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.

This research presents a new theory that explains analytically the behaviour of any fully developed incompressible turbulent pipe flow, steady or unsteady. We propose the name of theory of underlying laminar flow (TULF), because its main consequence is the description of any turbulent pipe flow as the sum of two components: the underlying laminar flow (ULF) and the purely turbulent component (PTC). We use the framework of the TULF to explain analytically most of the important and interesting phenomena reported in He & Jackson (J. Fluid Mech., vol. 408, 2000, pp. 1–38). To do so, we develop a simple model for the pressure gradient and Reynolds shear stress that could be applied to the linearly accelerated pipe flow described by He & Jackson (2000). The following features of the unsteady flow are explained: the deformation undergone by the mean velocity profiles during the transient, the velocity overshoot observed in the more rapid excursions, the dual deformation of mean velocity profiles when overshoots are present, the laminarisation effects described during acceleration, the rapid decrease of the Reynolds shear stress upon approaching the wall that brings forth the laminar sublayer, and some other minor effects. A new field is defined to characterise the degree of turbulence within the flow, directly calculable from the theory itself. Arguably, this new field would describe the degree of turbulence in a pipe flow more accurately than the familiar turbulence intensity parameter. Finally, a paradox is found in the deformation of the unsteady mean velocity profiles with respect to equal-Reynolds-number steady profiles, which is duly explained. The research also predicts the occurrence of mean velocity undershoots if the flow is decreased rapidly enough.

Experimental evidence yields a wide variety of starting turbulent pipe flows, usually with greatly deformed mean velocity profiles. Some experimental tests attain profiles with maximum values in the near-wall region, while some others report well-defined local concavities within globally convex mean velocity profiles. To the authors’ knowledge, no available explanation yet exists for such a kind of behavior. This theoretical research studies the specific effects that certain patterns of Reynolds shear stress cause on the mean velocity field obtained in unsteady turbulent flows. A simple model of transient Reynolds shear stress is devised, and this model is used to calculate the mean velocity field of starting turbulent flow. Those mean flow patterns are related to the actual velocity profiles reported in the experimental literature on starting flow. We learn how the different Reynolds shear stress patterns contribute to create the resulting mean velocity patterns and which particular configuration of Reynolds shear stress is responsible for each one of the reported experimental velocity profiles. We explain why, how, where, and when each particular deformation in the unsteady mean velocity profile is caused, and the relationship between each type of deformation and the Reynolds shear stress that brings it forth. We issue some predictions identifying types of flow that, to our knowledge, have not yet been reported in the experimental literature, and we offer clues for those experimental researchers willing to discover the predicted flow patterns. This research continues the exposition of the theory of underlying laminar flow initiated in previous papers.

An analytic model (AM) describes the dynamical behavior of a Newtonian fluid that is suddenly released to the atmosphere from a pressurized vessel. The discharge process is a very fast transient phenomenon in which the liquid transits from rest to a highly turbulent motion, constituting a two-phase flow with a liquid–air interface. The AM has a number of parameters that can be adjusted to conform to experimental or simulation data. This AM is then used to assess the ability of some relevant computational fluid dynamics (CFD) turbulence models to simulate the fast transient behavior described by the AM. The detached eddy simulation (DES) $k-\omega$ shear-stress-transport with scale-adaptive-simulation (SSTSAS) turbulence model provides an acceptable agreement with the AM because it can reproduce the intense wall friction generated in the transient motion. The CFD results suggest that deceleration plays a very prominent role in generating turbulence near the wall. The cross-section velocity and turbulence fields profiles for the CFD model are also discussed.

This research reports the mean-velocity field associated with a general plane-parallel flow, regardless of its being laminar, turbulent, steady-state, unsteady, or transient. The Reynolds-averaged Navier–Stokes equation is posed, with proper initial and boundary conditions, and the solution is developed in an easy-to-follow fashion. The time-dependent general analytic solution is obtained, which is the sum of three components: (i) the transient decay of the initial mean velocity, (ii) the unsteady mean velocity directly created by the mean pressure gradient, and (iii) the unsteady mean velocity originated from the flow's Reynolds shear-stress gradient. Each one of these components has a different evolution in time, resulting in an asynchronism among them that yields deformed mean-velocity profiles. The formalism is applied to study the transient flow created when an initial steady-state flow is accelerated or decelerated up to a final steady state. A rapidly accelerated version of this problem was already studied in a DNS by He and Seddighi [“Turbulence in transient channel flow,” J. Fluid Mech. 715, 60–102 (2013)]. We show that DNS results concerning mean velocity are qualitatively reproduced by our approach, including surprising features like the flattening of transient mean-velocity profiles, the middle mean-velocity overshoot, global laminarization, and the enhancement of the viscous sublayer related to the notion of hyperlaminarity already introduced by the authors. The decelerated case presents sharpening of mean-velocity profiles, middle mean-velocity undershoots, global turbulentization, and the destruction of the viscous sublayer, and poses predictions that await experimental confirmation. This research continues the exposition of the theory of underlying laminar flow initiated in previous papers.