Turbulent Core Research Articles

A 1+ Mechanism Model for Predicting the Mixed-Oil Concentration in Multiproduct Pipelines

Summary Petroleum products are frequently transported successively through the same multiproduct pipeline. Due to turbulent and convective diffusion mass transfer, two adjacent oils will mix with each other, forming a mixed-oil segment. Accurate and rapid prediction of mixed-oil concentration is crucial for the precise management of mixed-oil segments. Conventional 1D modeling methods exhibit shortcomings in accurately representing the asymmetric distribution characteristics of mixed-oil concentration curves, and high-dimensional models are not practically applied due to their prohibitive computational time costs. Building on the 1D model framework, this paper proposes a “1+” mechanism model by considering the convective mass transfer behavior between the turbulent core region and the laminar boundary layer, and new governing equations and corresponding numerical solution methods are also introduced. Simulation experiments affirm the ability of the new model to characterize the asymmetric distribution features of mixed-oil concentration curves, along with its high computational efficiency in engineering applications. This is demonstrated by the computational time of approximately 30 seconds for simulating a pipeline of 300 km in length (Δx = 10 m, Δt = 1 second, CPU: i5-12500H, RAM: 16 GB). When applied to pipelines in industrial scenarios, the new model is shown to accurately predict the distribution of mixed-oil concentration curves. The research findings are significantly beneficial in assisting field personnel to gain advanced insights into the mixed-oil concentration distribution at the station, enabling timely and well-informed strategies for handling mixed-oil segment, thereby enhancing the operational efficiency of multiproduct pipelines.

On The Determination Of Conditional Statistics Along Gradient Trajectories At The Turbulent/Non-Turbulent Interface Of Jet Flows.

Conditional sampling and averaging are valuable techniques for discerning and quantifying notable regions within turbulent flows. These methods have been particularly prevalent in experimental and numerical investigations of turbulent shear flows. Conditional statistics effectively analyze the dynamics and characteristics of turbulent flows, offering insights into transitional behaviors and distinct features within these regimes. This approach is instrumental in studying turbulent shear flows, such as jets or mixing layers, where a well-defined zone separates the turbulent core from the non-turbulent surrounding fluid. This zone, known as the Turbulent/Non-Turbulent Interface (TNTI), plays a crucial role in various phenomenological changes, including the transfer of mass, momentum, and scalar fluxes. While statistics in jet flows are often reported along the radial direction for a given downstream position, this method can obscure the underlying physical processes. Scalar dissipation rate, transport, or turbulent kinetic energy involve velocity or concentration gradients at the flow interface. To date, the impact of sampling direction on conditional statistics within jet flows has not yet been thoroughly discussed. This study focuses on determining gradient trajectories at the interface of turbulent flows. Gradient trajectories have been used to explore structures in turbulent flows, proving effective in analyzing homogeneous shear turbulence. This study introduces a methodology for sampling conditional data by computing gradient trajectories intersecting the TNTI. The primary objective is to verify whether sampling statistics along the gradient of scalar concentration provide a more detailed understanding of the processes occurring near the TNTI. The methodology involves computing a field of gradient trajectories from concentration fields obtained through Planar Laser-Induced Fluorescence (PLIF) in a N2/N2 jet with Re = 2900. Conditional statistics at the TNTI of a jet flow along the gradient trajectory for a given downstream position are calculated and reported. The paper aims to compare conditional statistics along gradient trajectories with those obtained along radial and normal directions at the TNTI. It is expected that gradient trajectory statistics align more closely with normal direction statistics near the interface and diverge as it gets into the jet or coflow fluid.

