Alberto de Lozar

The onset of turbulence in pipe flow

The lifetimes of injected jet puffs are used to determine the critical point at which turbulent pipe flow is sustained. 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.

Eliminating Turbulence in Spatially Intermittent Flows

Taming Turbulence When fluid flows through a pipe, if the inertial forces are increased or the viscosity is decreased, the flow will become increasing noisy and will shift from being laminar to turbulent. Turbulence can be triggered by roughness in the pipe or other irregularities, which cause local eddies that grow into full-scale disruption of the otherwise smooth flow. Hof et al. (p. 1491; see the Perspective by McKeon) show that a continuous turbulent eddy, downstream, eliminates the growth of upstream disturbances and can prevent the overall flow from becoming turbulent. Unlike many other control methods, the energy cost for implementing this strategy is less than the benefit gained by maintaining a laminar flow. Injection of jets of water is used to control the transition from laminar to turbulent flow in pipes. 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.

Experimental investigation of laminar turbulent intermittency in pipe flow

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.

An experimental study of the decay of turbulent puffs in pipe flow.

As reported in a number of recent studies, turbulence in pipe flow is transient for Re<2000 and the flow eventually always returns to the laminar state. Generally, the lifetime of turbulence has been observed to increase rapidly with Reynolds number but there is currently no accord on the exact scaling behaviour. In particular, it is not clear whether a critical point exists where turbulence becomes sustained or if it remains transient. We here aim to clarify if these conflicting results may have been caused by the different experimental and numerical protocols used to trigger turbulence in these studies.

Direct Numerical Simulations of a Smoke Cloud-Top Mixing Layer as a Model for Stratocumuli

A radiatively driven cloud-top mixing layer is investigated using direct numerical simulations. This configuration mimics the mixing process across the inversion that bounds the stratocumulus-topped boundary layer. The main focus of this paper is on small-scale turbulence. The finest resolution (7.4cm) is about two orders of magnitude finer than that in cloud large-eddy simulations (LES). A one-dimensional horizontally averaged model is employed for the radiation. The results show that the definition of the inversion point with the mean buoyancy of hbi(zi) 5 0 leads to convective turbulent scalings in the cloud bulk consistent with the Deardorff theory. Three mechanisms contribute to the entrainment by cooling the inversion layer: a molecular flux, a turbulent flux, and the direct radiative cooling by the smoke inside the inversion layer. In the simulations the molecular flux is negligible, but the direct cooling reaches values comparable to the turbulent flux as the inversion layer thickens. The results suggest that the direct cooling might be overestimated in lessresolved models like LES, resulting in an excessive entrainment. The scaled turbulent flux is independent of the stratification for the range of Richardson numbers studied here. As suggested by earlier studies, the turbulent entrainment only occurs at the small scales and eddies larger than approximately four optical lengths (60m in a typical stratocumulus cloud) perform little or no entrainment. Based on those results, a parameterization is proposed that accounts for a large part (50%‐100%) of the entrainment velocities measured in the Second Dynamics and Chemistry of the Marine Stratocumulus (DYCOMS II) campaign.

Mixing Driven by Radiative and Evaporative Cooling at the Stratocumulus Top

AbstractThe stratocumulus-top mixing process is investigated using direct numerical simulations of a shear-free cloud-top mixing layer driven by evaporative and radiative cooling. An extension of previous linear formulations allows for quantifying radiative cooling, evaporative cooling, and the diffusive effects that artificially enhance mixing and evaporative cooling in high-viscosity direct numerical simulations (DNS) and many atmospheric simulations. The diffusive cooling accounts for 20% of the total evaporative cooling for the highest resolution (grid spacing ~14 cm), but this can be much larger (~100%) for lower resolutions that are commonly used in large-eddy simulations (grid spacing ~5 m). This result implies that the κ scaling for cloud cover might be strongly influenced by diffusive effects. Furthermore, the definition of the inversion point as the point of neutral buoyancy allows the derivation of two scaling laws. The in-cloud scaling law relates the velocity and buoyancy integral scales to a...

