The effect of initial perturbation on the hydrostatic adjustment

The effect of initial perturbation on the hydrostatic adjustment is investigated based on the linear model describing the dynamics and thermodynamics of a non-static, compressible and isothermal dry atmosphere. The direction of adjustment between the vertical gradient of pressure field and the buoyance field is examined by using the wave theory in the homogeneous medium; and the physical essence of atmospheric movement is presented from the perspective of energy partition and conversion during the hydrostatic adjustment. The theoretical results show that the causal relationships between the vertical gradient of pressure field and the buoyancy field, the u branch of horizontal flow field and the vertical gradient of pressure field are affected by the helical structure of wave, the horizontal basic flow and the initial perturbation properties during the balance of atmospheric static equilibrium is destroyed, where the characteristic of initial perturbation determines the contribution of each branch of the acoustic-gravity waves in the process of hydrostatic adjustment, and affecting the evolution of the physical fields with time. Under the condition that the horizontal basic flow is the westerly jet, themesoscale system is sensitive to the initial perturbation, the direction of adjustment is from the vertical gradient of pressure field to the buoyancy field in the first twenty minutes after the static equilibrium state is destroyed by the initial perturbations of velocity or density. The direction of adjustment is from the buoyancy field to the vertical gradient of pressure field in the early stage and the later stage after the balance is destroyed by the initial perturbation of pressure, while the direction is opposite in the middle stage. The adaptive relationship between the vertical gradient of pressure field and the u branch of horizontal flow field is insensitive to the initial perturbation properties but is more sensitive to the scale of perturbation. Experiments show that, when the balance is destroyed, in the micro-scale system, the vertical gradient of pressure field is the cause of atmospheric motion, and in the mesoscale system, the u branch of horizontal flow field is the cause of atmospheric motion. At the same time, the initial perturbation affects the partition ratio and conversion of perturbation energy during the adjustment process, the physical pattern of hydrostatic adjustment is different for the reason of different initial perturbations.