Analytical Solution for number densities in the Homosphere

TitleAnalytical Solution for number densities in the Homosphere
Publication TypeJournal Article
Year of Publication2004
AuthorsTan, A, Ramachandran, R
JournalEOS Transactions
AbstractAtmospheric number densities are governed by a differential equation obtained from the hydrostatic equation and the perfect gas equation. In the homosphere, the average molecular weight of gases is constant and the density is governed by the altitudinal variation of gravitational acceleration and temperature only. Exact solutions for the number densities are obtained in the troposphere and mesosphere (where the temperature decreased linearly with altitude) and in the stratosphere (where the temperature increased linearly with altitude). The results are in close agreement with those given by the U. S. Standard Atmosphere in tabular form. The density profiles in logarithmic scale exhibit negative curvatures (convexity upwards) in the troposphere and mesosphere and positive curvature (concavity upwards) in the stratosphere. The magnitude of the curvature depends on the slope of the temperature profile and is the greatest in the troposphere followed by the mesosphere and stratosphere in that order. The inflection points in the density profiles (in logarithmic plot) mark the locations of the tropopause, stratopause and mesopause.
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