Abstract: In order to research the three-dimensional hydrostatic adjustment mechanism, the dispersion characteristics of acoustic gravity wave, analytical solutions and the energy conversion equation are deduced by the hydrostatic adjustment equations. The results show that the wave of controlling the hydrostatic adjustment process is the dispersion of acoustic gravity wave and internal gravity wave, and the acoustic gravity wave and the internal gravity wave are distinguished by the frequency of the horizontal direction. The frequency of acoustic gravity wave increases with the increasing horizontal and vertical wave number. Taking the paraxial approximation, analytical solutions of the hydrostatic adjustment process exist in the space spiral surface. It can provide an alternative mechanism for channeling heat and momentum from one region to another in the atmosphere and provide a new perspective to cutting edge research in meteorology. Vertical velocity plays an important role in the energy conversion. Conversions between the kinetic energy and the available potential energy, and between the available potential energy and the available elastic energy are only happen in the vertical direction. The hydrostatic adjustment process is in energy conservation and potential vorticity conservation. The magnitude of available potential energy is ten times bigger than that of the available elastic energy in the final equilibrium state.