Vertically propagating waves in an atmosphere with Newtonian cooling inversely proportional to density

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Abstract
The behavior of vertically propagating waves is investigated for an atmosphere with Newtonian cooling, where the cooling rate coefficient is very small near the ground and increases inversely with the atmosphere's density away from the ground. This model for dissipation is unrealistic. However, the results obtained are very similar to those obtained by Yanowitch (1967a, b), who investigated the behavior of waves in a viscous atmosphere where the kinematic viscosity is inversely proportional to atmospheric density. The present calculations are, in general, far simpler than those of Yanowitch, and suggest that many of his results follow from the variation of dissipation with height and not from specific details of the physics. It is suggested that the present calculations may provide convenient estimates of the effects of dissipation in more realistic situations.

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