Shear flows undergo a sudden transition from laminar to turbulent motion as the velocity increases, and the onset of turbulence radically changes transport efficiency and mixing properties. Even for the well-studied case of pipe flow, it has not been possible to determine at what Reynolds number the motion will be either persistently turbulent or ultimately laminar. We show that in pipes, turbulence that is transient at low Reynolds numbers becomes sustained at a distinct critical point. Through extensive experiments and computer simulations, we were able to identify and characterize the processes ultimately responsible for sustaining turbulence. In contrast to the classical Landau-Ruelle-Takens view that turbulence arises from an increase in the temporal complexity of fluid motion, here, spatial proliferation of chaotic domains is the decisive process and intrinsic to the nature of fluid turbulence.

The collapse of turbulence, observable in shear flows at low Reynolds numbers, raises the question if turbulence is generically of a transient nature or becomes sustained at some critical point. Recent data have led to conflicting views with the majority of studies supporting the model of turbulence turning into an attracting state. Here we present lifetime measurements of turbulence in pipe flow spanning 8 orders of magnitude in time, drastically extending all previous investigations. We show that no critical point exists in this regime and that in contrast to the prevailing view the turbulent state remains transient. To our knowledge this is the first observation of superexponential transients in turbulence, confirming a conjecture derived from low-dimensional systems. [4][5][6]. Surprisingly, at relatively low Reynolds numbers (Re & 2000) the turbulent state is not stable and after long times suddenly collapses [7][8][9][10][11][12]. This behavior is reminiscent of memoryless processes in nonlinear systems. In phase space the dynamics can be described by a complex structure giving rise to the disordered dynamics, a socalled chaotic repeller [13]. Underlying such a structure are unstable states and for pipe flow unstable solutions to the governing equations have been identified in the form of traveling waves [14,15]. Surprisingly clear transients of such traveling waves were observed in experiments [16,17] confirming their relevance to the turbulent dynamics. More recently traveling wave transients were also reported in numerical studies [18,19].A way to probe the validity of this model is to measure the lifetime of turbulence in the transient regime. Previous experimental and numerical lifetime measurements have shown approximately exponential probability distributions [8,10,11,20,21] which suggests that the probability for a turbulent structure to decay is independent of its age and hence that this process is memoryless as would be expected for the escape from a chaotic saddle. Here the probability for a flow to still be turbulent after a time t at a fixed Reynolds number (Re) is then given bywhere is the characteristic lifetime ( À1 can be also interpreted as the escape rate) and t 0 is the initial time period required for turbulence to form after the disturbance has been applied to the laminar flow at t ¼ 0. an infinite lifetime is only reached in the asymptotic limit Re ! 1. Subsequently a number of studies have questioned this finding and again entertained the occurrence of a boundary crisis [11,22,23]. A clear constraint of all previous investigations is the limited range in lifetimes measured. Typically scaling laws were postulated from data covering 2 orders of magnitude. Numerical simulations are particularly problematic because in order to capture the quantitatively correct behavior computations have to be carried out in large domains, which severely restricts the number of realizations N that are manageable (N < 50) [11]. Consequently the statistics are often insufficiently resolved resulting in a...

Flows through pipes and channels are the most common means to transport fluids in practical applications and equally occur in numerous natural systems. In general, the transfer of fluids is energetically far more efficient if the motion is smooth and laminar because the friction losses are lower. However, even at moderate velocities pipe and channel flows are sensitive to minute disturbances, and in practice most flows are turbulent. Investigating the motion and spatial distribution of vortices, we uncovered an amplification mechanism that constantly feeds energy from the mean shear into turbulent eddies. At intermediate flow rates, a simple control mechanism suffices to intercept this energy transfer by reducing inflection points in the velocity profile. When activated, an immediate collapse of turbulence is observed, and the flow relaminarizes.

Abstract. Aircraft borne optical in situ size distribution measurements were performed within Arctic boundary layer clouds with a special emphasis on the cloud top layer during the VERtical Distribution of Ice in Arctic clouds (VERDI) campaign in April and May 2012. An instrumented Basler BT-67 research aircraft operated out of Inuvik over the Mackenzie River delta and the Beaufort Sea in the Northwest Territories of Canada. Besides the cloud particle and hydrometeor size spectrometers the aircraft was equipped with instrumentation for aerosol, radiation and other parameters. Inside the cloud, droplet size distributions with monomodal shapes were observed for predominantly liquid-phase Arctic stratocumulus. With increasing altitude inside the cloud the droplet mean diameters grew from 10 to 20 µm. In the upper transition zone (i.e., adjacent to the cloud-free air aloft) changes from monomodal to bimodal droplet size distributions (Mode 1 with 20 µm and Mode 2 with 10 µm diameter) were observed. It is shown that droplets of both modes coexist in the same (small) air volume and the bimodal shape of the measured size distributions cannot be explained as an observational artifact caused by accumulating data point populations from different air volumes. The formation of the second size mode can be explained by (a) entrainment and activation/condensation of fresh aerosol particles, or (b) by differential evaporation processes occurring with cloud droplets engulfed in different eddies. Activation of entrained particles seemed a viable possibility as a layer of dry Arctic enhanced background aerosol (which was detected directly above the stratus cloud) might form a second mode of small cloud droplets. However, theoretical considerations and model calculations (adopting direct numerical simulation, DNS) revealed that, instead, turbulent mixing and evaporation of larger droplets are the most likely reasons for the formation of the second droplet size mode in the uppermost region of the clouds.

In shear flows, turbulence first occurs in the form of localized structures (puffs/spots) surrounded by laminar fluid. We here investigate such spatially intermittent flows in a pipe experiment showing that turbulent puffs have a well-defined interaction distance, which sets their minimum spacing as well as the maximum observable turbulent fraction. Two methodologies are employed. Starting from a laminar flow, puffs are first created by locally injecting a jet of fluid through the pipe wall. When the perturbation is applied periodically at low frequencies, as expected, a regular sequence of puffs is observed where the puff spacing is given by the ratio of the mean flow speed to the perturbation frequency. At large frequencies however puffs are found to interact and annihilate each other. Varying the perturbation frequency, an interaction distance is determined which sets the highest possible turbulence fraction. This enables us to establish an upper bound for the friction factor in the transitional regime, which provides a well-defined link between the Blasius and the Hagen-Poiseuille friction laws. In the second set of experiments, the Reynolds number is reduced suddenly from fully turbulent to the intermittent regime. The resulting flow reorganizes itself to a sequence of constant size puffs which, unlike in Couette and Taylor-Couette flow are randomly spaced. The minimum distance between the turbulent patches is identical to the puff interaction length. The puff interaction length is found to be in agreement with the wavelength of regular stripe and spiral patterns in plane Couette and Taylor-Couette flow.