A symmetry-breaking inertial bifurcation in a cross-slot flow

• A new bifurcation phenomenon is reported for a two-dimensional cross-slot geometry.
• At low Reynolds numbers the flow remains steady and symmetric with identical regions of standing recirculations.
• Above a critical Reynolds number a supercritical pitchfork bifurcation is observed.
• A pair of steady asymmetric solutions occurs with larger recirculation regions on one of the cross-slot sidewalls.
• The dynamics of the bifurcation are investigated and compared with that observed for inertialess viscoelastic fluid flow.

In the current paper we investigate, using a numerical technique, a new bifurcation phenomenon for a Newtonian fluid flowing through a two-dimensional so-called “cross-slot” geometry. A cross-slot, or cross-channel, geometry is formed by an “horizontal” planar channel along which two incoming fluid streams are made to impinge on each other, and an intersecting “vertical” channel which carries the outlet flow, with the other two streams now moving away from the central section and leaving through the vertical channel exits. At low Reynolds numbers (Re) the flow remains steady and symmetric and identical regions of standing recirculation attached to the four corners increase linearly in size with Re. At a critical Reynolds number (=1490 ± 10) a supercritical pitchfork bifurcation is observed beyond which the unstable symmetrical solution is replaced by a pair of steady asymmetric solutions (each corresponding to larger recirculation regions on one vertical sidewall). The dynamics of the bifurcation are investigated in detail and a comparison made with the bifurcation observed for inertialess viscoelastic fluid flow.