Small Froude number asymptotics in two-dimensional two-phase flows

Abstract

A nonlinear wave equation is derived describing the behavior of gas- and liquid-fluidized beds in the small Froude number regime. It represents a two-dimensional perturbation of the Korteweg--de Vries equation and is shown to constitute a valid approximation of the original system. While greatly simplifying the analytical and numerical investigation of two-phase flow in fluidized beds, it also leads to the conclusion that the underlying model does not significantly discriminate between gas- and liquid-fluidized beds near the stability limit. An amplitude equation is derived governing the growth and stability of solitary plane waves. The results are linked to those obtained by previous nonapproximative analyses. It is expected that this analysis is applicable to other multiphase and traffic flow models due to the similarity in the governing equations and the completeness of the reduced wave equation.