Interactions of two jets in a channel: solution multiplicity and linear stability

Abstract

The steady, two-dimensional, isothermal flow of an incompressible Newtonian fluid in a semi-infinite channel is modelled using a finite-element method. The flow is driven by injecting two identical jets through symmetrically placed slit-like nozzles into the otherwise closed end of the channel. Multiple steady-state solutions are observed for Reynolds numbers greater than 18.8, where seven solutions have been found. Six of these solutions exist on branches that are not connected to the Stokes flow solution via continuation in the Reynolds number. Further bifurcations of these solutions has led to the discovery of 17 solutions at a Reynolds number of 40. A two-dimensional linear stability analysis of the solution branches shows that for Reynolds numbers in the range of 18.8 to 26.8 there are three stable solutions. One solution is symmetric about the channel centreline while the other two stable solutions are a pair of mirror-image asymmetric flows. For Reynolds numbers in the range 26.8 to 40, there are four known stable solutions consisting of two asymmetric solutions and their mirror-images.