Propagators of atmospheric motions 1. Excitation by point impulses

Linear equations for the motions of inviscid ideal gas atmospheres are considered, a brief description of the climatology of the relevant propagation parameters being given. An operational formalism is developed for obtaining elementary solutions for point impulse sources. The propagation of a pulse according to the Boussinesq gravity wave model is analyzed in terms of convergent series solutions for small time and in terms of asymptotic series solutions for large time. Elementary propagators for the gravity wave mode and buoyancy oscillation mode are defined by contour integrals about the singularities of the propagator operator. The theory is extended to the propagation of a pulse in a stratified compressible atmosphere. All motion is then confined within an acoustic front expanding radially with the speed of sound. Series solution in powers of the distance behind the front is described. Sufficiently far behind the front, the motion is given by an acoustic oscillation, buoyancy oscillation, and gravity wave mode. Consideration of the analogous problem, except for a hydrostatic atmosphere on a rotating plane, indicates when and where the assumptions of hydrostatic balance and absence of rotation are tenable. With rotation, a potential vorticity mode describing time‐independent motion also occurs, or, if the variation of the earth's vorticity is included in the model, Rossby waves occur. Addition of a lower boundary is discussed with emphasis on the horizontal propagation of the Lamb wave mode. Impulsive addition of heat excites a Lamb pressure wave pulse strongly modulated by buoyancy oscillations.