Abstract
A simple model for the structure of a non-rotating Hadley regime in an atmosphere with large thermal inertia is developed. The radiative fluxes are estimated by using a linearization about the radiative equilibrium state and the dynamical fluxes are estimated by using scaling analysis. The requirement that differential heating by these fluxes be in balance in both the meridional and vertical directions leads to two equations for the mean static stability and meridional temperature contrast. The solution depends on two parameters: the strength of the radiative heating, as measured by the static stability Ae of the radiative equilibrium state; and the ratio of the time it takes an external gravity wave to traverse the atmosphere to the time it would take the atmosphere to cool off radiatively, denoted by ε.
In the deep Venus atmosphere ε ≈ 10−5; the equations are therefore analyzed in the limit ε → 0. The large-scale dynamics has virtually the same effect on the lapse rate as small-scale convection: if Ae > 0 the radiative lapse rate is unchanged, while if Ae < 0 the lapse rate becomes subadiabatic, but only by an amount of order ε⅔. Therefore, one need not invoke convection to explain the approximate adiabatic lapse rate in the Venus atmosphere, but a greenhouse effect is necessary to explain the high surface temperatures. The other properties of the solutions when Ae < 0 are consistent with observational evidence for the deep atmosphere: the horizontal velocities are typically ∼2 m sec−1, the vertical velocities ∼½ cm sec−1, and the meridional temperature contrast is unlikely to exceed 0.1K.
The same approach is used to study the time-dependent problem and determine how long it would take for a perturbed atmosphere to reach equilibrium. If Ae > 0 the adjustment is primarily governed by the radiative time scale, which is about 100 earth years for the deep Venus atmosphere. If Ae < 0 the adjustment is governed by an advective time scale which may be as short as 20 earth days. Published numerical studies of the deep circulation have only treated the first case, but their integrations were not carried beyond about 200 earth days and therefore do not describe true equilibrium states. Only the second case, Ae < 0, is consistent with the observations and it would be relatively easy to study numerically.
