Stability of flows in channels

Laminar stability flow for incompressible fluid flow in two dimensional symmetric channels of variable width is reviewed through a survey of various related topics,
Many authors whose works are reviewed here investigated linear stability using the "WKB' method in which regions of growth of a small disturbance to the basic flow and regions of decay were determined. A modification of this method was employed by some authors as a distinct improvement on quasi-parallel theory which provides the formal lowest-order growth rates but is inadequate in determining the growth rates as a function of a downstream variable and can only indicate when a particular wave is growing or decaying at a particular point.
An asymptotic solution was imposed on the disturbance equation and the resulting differential equations have at lowest-order the Orr--Sommerfeld equation on which much of the subsequent work in laminar stabi1ity depends. The second order correction to the growth rates was the highest order in the works reviewed.The criteria of stability that was adopted was such that if a wave grows through a given region of the channel, then the flow is said to be unstable while if the waves decay through a particular region the flow is said to be stable. Neutral stability curves were used in distinguishing the two regions described above.