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and thus Di varies with density as n. However, since K varies typically as n~0,5 it can be seen that, although K dominates at higher pressures in the homosphere, it increases more slowly with height than Dt and hence at some altitude for a given species, Dt becomes greater and dominates at all higher altitudes. It should thus be noted that the homopause level, where Di = K, is actually dependent on the molecule under consideration. For the giant planets, it is presumed that, unless stated otherwise, the word homopause refers to the methane homopause. The time constants for reaching diffusive equilibrium by the two processes are td = H 1a/Di and tk = H2alK, respectively, via reasoning introduced in Section 3.2.2.

The effect of eddy mixing on vertical profiles may be conveniently explained with the example of ammonia on Jupiter and Saturn. Ammonia should condense at approximately 700mbar for Jupiter and 1.8 bar for Saturn and above that, in the absence of eddy mixing, the partial pressure initially follows the saturated vapor pressure curve. At higher altitudes, solar ultraviolet (UV) radiation photolyzes ammonia and leads to an even greater rate of decrease of abundance with height. If the eddy-mixing coefficient is high, then more ammonia would be expected at the photolysis altitudes because fresh ammonia is transported there faster than it can be photolyzed. Conversely if the eddy-mixing coefficient is low, then very little ammonia is expected at the photolysis altitudes since the new ammonia will be photolyzed as fast as it can arrive there. Hence, by measuring the ammonia mixing ratio profile, we can estimate the value of K(z) in the upper troposphere. Another good indicator of the upper tropospheric eddy-mixing coefficient for Jupiter and Saturn is the vertical profile of phosphine, which is also photolyzed in the region of the tropopause. The profiles of ammonia and phosphine may be estimated from thermal-IR and near-IR remotely sensed measurements for Jupiter and Saturn, but not for Uranus and Neptune, where abundances are too low. At higher altitudes, methane photochemistry becomes important, which produces hydrocarbons such as ethane and acetylene. Measurements of the vertical distribution of these gases may be derived from thermal-IR measurements for all of the giant planets and used to infer the value of K(z) at these altitudes. Finally, estimates of the value of K(z) at the methane homopause may be made from observations at two UV wavelengths (Atreya, 1986): Lyman-a (1,216 A), and helium 584 A. The Jovian planets are relatively bright at Lyman-a wavelengths, primarily through the resonance scattering of incident sunlight by hydrogen atoms. Methane is a strong UV absorber and hence only those hydrogen atoms that are above the methane homopause level may contribute to this radiation. Hence, for atmospheres with large eddy diffusion coefficient (high homopause) fewer hydrogen atoms may contribute to the resonance scattering and thus the measured intensity is less. Similarly helium atoms in the Jovian planets resonantly scatter photons at 584 A. However, in this case as K(z) increases, the measured intensity increases (rather than decreases as it does for Lyman-a) since the abundance of helium at the top of the homosphere is greater. However, to interpret the He 584 A observations independent measurements of the temperature in the scattering region are also required, which are difficult to estimate.

A combination of many of these measurements has been used to estimate the variation of K(z) with pressure for all of the giant planets, which is shown in Figure 4.3 (after Fouchet et al., 2003), where the estimates in table 4.2 of Atreya et al. (1999) are also shown as cross symbols. Also plotted as dotted lines are the profiles of the molecular diffusion coefficient for methane calculated from the semi-empirical formula (after Moses et al., 2000):

where the temperature profiles shown earlier in Figure 4.1 have been used. The greater rate of increase with height of D than K is clearly seen and the level where

Eddy Qnd Diffusion Coefficients (cm1 s"') Eddy ond Diffusion Coefficients (cm* s'1

101 102 103 104 105 106 tO2 103 104 105 106 107

Eddy ond Diffusion Coefiicients (cm2 s'1) Eddy ond Diffusion Coefficients (cm2 s'1

Figure 4.3. Variation of eddy mixing and molecular diffusion coefficients with height in the giant planet atmospheres. Solid lines are eddy diffusion coefficient profiles (from Fouchet et al., 2003). Dotted lines are the molecular diffusion coefficients of methane calculated from Equation (4.27). Cross symbols are estimates of eddy diffusion coefficients from Table 4.2.

101 102 103 104 105 106 tO2 103 104 105 106 107

Eddy ond Diffusion Coefiicients (cm2 s'1) Eddy ond Diffusion Coefficients (cm2 s'1

Figure 4.3. Variation of eddy mixing and molecular diffusion coefficients with height in the giant planet atmospheres. Solid lines are eddy diffusion coefficient profiles (from Fouchet et al., 2003). Dotted lines are the molecular diffusion coefficients of methane calculated from Equation (4.27). Cross symbols are estimates of eddy diffusion coefficients from Table 4.2.

the curves meet is the methane homopause. It can be seen that the methane homopause occurs at a pressure of approximately 10 bar for both Jupiter and Saturn, indicating active vertical eddy mixing, but that turbulence in Neptune's stratosphere is less active with the methane homopause at 10 bar. The vertical mixing in Uranus' atmosphere can be seen to be particularly sluggish with the homopause at ~10~5 bar.

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