Osborne Reynolds pipe flow: Direct simulation from laminar through gradual transition to fully developed turbulence

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Abstract
Significance: The precise dynamics of disturbance energy growth and breakdown in pipe transition is a century-old unresolved problem in fluid mechanics. In this paper, we demonstrate that the mystery attributed to the breakdown process of the Osborne Reynolds pipe transition can be partially resolved with a direct, spatially evolving simulation that carries weakly but finitely perturbed laminar inflow through gradual rather than abrupt transition arriving at the fully developed turbulent state. Some of the previously attributed abruptness and mysteriousness was perhaps due to the inability to study the process accurately with very fine spatial and temporal resolution. The energy norm was found to grow exponentially rather than algebraically. The sensitivity of the transition process to pipe entrance conditions is demonstrated.

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