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Compatibility Conditions, Complex Frequency, and Complex Vertical Wave Number for Models of Gravity Waves in the Thermosphere
Author(s) -
Broutman Dave,
Knight Harold,
Eckermann Stephen D.
Publication year - 2020
Publication title -
journal of geophysical research: space physics
Language(s) - English
Resource type - Journals
eISSN - 2169-9402
pISSN - 2169-9380
DOI - 10.1029/2020ja028011
Subject(s) - thermosphere , dispersion relation , gravity wave , physics , wavenumber , gravitational wave , dissipation , prandtl number , classical mechanics , wave propagation , mechanics , geophysics , thermodynamics , optics , convection , ionosphere , quantum mechanics
Abstract Gravity wave propagation from the troposphere into the thermosphere has often been modeled by assuming a complex vertical wave number m , with the imaginary part accounting for viscous and thermal dissipation. An alternative is to assume a complex wave frequency ω , which leads to a simpler form of the dispersion relation and different wave solutions described by complex‐ ω ray theory. Here the solutions of complex ω and complex m are analyzed in terms of the compatibility conditions ∇× k =0 and k t =−∇ ω , where k is the wave number vector. Estimates derived here suggest that the complex‐ ω ray solutions can violate compatibility conditions above altitudes of weak viscosity. A possible consequence of this violation is an overestimation of the viscous damping of thermospheric gravity waves. The present results are based on a numerical solution of the viscous gravity‐wave dispersion relation in the anelastic approximation with a Prandtl number of unity and using conventional specifications of the dynamic viscosity of the thermosphere. Theoretical solutions for complex m are also derived in the weak and strong viscosity limits.