Feigenbaum universality in subcritical Taylor-Couette flow Feigenbaum universality is shown to occur in subcritical shear flows. Our testing ground is the counter-rotation regime of the Taylor–Couette flow, where numerical calculations are performed within a small periodic domain. The accurate computation of up to the seventh period-doubling bifurcation, assisted by a purposely defined Poincaré section, has enabled us to reproduce the two Feigenbaum universal constants with unprecedented accuracy in a fluid flow problem. We have further devised a method to predict the bifurcation diagram up to the accumulation point of the cascade based on the detailed inspection of just the first few period-doubling bifurcations. Remarkably, the method is applicable beyond the accumulation point, with predictions remaining valid, in a statistical sense, for the chaotic dynamics that follows. 1010 Cambridge University Press application/pdf