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

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.