Separated flow models—I. Analysis of the averaged and local instantaneous formulations

Abstract

Procedures for deriving averaged conservation equations and jump conditions for two-phase flow are discussed. Averaged working equations for stratified horizontal flow are derived and analyzed to illustrate that interfacial configuration, or flow regimes, must be considered in order to avoid inconsistencies in the model. The corresponding local instantaneous two-dimensional equations are also analyzed for propagation of disturbances in stratified flow. It is shown that the linear stability conditions for long waves are the same for both the averaged and local instantaneous cases. However, for finite amplitude waves the local instantaneous formulation leads to higher order dispersion terms that do not appear to arise in the averaged equations. In particular it is shown that finite amplitude waves are described by forms of the nonlinear Korteweg-deVries equation that can give rise to waves of permanent shape, and have fairly general classes of exact solutions.