Stability and Perturbation Enstrophy Transfer Mechanism of Flow in Slightly Divergent Channels

Abstract

The global linear stability of a 2-D viscous incompressible flow through a slightly divergent finite length channel is investigated using the stream function–vorticity formulation. The flow problem is studied under inlet–outlet nonperiodic boundary conditions using a stabilized finite element method. The perturbation eigenmodes, growth rates, as well as perturbation enstrophy transfer mechanisms are analyzed to demonstrate the inlet–outlet interactions of the base flow and the perturbation enstrophy. Results show that slightly divergent channel brings the critical Reynolds number to a low value. The eigenmode is different from the classical normal mode of perturbations. It is also found that slight divergence moves the maximum envelope of the least-stable eigenmode upstream in the flow bulk. Exchange of stability is eventually triggered above the critical Reynolds number as analyzed in the transfer mechanism for the perturbation enstrophy.