THE DEVELOPMENT OF SMALL PERTURBATION METHOD AND STUDY RESULTS FOR THE STABILITY OF HYDROSTATIC EQUILIBRIUM OF TWO GASES IN THE GRAVITY FIELD

G. A. Grishina
VANT. Ser.: Mat. Mod. Fiz. Proc. 1995. Вып.1-2. С. 95-102.

      A brief presentation is given for the general approach to small perturbation method. The solution for the disturbed problem is represented as Taylor series from the variations of initial-boundary conditions of the undisturbed problem. The differential equations are given for the evaluation on the first and second derivatives of this series.
      The problem for the stability investigation of the equilibrium in the gravity field of two contacting gases is solved analytically. The solution found from the sum of two variations shows how the sinusoidal boundary shape changes with time and jets form when the upper medium is heavier than the lower one. The problem is given as an example of how to account approximation in the investigations of flow stability with the small perturbation method.