Viscosity in the high atmosphere

Abstract

The kinematic viscosity η/ρ approaches infinity as the density ρ approaches zero, since the results of kinetic theory show that the molecular viscosity η is independent of density. The elementary viscosity derivations use a linear velocity profile which implies near infinite streaming velocities as the density becomes small. The streaming velocities must be finite, and the velocity profile must have an upper and a lower limit in the atmosphere. It is shown that the viscous stress must approach zero with decreasing density when the velocity profile is bounded. Either the velocity gradients or the corrected viscosity coefficients become small in the higher atmosphere. The viscous effect depends on a length scale representative of the wind shear and is a maximum in the lower F-region for scales comparable to those representative of the air currents studied in synoptic meteorology.