Stability of divergent channel flows - A numerical approach

Estimates are obtained of the spatial growth rates for disturbances in divergent channels by a numerical finite difference method that gives results in reasonably good agreement with those reported by Eagles and Weissman (1975) and Eagles and Smith (1980). It is shown that the method proposed by Eagles and Weissman is numerically quite accurate in practice for channel flows. Attention is called to the way in which the upstream and downstream boundary conditions used have very little influence on the solution at moderate distances from the computational end points. This is seen to be consistent with the modal approach of linear stability theory as applied by, among others, Bouthier (1973) and Eagles and Smith in that the dominant eigenvalue would seem to be coming into effect as one moves downstream, swamping the effect of the various conditions imposed at xi = 0. It is noted that the tendency for all modes to decay as xi becomes larger is also strikingly consistent with the decay of the present solutions, independent of the precise boundary conditions imposed at xi = xi sub 1 (a strong feature of these calculations).