Detection of the irrotational boundary using machine learning methods

Four machine learning methods, i.e., self-organizing map (SOM), Gaussian mixture model (GMM), eXtreme gradient boosting (XGBoost), and contrastive learning (CL), are used to detect the irrotational boundary (IB), which represents the outer edge of the turbulent and non-turbulent interface layer. To accurately evaluate the detection methods, high-resolution databases from direct numerical simulations of a temporally evolving turbulent plane jet are used. It is found that except for the SOM method, the general contour of the IB appears to be effectively captured using the GMM, XGBoost, and CL methods, which indicate the turbulent and non-turbulent regions can be roughly recognized. Furthermore, the intrinsic features of the detected IB using the GMM, XGBoost, and the CL methods are quantitatively evaluated. Unlike the conventional vorticity norm method, the three machine learning methods do not rely on a single threshold of vorticity magnitude to separate the turbulent and non-turbulent regions. A small part of the detected IB using the three machine learning methods is characterized by the rotational motions, which are expected to be only found inside the turbulent sublayer and turbulent core region. Compared to the vorticity norm and XGBoost methods, the fractal dimensions of the IB detected by the GMM and CL methods are relatively small, which are related to the missing detection of some highly contorted elements. With the three machine learning methods, a large part of the detected IB is characterized by a convex shape, similarly as with the vorticity norm. However, the probability density function profiles of the local curvature of the detected IB differ greatly between the three machine learning methods and the vorticity norm. A mild variation of the mean conditional distributions of the vorticity magnitude can be observed across the detected IB by the three machine learning methods. This study first implies that using the machine learning methods the turbulent and non-turbulent regions can be roughly distinguished, but it is still challenging to obtain the intrinsic features of the detected IB.

Disk Wind Feedback from High-mass Protostars. IV. Shock-ionized Jets

Massive protostars launch accretion-powered, magnetically collimated outflows, which play crucial roles in the dynamics and diagnostics of the star formation process. Here we calculate the shock heating and resulting free–free radio emission in numerical models of outflows of massive star formation within the framework of the Turbulent Core Accretion model. We postprocess 3D magnetohydrodynamic simulation snapshots of a protostellar disk wind interacting with an infalling core envelope, and calculate shock temperatures, ionization fractions, and radio free–free emission. We find heating up to ∼107 K and near-complete ionization in shocks at the interface between the outflow cavity and infalling envelope. However, line-of-sight averaged ionization fractions peak around ∼10%, in agreement with values reported from observations of massive protostar G35.20-0.74N. By calculating radio-continuum fluxes and spectra, we compare our models with observed samples of massive protostars. We find our fiducial models produce radio luminosities similar to those seen from low- and intermediate-mass protostars that are thought to be powered by shock ionization. Comparing to more massive protostars, we find our model radio luminosities are ∼10–100 times less luminous. We discuss how this apparent discrepancy either reflects aspects of our modeling related to the treatment of cooling of the post-shock gas or a dominant contribution in the observed systems from photoionization. Finally, our models exhibit 10 yr radio flux variability of ∼5%, especially in the inner 1000 au region, comparable to observed levels in some hypercompact H ii regions.

Spatially evolving cascades in wall turbulence with and without interface

Direct numerical simulations of channel flow and temporal boundary layer at a Reynolds number $Re_{\tau } = 1500$ are used to assess the scale-by-scale mechanisms of wall turbulence. From the peak of turbulence production embedded at the small scales of the near-wall region, spatially ascending reverse cascades are generated that move through self-similar eddies growing in size with the wall distance. These fluxes are followed by spatially ascending forward cascades through detached eddies thus reaching sufficiently small scales where eventually scale energy is dissipated. This phenomenology is shared by both boundary layer and channel flow and is recognized as a robust physical feature characterizing wall turbulence in general. Specific features related to the flow configuration are indeed identified in the outer region. In particular, the central region of channels is characterized by a generalized Richardson energy cascade where large scales are in equilibrium with small scales at different wall distances through a combined forward cascade and spatial flux. On the contrary, the interface region of boundary layers is characterized by an almost two-dimensional physics where spatially ascending reverse cascades sustain long and wide interface structures with a forward cascade that survives only in the wall-normal scales. The overall scenario consists in a variety of scale motions that while protruding from the turbulent core towards the external region, squeeze at the interface thus sustaining vertical shear in a thin layer. The observed multidimensional physics sheds light on the complex interactions between outer entrainment and near-wall self-sustaining mechanisms with possible repercussions for theories.

