Transitions and instabilities of two-dimensional flow in a symmetric channel with
a suddenly expanded and contracted part are investigated numerically by three
different methods, i.e. the time marching method for dynamical equations, the SOR
iterative method and the finite-element method for steady-state equations. Linear
and weakly nonlinear stability theories are applied to the flow. The transitions are
confirmed experimentally by flow visualizations. It is known that the flow is steady
and symmetric at low Reynolds numbers, becomes asymmetric at a critical Reynolds
number, regains the symmetry at another critical Reynolds number and becomes
oscillatory at very large Reynolds numbers. Multiple stable steady-state solutions
are found in some cases, which lead to a hysteresis. The critical conditions for the
existence of the multiple stable steady-state solutions are determined numerically and
compared with the results of the linear and weakly nonlinear stability analyses. An
exchange of modes for oscillatory instabilities is found to occur in the flow as the
aspect ratio, the ratio of the length of the expanded part to its width, is varied, and
its relation with the impinging free-shear-layer instability (IFLSI) is discussed.
Weakly nonlinear stability analysis of triple diffusive convection in a Maxwell fluid saturated porous layer