Analytic Solutions of the Heat Conduction Equation in the Thermosphere

摘要

It is shown that the approximate one-dimensional equations of conservation of mass, momentum, and energy in the thermosphere, when expressed in an isobaric frame, have simple analytic Green's function solutions. Errors in the hydrostatic assumption are shown to be remarkably small, even for major temperature changes occurring over tens of minutes. Nonlinear error terms are estimated to be 10 percent in the temperature. The forms of the solutions depend upon the existence of a fixed-temperature lower boundary. It is suggested that this boundary should be identified with the level at which turbulence ceases (the 'turbopause'). The usual concept of conduction-cooling time depends strongly upon the type of heating and may lead to a gross underestimate of the time required to reach a steady state. Comparison of the daily variation of temperature calculated on the basis of photoionization heating with results using more accurate numerical methods demonstrates the usefulness of the simple analytic approach. (Author)