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The laminar-turbulent boundary S is the set separating initial conditionswhich relaminarise uneventfully from those which become turbulent. Phase spacetrajectories on this hypersurface in cylindrical pipe flow look to be chaoticand show recurring evidence of coherent structures. A general numericaltechnique is developed for recognising approaches to these structures and thenfor identifying the exact coherent solutions themselves. Numerical evidence ispresented which suggests that trajectories on S are organised around only a fewtravelling waves and their heteroclinic connections. If the flow is suitablyconstrained to a subspace with a discrete rotational symmetry, it is possibleto find locally-attracting travelling waves embedded within S. Four new typesof travelling waves were found using this approach.

Transition in pipe flow: the saddle structure on the boundary of turbulence