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The aim in the dynamical systems approach to transitional turbulence is toconstruct a scaffold in phase space for the dynamics using simple invariantsets (exact solutions) and their stable and unstable manifolds. In large(realistic) domains where turbulence can co-exist with laminar flow, thisrequires identifying exact localized solutions. In wall-bounded shear flows thefirst of these has recently been found in pipe flow, but questions remain as tohow they are connected to the many known streamwise-periodic solutions. Here wedemonstrate the origin of the first localized solution in a modulationalsymmetry-breaking Hopf bifurcation from a known global travelling wave that has2-fold rotational symmetry about the pipe axis. Similar behaviour is found fora global wave of 3-fold rotational symmetry, this time leading to two localizedrelative periodic orbits. The clear implication is that all global solutionsshould be expected to lead to more realistic localised counterparts throughsuch bifurcations, which provides a constructive route for their generation.

The genesis of streamwise-localized solutions from globally periodic travelling waves in pipe flow