A. Governing equations of the model up previous next
A.a. Atmospheric model

The model atmosphere are described by a two-dimensional version of the anelastic system of Ogura and Phillips (1962). The effect of planetary rotation is not considered.


(A.1), (A.2) are the horizontal and vertical component of equation of motion, respectively. (A.3) is the continuity equation and (A.4) is the thermodynamic equation. are horizontal, vertical and time coordinate, respectively. are horizontal and vertical wind velocity, and are potential temperature and nondimensional pressure function deviation from those of basic state, respectively. are density, potential temperature and temperature in basic state. is gravitational acceleration whose value is equal to 3.72 msec-2. is radiative heating (cooling) rate per unit mass, which is described in appendix A.d in detail. is heating rate per unit mass owing to dissipation of turbulent kinetic energy, which is given by turbulent parameterization. in equation (A.1) 〜 (A.4) represents the turbulent diffusion owing to subgrid scale turbulent mixing as follows.


K is turbulent diffusion coefficient which is calculated by (A.9) and (A.10).

The nondimensional pressure function and potential temperature are defined as follows.

where and are pressure and that in basic state, is reference pressure (= 7 hPa), , is specific heat of constant pressure per unit mass and is atmospheric gas constant per unit mass. The values of and are set to be those of CO2 (734.9 Jkg-1K-1, 189.0 Jkg-1K-1). The basic state atmospheric structure is calculated by using the hydrostatic equation and euation of state for ideal gas as follows.


The perturbation of nondimensional pressure function is diagnosed by using the following equation which is derived from (A.1) to (A.3)


A numerical simulation of thermal convection in the Martian lower atmosphere.
Odaka, Nakajima, Ishiwatari, Hayashi,   Nagare Multimedia 2001
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