Scaling laws for the heterogeneously heated free convective boundary layer

AbstractThe heterogeneously heated free convective boundary layer (CBL) is investigated by means of dimensional analysis and results from large-eddy simulations (LES) and direct numerical simulations (DNS). The investigated physical model is a CBL that forms in a linearly stratified atmosphere heated from the surface by square patches with a high surface buoyancy flux. Each simulation has been run long enough to show the formation of a peak in kinetic energy, corresponding to the “optimal” heterogeneity size with strong secondary circulations, and the subsequent transition into a horizontally homogeneous CBL.Scaling laws for the time of the optimal state and transition and for the vertically integrated kinetic energy (KE) have been developed. The laws show that the optimal state and transition do not occur at a fixed ratio of the heterogeneity size to the CBL height. Instead, these occur at a higher ratio for simulations with increasing heterogeneity sizes because of the development of structures in the d...

Evaporative cooling amplification of the entrainment velocity in radiatively driven stratocumulus

Evaporative cooling monotonically increases as the thermodynamical properties of the inversion allow for more evaporation in shear-free radiatively-driven stratocumulus. However, the entrainment velocity can deviate from the evaporative-cooling trend and even become insensitive to variations in the inversion properties. Here, the efficiency of evaporative cooling at amplifying the entrainment velocity is quantified by means of direct numerical simulations of a cloud-top mixing layer. We demonstrate that variations in the efficiency modulate the effect of evaporative cooling on entrainment, explaining the different trends. These variations are associated with the evaporation of droplets in cloud holes bellow the inversion point. The parametrization of the efficiency provides the evaporative amplification of the entrainment velocity as a function of a single parameter that characterizes the inversion. The resulting entrainment velocities match our experiments and previous measurements to within ±25%. The parametrization also predicts the transition to a broken cloud field consistently with observations.

Reduction of the Entrainment Velocity by Cloud Droplet Sedimentation in Stratocumulus

AbstractThe effect of sedimentation on stratocumulus entrainment is investigated using direct numerical simulations of a cloud-top mixing layer driven by radiative and evaporative cooling. The simulations focus on the meter and submeter scales that are expected to be relevant for entrainment, and the finest grid spacing is Δx = 26 cm. The entrainment velocity is investigated from the analysis of the integrated-buoyancy evolution equation, which is exactly derived from the flow evolution equations. The analysis shows that sedimentation interacts with entrainment through two different mechanisms. As previously reported, sedimentation prevents droplets from evaporating in the entrainment zone, which in turn reduces the entrainment velocity. Here it is shown that sedimentation also promotes a positive buoyancy flux that directly opposes entrainment. The strengths of both mechanisms are characterized by two different settling numbers, which allow for predicting which meteorological conditions favor the reducti...

Interaction of turbulent spots in pipe flow

The process of transition from laminar to turbulent regime in shear driven flows is still an unresolved issue. Localized turbulent regions or spots occur in pipe flow for Reynolds numbers around 2000. Typically in this regime an intermittent change between laminar and turbulent flow is observed (Wygnanski). Indeed, even if a large section of the laminar flow is uniformly perturbed localized turbulent spots emerge rather than an extended region of turbulence. A good understanding of this localization process is crucial for the comprehension of the transition to turbulence. We investigate the interaction of such turbulent spots in pipe flow for Reynolds numbers from 1900 to 2500. Turbulence is created locally by injecting a jet of water through a small hole in the pipe wall. For small perturbation frequencies the spacing of the turbulent spots downstream is inversely proportional to the frequency. It is observed that for distances less than approximately 20 pipe diameters turbulent spots start to interact and annihilate each other. The interaction distance is measured as a function of Reynolds number. We are also studying the effect of amplitude of the perturbations on the mutual interaction of the puffs. This investigation is closely related to spatially turbulent laminar periodic patterns which were earlier observed in other shear driven flows like Taylor-Couette or plane Couette (Prigent et al), (D. Barkley and L. Tuckerman).