On the importance of the purely gravitationally induced density, pressure, and temperature variations in gravity waves: Their application to airglow observations

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Abstract
A quantitative study is made of the relative importance of the purely gravitationally induced compression (GIC) due to fluid particle altitude change and the actual “wave compression” which can occur at a fixed altitude in a gravity wave. The results for density, pressure, and temperature variations show the following: (1) the GIC effects predominate (>95%) for υ/c <20%, where υ is the horizontal phase velocity and where very simple formulas can be obtained; (2) the relative importance depends strongly on frequency for wave periods less than 10 min but becomes totally independent of frequency for periods greater than 20 min; and (3) the temperature measurements can be quickly converted to height variations wherever the GIC effect predominates; in general, the conversion is equivalent to the adiabatic lapse rate, i.e., a 10° temperature variation corresponds to a height change of 1 km. In addition, the total kinetic energy density can be simply expressed in terms of height variation and, whenever the GIC effects predominate, can be very easily obtained from temperature measurements. An interesting by‐product has been that for waves of small horizontal phase speed, the total wave kinetic energy at any frequency is equal to the kinetic energy of the natural (Brunt) oscillation of an air parcel with the same vertical displacement.