Osborne reynolds' pipe flow: Direct computation from laminar through transition to fully-developed turbulence

The most fundamental internal flow has been computed accurately from first-principle in laboratory framework. It exhibits a turbulence onset scenario that bears certain similarities to, and differences from, the bypass transition in the narrow sense found in the most basic external flow under free-stream turbulence, which has also been computed concurrently. In both flows, finite, weak, and well-controlled turbulent perturbations introduced at the inlet far away from the wall excite large semi-regular Lambda structures upstream of breakdown. Breakdown is directly caused by the formation of hairpin packets in the near-wall region. One major difference is that the transitional pipe flow exhibits a distinct overshoot in skinfriction over the corresponding turbulent flow value, whilst the transitional boundary layer does not. It is found that the energy norm associated with weak, localized, finite-Amplitude perturbations in the fully-developed laminar pipe flow are capable of growing exponentially, despite the fact that infinitesimally small disturbances will not grow exponentially in this flow. This is the first time in fluid mechanics research that the Osborne Reynolds pipe flow has been accurately simulated starting from fully-developed laminar state, through the whole process of transition, then early turbulent region, and eventually arriving at the fully developed turbulent pipe flow state.