Polar Symmetric Flow of a Viscous Compressible Atmosphere: An Application to Mars

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  • 1 The Laboratory for Planetary Atmospheres, Goodard Space Flight Center, Greenbelt, Md. 20771
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Abstract

The atmosphere is assumed to be driven by a polar symmetric temperature field and the equations of motion in pressure ratio coordinates are linearized by considering the zero order in terms of a thermal Rossby number RδT(2aΩ)2 where δT is a measure of the latitudinal temperature gradient. When the eddy viscosity is greater than 106 cm2S−1 boundary layer extends far up into the atmosphere making the geostrophic approximation invalid for the bulk of the atmosphere. The surface pressure gradient exhibits a latitudinal dependence opposite that of the depth-averaged temperature. The magnitude of the gradient is dependent upon the depth of the boundary layer, which depends upon the eddy viscosity, the boundary conditions imposed at the surface, and upon the temperature lapse rate. Using a temperature model for Mars based on Mariner 9 infrared spectral data with a 30% increase in the depth-averaged temperature from the winter pole to the subsolar point, the following results were obtained for the increase in surface pressure from the subsolar point to the winter pole as a function of eddy viscosity and with no-slip conditions imposed at the surface:
i1520-0469-32-1-60-e1

The meridional cellular flow rate is also correlated with the eddy viscosity, causing a complete overturning of the atmosphere in tens of days for an eddy viscosity of 108cm2S−1 and in hundreds of days for 106cm2S−1 The implication of this overturning in the dust storm observed during the early part of the Mariner 9 mission is discussed briefly.

Calculations of the dynamic heating indicate the mechanism for a polar temperature inversion and high-altitude equatorial cooling.

Abstract

The atmosphere is assumed to be driven by a polar symmetric temperature field and the equations of motion in pressure ratio coordinates are linearized by considering the zero order in terms of a thermal Rossby number RδT(2aΩ)2 where δT is a measure of the latitudinal temperature gradient. When the eddy viscosity is greater than 106 cm2S−1 boundary layer extends far up into the atmosphere making the geostrophic approximation invalid for the bulk of the atmosphere. The surface pressure gradient exhibits a latitudinal dependence opposite that of the depth-averaged temperature. The magnitude of the gradient is dependent upon the depth of the boundary layer, which depends upon the eddy viscosity, the boundary conditions imposed at the surface, and upon the temperature lapse rate. Using a temperature model for Mars based on Mariner 9 infrared spectral data with a 30% increase in the depth-averaged temperature from the winter pole to the subsolar point, the following results were obtained for the increase in surface pressure from the subsolar point to the winter pole as a function of eddy viscosity and with no-slip conditions imposed at the surface:
i1520-0469-32-1-60-e1

The meridional cellular flow rate is also correlated with the eddy viscosity, causing a complete overturning of the atmosphere in tens of days for an eddy viscosity of 108cm2S−1 and in hundreds of days for 106cm2S−1 The implication of this overturning in the dust storm observed during the early part of the Mariner 9 mission is discussed briefly.

Calculations of the dynamic heating indicate the mechanism for a polar temperature inversion and high-altitude equatorial cooling.

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