A comparison between the 'local potential method' and the 'exact numerical procedure' (Application to the stability analysis of a hot layer of fluid)

Abstract

flli this paper the 'local potential method' as introduced by Prigogine and Glansdorff and applied to hydrodynamic $lability problems by Schechter and Himmelblau and the exact numerical procedure' used by Harris and Reid and others have been applied to determine the stability criteria of a hot layer of fluid with mean temperature changingata rate, which had already been determined by Krilhnamurtbi. While solving by the two methods and comparing the results with the known results it is found that unless sufficient representation for the eigenfunctions is ronsidered the 'local potential method' does not give good approximation and unless the initial guess is quite dose to tile actual result the 'exact numerical procedure' invulves long processes. It is found that two methods can be liabitably combined to give a useful procedure.