Characteristics of turbulent core–annular flow with water-lubricated high viscosity oil in a horizontal pipe

Direct numerical simulations are performed to investigate the characteristics of a turbulent core–annular flow with water-lubricated high viscosity oil in a horizontal pipe. Six different superficial velocity ratios ( $\,j_w/j_o = 0.057\unicode{x2013}0.41$ ) are examined by changing the water superficial velocity $j_w$ for a fixed oil superficial velocity $j_o$ . The pressure drops in the pipe and the shapes of the phase interface agree well with those from previous experiments. The oil core flow is almost a plug flow, and the gaps between the phase interface and pipe wall are narrow and wide near the upper and lower surfaces of the pipe, respectively, due to the buoyancy. Within a narrow gap, water is confined mostly in a valley region of the wavy phase interface and hardly goes through its crest. On the other hand, water near the phase interface at a wide gap convects downstream almost at the core speed and the flow near the wall is similar to that of single-phase wall-bounded turbulent flow. The annular flow is characterized by three different regimes depending on the clearance Reynolds number ( $Re_c$ ) based on the core velocity and local gap size: laminar Couette flow driven by the core for $Re_c \le 600$ , transitional flow for $600 < Re_c < 2500$ and turbulent flow for $Re_c \ge 2500$ . The minimum pressure drop occurs at $j_w/j_o = 0.11$ in the early transition regime. For all $j_w/j_o$ considered, the negative lift force acting on the core comes from the pressure force which balances the buoyancy.

Overall lift-off characteristics of CH4/H2 non-premixed jet flames in laminar/turbulent transition

The effects of adding hydrogen to methane were investigated through the transition between laminar and turbulent regimes based on the characteristics of non-premixed lifted flames. Lift-off heights can show complex trends depending on the fuel tube diameter, jet velocity, and hydrogen ratio. In the laminar regime, the lift-off heights were smaller than the laminar mixing core and decreased with hydrogen addition. In the turbulent regime, the lift-off heights could be much smaller or larger than the turbulent core when the jet velocities were smaller or larger than specific criteria, respectively. Such transitional phenomena were discussed based on the theories related to flow development, premixed flame, and edge flame structures. These included the mixing layer, quenching distance, flow re-direction, Damköhler number, turbulent flame speed, etc. Meanwhile, existing relationships between the lift-off heights and the flow velocities showed significant deviations when the hydrogen ratio was large. An improved relationship between the lift-off heights and the fuel jet velocities was proposed, considering the influence of the virtual origin and the flammable mixing layer. This relationship will apply to various fuel compositions such as propane, methane, hydrogen, and their mixtures. In addition, the blow-off mechanism was explained based on the turbulent burning velocity. Finally, the overall stabilization modes and mechanisms of the lifted flames were explained.

Turbulent/non-turbulent interfaces in equilibrium and non-equilibrium regions in the absence of mean shear

Direct numerical simulations (DNS) of turbulent fronts evolving into a non-turbulent flow region in the absence of mean shear are generated for both classical (equilibrium) and non-equilibrium turbulence in order to study the characteristics of the turbulent/non-turbulent interface (TNTI) that separates regions of turbulent from non-turbulent (or irrotational) flow. The effects of the non-equilibrium can be observed in a number of statistics computed in the turbulent core region of the turbulent evolving fronts, such as the Reynolds dependance of the normalised dissipation Cɛ, which exhibits a power law (for non-equilibrium turbulence) close to Cɛ∼Reλ−n, where Reλ is the Taylor based Reynolds number and n≈1 is a constant. However the non-equilibrium condition of the turbulent core region does not affect the main characteristics of the TNTI layer bounding this region, which is similar in equilibrium and non-equilibrium turbulence. In particular, the thickness of the TNTI layer is similar in both equilibrium and non-equilibrium turbulence.

