerical simulation of thermal convection in the Martian lower atmosphere with a two-dimensional anelastic model