Wave Action Conservation, Eliassen‐Palm Flux and Nonacceleration Conditions Within Atmospheres of Variable Composition

Abstract The foundational conservation equations of Eliassen and Palm (EP) and Bretherton and Garrett (BG) governing the pseudomomentum and action of waves in geophysical fluids are shown to be approximations that do not hold generally within atmospheres of varying mass composition, such as the Earth's thermosphere and other planetary atmospheres. Standard BG/EP conservation equations assume a fixed connection between mean‐state entropy and pressure that breaks down when composition varies. New entropy‐corrected (EC) forms of these equations are derived that conserve total energy and momentum in atmospheres where composition varies. Three separate and largely independent derivations are presented that all lead to the same EC forms of these equations and their associated diagnostics, such as nonacceleration conditions. Since EC forms present as corrective scaling factors to standard BG/EP equations, existing models and diagnostics are easily generalized. Representative thermospheric calculations reveal that the EC equations remove systematic energy and momentum biases of up to 40% that in turn lead steady conservative waves to grow more rapidly in amplitude with increasing altitude.