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Many transitional wall-bounded shear flows are characterised by thecoexistence in state-space of laminar and turbulent regimes. Probing the edgeboundary between the two attractors has led in the last decade to the numericaldiscovery of new (unstable) solutions to the incompressible Navier-Stokesequations. However, the iterative bisection method used to achieve this canbecome prohibitively costly for large systems. Here we suggest a simplefeedback control strategy to stabilise edge states, hence accelerating theirnumerical identification by several orders of magnitude. The method isillustrated for several configurations of cylindrical pipe flow. Travellingwaves solutions are identified as edge states, and can be isolated rapidly inonly one short numerical run. A new branch of solutions is also identified.When the edge state is a periodic orbit or chaotic state, the feedback controldoes not converge precisely to solutions of the uncontrolled system, butnevertheless brings the dynamics very close to the original edge manifold in asingle run. We discuss the opportunities offered by the speed and simplicity ofthis new method to probe the structure of both state space and parameter space.

Surfing the edge: using feedback control to find nonlinear solutions