On the analytic explanation of experiments where turbulence vanishes in pipe flow

Abstract

The present research will provide an analytical explanation to experiments destabilising turbulence in pipe flow reported in Kuehnen et al. (Nat. Phys., vol. 14, 2018, 386–390). Those experiments show four methods by which turbulence vanishes from steady-state pipe flow, without decreasing its bulk velocity, until it becomes completely laminar. The explanation is based on our theory of underlying laminar flow (TULF), which has already been successfully applied to account for other uncommon experiments reported in the literature. The TULF is founded on the Reynolds-averaged Navier–Stokes equations and thus is a theory of ensemble-averaged flows. The zero theorem for steady-state flow is introduced as a universal result that will help explain the laminarisation process described in experiments. After presenting the most comprehensive solution for the mean pipe flow governing equation that, to our knowledge, has ever been reported, we uncover a general sequence for laminarisation, called the laminarisation pattern, and we introduce a mathematical model for it. We show that a drastic decrease in a flow's mean-pressure gradient, while maintaining constant its Reynolds number, is necessary and sufficient to erase turbulence. Equations derived from our model are used to calculate the minimum pressure gradient necessary to cause complete laminarisation in each experiment. Results are then contrasted with reported experimental data, with noticeable agreement. We also propose a figure of merit to assess the efficiency of each laminarisation method. Having disclosed the intrinsic mechanism leading to complete laminarisation, we expect researchers will propose other ingenious methods to achieve it.