The nature of the transition to turbulence in weakly-curved pipe flow

In wall-bounded shear flows, turbulence arises abruptly, and typically in spite of the linear stability of the laminar base flow. Recent experiments and simulations have established an analogy to absorbing-state phase transitions; more specifically in the universality class of directed percolation (DP). While good agreement with this framework has been demonstrated for Couette type and shear-driven flows, the situation in pressure driven flows is less clear. In particular for pipe flow, measurements of universal characteristics such as critical exponents appear beyond reach, given the extremely large temporal and spatial scales that are relevant close to the critical point. Even conservative estimates suggest that such studies would require pipes more than 10¹⁰ diameters in length. We circumvent this problem here by introducing a second parameter: pipe curvature. As shown, even for very weakly curved pipes (radius ratio of around 6 x10^-4) the relevant time scales, such as puff decay and splitting times are lower by four orders of magnitude, while the overall nature of the transition appears unchanged. This reduction in time scales is explained by a shift of the transition point. In addition preliminary results on the universal aspects of this transition are presented.