Vertical Mixing

Abstract

The distribution of constituents in a planetary atmosphere can be obtained by solving the continuity equation of the following form,

$$\frac{{d{\phi _i}}}{{dz}} = Pi - Li,$$

(4.1)

where P_i and L_i are respectively production and chemical loss rates per unit volume, and Ф_i is the vertical flux of the i^th constituent. Ф _i obeys the diffusion equation,

$${\phi _i} = {n_i}({w_D} + {w_K}),$$

(4.2)

where n _i is the number density of the constituent, and w_D and w_K are respectively its molecular and eddy diffusion velocities. The latter can be expressed in terms of the density and thermal gradients (Colegrove et al. 1966), so that

$${\phi _i} = {n_i}\left[ { - {D_i}\left( {\frac{1}{{{n_i}}}\frac{{d{n_i}}}{{dz}} + \frac{1}{{{H_i}}} + \frac{1}{T}\frac{{dT}}{{dz}}} \right) - K\left( {\frac{1}{{{n_i}}}\frac{{d{n_i}}}{{dz}} + \frac{1}{{{H_a}}} + \frac{1}{T}\frac{{dT}}{{dz}}} \right)} \right]$$

(4.3)

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