Degeneracy of turbulent states in two-dimensional channel flow

We revisit two-dimensional channel flow with fixed volume flux for Reynolds numbers via direct numerical simulations and uncover a region of multistability of turbulent states. New asymmetric states (based on comparing the time-averaged mean shear on each of the channel walls) exist for at least when alongside the known symmetric solution ( is the channel height and is the mean flow rate). Both the symmetric and asymmetric states resemble a travelling wave even at an order of magnitude above the primary bifurcation at with the asymmetric state showing heightened turbulent behaviour near one of the channel walls. These asymmetric states display up to reduction in pressure gradient compared with their symmetric counterparts. The saddle state between the two apparent attractors is shown to be the travelling wave solution which originates from the primary bifurcation. By , the symmetric solution has become unstable leaving only the asymmetric state and its reflected counterpart as attractors until at least . At , the pair of asymmetric states become connected so that the 'turbulent' wall switches apparently randomly and infrequently. In this way, the symmetry of the flow is then restored but only after averaging over extremely long times ().

Automated summary

By conducting direct numerical simulations of two-dimensional channel flow with fixed volume flux for Reynolds numbers, it was found that there exist asymmetric turbulent states with heightened turbulent behavior near one of the channel walls and with a significant reduction in pressure gradient compared to symmetric counterparts. The symmetric solution becomes unstable at a critical point, leaving only the asymmetric state and its reflected counterpart as attractors, which eventually become connected to apparently random and infrequent wall switches. The symmetry of the flow is eventually restored after averaging over extremely long times.