Propagation and interference of thermal waves in turbulent thermal convection

We observe propagation and interference of two coherent thermal waves in the highly turbulent core of convective Rayleigh-B\'enard flow of cryogenic helium gas generated by top and bottom boundaries with harmonically oscillating temperatures. When the same amplitude of modulation is applied to both plates at slightly different frequencies, the resulting temperature interference pattern in the turbulent core shows a periodic increase and decrease in amplitude. If the observed time record of thermal wave interference were converted to corresponding pressure oscillations and shifted to higher frequencies, one would hear the acoustic beats often used, e.g., in tuning stringed musical instruments.

Properties of the turbulent/non-turbulent layer of a turbulent Boussinesq plume: A study using direct numerical simulation

The turbulent/non-turbulent layer (TNTL) in a turbulent Boussinesq plume is analyzed using direct numerical simulations. The Reynolds number (Re) used in the simulation, based on the scales defined at the bottom hot patch, is 2000, and the Reynolds number (Reλ) based on the Taylor microscale (λ) is 114.4 in the self-similar region. The flow is sufficiently resolved till the Kolmogorov scale. The outer edge of the TNTL is detected using the vorticity magnitude. Conditional statistics of various quantities are calculated with reference to the outer edge of the TNTL, which is referred to as the irrotational boundary (IB). The profiles of conditional vorticity magnitude are used to identify the TNTL and determine its thickness. The presence of viscous superlayer (VSL) and turbulent sublayer (TSL) within the TNTL is revealed by exploring the conditional profiles of the enstrophy transport equation. The baroclinic torque, which is a source of vorticity, has been shown to be inconsequential in determining the width of the VSL. The widths of the TNTL and the VSL are determined to be δTNTL≈15η and δVSL≈3.12η, respectively, where η is the Kolmogorov length scale. This gives the width of the TSL as δTSL=δTNTL−δVSL≈13.88η. The invariants of the velocity gradient tensor have been analyzed across the TNTL. The joint probability density function of the invariants Q and R shows a teardrop shape within the turbulent core. The teardrop shape is not fully developed within the TNTL. The TNTL and the turbulent core have a mixed tendency for irrotational dissipation, vortex sheets, and vortex tubes. When normalized by Kolmogorov length and velocity scales, the conditional statistics of the TNTL of the plume are similar to other turbulent flow types, and hence, this provides additional evidence for the universality of small-scale motion within/around the TNTL of various turbulent flows.

A numerical simulation study of the micro-mechanism of CO2 flow friction in fracturing pipe string

CO2 fracturing is a critical technique for carbon capture, utilization, and storage (CCUS). It has a crucial role in oil-gas development and combating climate change. However, the high flow friction severely affects the fracturing construction. The micro-mechanism of CO2 vertical flow friction in fracturing pipe string is unclear, and it is difficult to experimentally simulate the fracturing conditions. Computational Fluid Dynamics model is used to investigate the micro-mechanism of CO2 flow friction in fracturing conditions to reduce friction. A turbulence model was optimized to accurately calculate the friction of CO2 pipe flow. Subsequently, the relationships between the velocity profile, friction factor, and thickness of viscous sublayer of pure CO2 and thickened CO2 were analysed in fracturing pipe string, wherein the temperature and pressure were in the range of 253.15–343.15 K and 10–60 MPa, respectively. In this paper, the micro-mechanism of CO2 flow friction in fracturing pipe string was revealed and the situation of thickened CO2 was additionally considered, since the effect of the thickener has generally been ignored in previous numerical investigations. The results demonstrated that a uniform velocity profile reduced the friction factor. The temperature and pressure changed the relationship between the thickness of viscous sublayer and roughness, which caused the variation in the friction factor of pure CO2 and thickened CO2. The effect of roughness height on flow was different in the viscous sublayer and turbulent core region. A method was proposed to reduce the friction by optimizing the CO2 thickener and changing flow temperature and pressure.

