I. Meridional Energy Balance of Uranus. II. Viscosity of Rock-Ice Mixtures. III. The Thermosphere of Titan

Citation

Friedson, Andrew James (1987) I. Meridional Energy Balance of Uranus. II. Viscosity of Rock-Ice Mixtures. III. The Thermosphere of Titan. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/65ch-hj35. https://resolver.caltech.edu/CaltechTHESIS:01292013-151449809

Abstract

Part I:

The seasonal meridional energy balance and thermal structure of the atmosphere of Uranus is investigated using a two-dimensional radiative-convective-dynamical model. Diurnal-average temperatures and heat fluxes are calculated as a function of pressure, latitude, and season. In addition to treating radiation and small-scale convection in a manner typical of conventional radiative-convective models, the dynamical heat fluxes due to large-scale baroclinic eddies are included and parameterized using a mixing length formulation (Stone, 1972; Ingersoll and Porco, 1978). The atmosphere is assumed to be bounded below by an adiabatic, fluid interior with a single value of potential temperature at all latitudes. The internal heat flux is found to vary with latitude and season. The total internal power and the global enthalpy storage rate are seen to oscillate in phase with a period of 1/2 Uranian year. On an annual-average basis, equatorward heat transport can take place in both the atmosphere and the convective interior. For a weak internal heat source, the meridional transport takes place predominantly in the atmosphere. If the internal heat source is larger, a greater share of the transport is taken up by the interior. For a value of the internal heat near the current upper limit for Uranus (~27% of the absorbed sunlight), about 1/3 of the equatorward heat transport at mid-latitudes occurs in the interior. For a given internal heat source, placing the peak of the solar heating at high altitudes or depositing the solar energy into a narrow altitude range favors heat transport by the atmosphere over the interior. Deep penetration of sunlight favors transport by the interior. For the time corresponding to the Voyager 2 Uranus encounter, the effective temperature at the south (sunlit) pole is calculated to be ~1.5 K higher than that at the equator. Horizontal contrasts of the mean 450-900 mbar temperature are found to be less than ≤ 1.5 K, in fair agreement with Voyager 2 IRIS results (Hanel et al., 1986), but the model fails to reproduce the local minimum in this temperature seen at 30°S. Nevertheless, it is concl uded that meridional heat transport in the atmosphere is efficient in keeping seasonal horizontal temperature contrasts below those predicted by radiative-convective models (Wallace, 1983).

Part II:

Theory and experiments are used to establish lower and upper bounds on the ratio of actual viscosity to pure ice viscosity for a suspension of rock particles in a water ice matrix. For typical conditions encountered in icy satellites, this ratio is of order ten or possibly larger, depending on unknown factors such as the particle size distribution. It is shown that even this modest increase in viscosity may be enough to have caused a failure of solidstate convective self-regulation early in the evolution of a homogeneous, rock-water ice satellite, provided the satellite is large enough and sufficiently silicate-rich. The criteria for this failure are satisfied by Ganymede and are marginal for Callisto, if the silicates are hydrated. Failure of self-regulation means that the viscosity is too high for the interior to remain completely solid and eliminate the heat production of long-lived radioisotopes by solid state convection. Partial melting of the ice then occurs. It is further shown that satellites of this size may then undergo runaway differentiation into a rock core and almost pure ice mantle, because the gravitational energy release is sufficient to melt nearly all the ice, and the Rayleigh-Taylor instability time scale is short. (Although the high pressure phases of ice melt, the resulting water quickly refreezes at a higher level.) We conjecture that these results explain the striking surface dissimilarity of Ganymede and Callisto, if these satellites accreted cold and undifferentiated. Ganymede may have gone supercritical (melted and differentiated) because of a failure of self-regulation, whereas Callisto remained undifferentiated to the present day. Like all proposed explanations for the Ganymede-Callisto dichotomy, this conjecture cannot be quantified with confidence, because of inadequate or incomplete observations, theory and experimental data.

Part III:

The diurnal variation of the vertical structure of Titan's thermosphere is calculated through simultaneous solution of the equations of heat transfer and hydrostatic equilibrium. The temperature and density profiles are found above the mesopause. The dynamical response of the thermosphere to heating is for the most part neglected. Nevertheless, we are able to draw some interesting qualitative and quantitative conclusions regarding the vertical structure. Heating of the upper thermosphere occurs primarily through absorption of solar Lyman α radiation by methane, with an additional amount of heating (≤ 20%) due to low-energy magnetospheric electron precipitation. The heat is conducted downward to the mesopause, where it is removed by IR cooling due principally to acetylene. The mesopause is found to occur where the density is 2.2 x 10¹² cm^-3 (736 km) and has a temperature of ~110 K. The exospheric temperature is unlikely to exceed 225 K in the course of a Titan day. The diurnally averaged exospheric temperature is in the range 187-197 K, depending on the amount of magnetospheric electron heating that is included in the model. The amplitude of the diurnal variation is found to be ≤ 28 K. We find that the vertical extent of the hydrogen cloud is too large to be explained in terms of simple thermal escape of hydrogen from a ~225 K exosphere and conclude that other processes must be important for populating or heating the neutral torus.

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