Traveling wave instability in a diverging–converging channel

The temporal linear stability of a pressure-driven flow in a diverging–converging channel with respect to the traveling wave disturbances is considered. The flow may develop under either the fixed mass flowrate constraint or the fixed pressure gradient constraint. It is shown that the variations in the channel geometry lead to the flow destabilization, as compared with the straight channel case. It is demonstrated that the critical disturbances have the form of two-dimensional waves. The global critical conditions describing the minimum critical Reynolds number required to create the instability for the specified geometry of the channel are given. It is shown that the flow developed under the fixed mass flowrate constraint is slightly more unstable than the flow developed under the fixed pressure gradient constraint. This difference increases with an increase of the amplitude of the channel divergence–convergence.