An internal wave in a viscous heat-conducting isothermal atmosphere

The effects of viscosity and heat conduction on the propagation of an internal wave generated by a simple harmonic localized disturbance are considered for the case of an isothermal compressible atmosphere. A similarity solution of the linearized equations shows that the velocities decay and the wave width increases away from the disturbance. Superpositions of this solution show how a few waves of small wavelength attenuate rapidly whereas waves of larger wavelength can increase in amplitude as they propagate upwards before eventually attenuating.