Internal gravity waves over an oscillating sunspot

Internal gravity waves excited in the overlying atmosphere by the proper vertical oscillations of an entire sunspot are studied. For simplicity, the oscillations of the sunspot are introduced into the model through the lower boundary conditions, by specifying oscillations in the vertical velocity. The characteristic radius of the oscillating region is assumed to equal the spot size and the frequency to correspond to the long-period natural oscillations of the spot. Results of numerical computations are presented. It is shown that internal gravity waves propagate nearly in the horizontal direction. Therefore, immediately above the spot, the wave energy drops exponentially with the height, in good agreement with the available observational data. The level where the amplitude and energy density of the wave are maximum rises slowly with distance from the spot.