On Viscous Fluid Flow Down an Inclined Plane and the Development of Roll Waves.

摘要

The authors develop a tractable, and mathematically rigorous, asymptotic theory for the development of instability in viscous fluid flow down an inclined plane, at supercritical Reynolds numbers. The theory involves consideration of an ill posed problem, and provides a new example of the way such problems come up in applied mathematics. It is shown how one may use additional information, inherent in the problem one really wishes to solve, in order to regularize this improperly posed problem. The authors discuss several numerical experiments and compare the results with experimental observations of 'roll waves' and 'slug flows' in inclined channels, at similar slopes and Reynolds numbers. The results are in agreement with observations.