Attenuation of Acoustic-Gravity Waves in an Isothermal Atmosphere: Consideration with the Modified Navier-Stokes and Heat-Transfer Equations

Abstract

Within the model of a dissipative isothermal atmosphere, the attenuation of acoustic−gravity waves (AGWs) is studied on the basis of the modified Navier−Stokes and heat-transfer equations. Besides the usually considered velocity gradient, the modification of these equations takes into account the additional transfer of the momentum and energy induced by AGWs due to the density gradient. This results in that additional terms appear in the hydrodynamic equations of motion and heat transfer. Under these assumptions, the local dispersion equation for AGWs in an isothermal dissipative atmosphere, as well as an expression for the damping decrement, is obtained. In the limiting cases of high frequencies (sound waves) and low frequencies (gravitational waves), the nature of the attenuation allows a clear physical interpretation. Special aspects of the time-dependent attenuation for the evanescent acoustic−gravity modes of various types, including the Lamb waves and Brent−Vaisala oscillations, are also considered.