Acoustic waves in a stratified atmosphere II. Three-dimemsional hydrodynamics

We investigate analytically the propagation of linear waves in a three-dime nsional, nonmagnetic, isothermal atmosphere stratified in plane-parallel la yers. The motivation is to study oscillations in the nonmagnetic chromosphe re and to assess the limitations of one-dimensional simulations of the K-2v bright point phenomenon. We consider an impulsively excited acoustic disturbance, emanating from a p oint source, and propagating outward as a spherical acoustic wave accompani ed by an internal gravity wave. The waves amplify exponentially in the upwa rd direction. A significant wave amplitude is therefore found only in a rel atively narrow cone about the vertical. The amplitude of the wave decreases with time. Because of the lateral spread, the wave amplitude decays faster in 2D and 3D simulations than in ID. The initial pulse, which travels at t he sound speed, carries most of the energy injected into the medium. Subseq uent wave crests leave the source region at ever-increasing phase speed, bu t slow to the sound speed as they approach the head of the wave. Important conclusions from the 3D solution that were not anticipated from t he plane-wave solution are: I. The bulk of the energy is emitted in the upward land downward direction; much less goes into the horizontal direction. 2. The wave profile narrows from the initial pulse through the amplitude ma xima in the wake of the pulse. As a consequence of both points, the shock-h eated regions in the wake of the initial pulse would weaken in strength and shrink in size. 3. The height at which a given wave amplitude is reached spreads outward fr om the symmetry axis of the disturbance as the wave propagates upward. Thus the diameter of the shock-heated region would increase as the acoustic wav e travels upward in the atmosphere.