Tree-based solvers for adaptive mesh refinement code FLASH – III: a novel scheme for radiation pressure on dust and gas and radiative transfer from diffuse sources

ABSTRACT Radiation is an important contributor to the energetics of the interstellar medium, yet its transport is difficult to solve numerically. We present a novel approach towards solving radiative transfer of diffuse sources via backwards ray tracing. Here, we focus on the radiative transfer of infrared radiation and the radiation pressure on dust. The new module, TreeRay/RadPressure, is an extension to the novel radiative transfer method TreeRay implemented in the grid-based Magneto-Hydrodynamics code Flash. In TreeRay/RadPressure, every cell and every star particle is a source of infrared radiation. We also describe how gas, dust, and radiation are coupled via a chemical network. This allows us to compute the local dust temperature in thermal equilibrium, leading to a significantly improvement over the classical grey approximation. In several tests, we demonstrate that the scheme produces the correct radiative intensities as well as the correct momentum input by radiation pressure. Subsequently, we apply our new scheme to model massive star formation from a collapsing, turbulent core of 150 M⊙. We include the effects of both, ionizing and infrared radiation on the dynamics of the core. We find that the newborn massive star prevents fragmentation in its proximity due to radiative heating. Over time, dust and radiation temperature equalize, while the gas temperature can be either warmer due to shock heating or colder due to insufficient dust–gas coupling. Compared to gravity, the effects of radiation pressure are insignificant for the stellar mass on the simulated time-scale in this work.

Turbulence Driving by Interstellar Pickup Ions in the Outer Solar Wind

We revisit the question of how the unstable scattering of interstellar pickup ions (PUIs) may drive turbulence in the outer solar wind and why the energy released into fluctuations by this scattering appears to be significantly less than the standard bispherical prediction. We suggest that energization of the newly picked-up ions by the ambient turbulence during the scattering process can result in a more spherical distribution of PUIs and reduce the generated fluctuation energy to a level consistent with the observations of turbulent intensities and core solar wind heating. This scenario implies the operation of a self-regulation mechanism that maintains the observed conditions of turbulence and heating in the PUI-dominated solar wind.

Near-infrared Polarimetry and H2 Emission toward Massive Young Stars: Discovery of a Bipolar Outflow Associated to S235 e2s3

We present a near-infrared H-band polarimetric study toward the S235 e2s3 protostar, obtained using the POLICAN instrument on the 2.1 m OAGH telescope. The images reveal a bipolar outflow with a total length of about 0.5 pc. The outflow nebulosity presents a high degree of linear polarization (∼80%) and reveals a centrosymmetric pattern with the polarization position angles. The polarization characteristics suggest their origin to be single scattering associated with dust in the outflow. Using multiwavelength archival data, we performed spectral energy distribution (SED) fitting based on radiative transfer models of turbulent core accretion theory. The best-fit SED model indicated that the protostar has a mass of 6.8 ± 1.2 M ⊙, with a disk accretion rate of 3.6 ± 1.2 × 10−4 M ⊙ yr−1 and a total bolometric luminosity of 9.63 ± 2.1 × 103 L ⊙. Narrowband H2 (2.12 μm) observations show shocked emission along the bipolar lobes tracing the jet’s interaction with the surrounding medium. The estimated H2 luminosity of the outflow is , which matched the known power-law correlation with the source bolometric luminosity, similar to other high-mass outflows. The orientation of the bipolar outflow was found to be parallel to the local magnetic field direction. The overall results assert the fact that the S235 e2s3 source is a massive young star driving a highly collimated bipolar outflow through disk accretion.

The SOFIA Massive (SOMA) Star Formation Survey. IV. Isolated Protostars

We present ∼10–40 μm SOFIA-FORCAST images of 11 isolated protostars as part of the SOFIA Massive (SOMA) Star Formation Survey, with this morphological classification based on 37 μm imaging. We develop an automated method to define source aperture size using the gradient of its background-subtracted enclosed flux and apply this to build spectral energy distributions (SEDs). We fit the SEDs with radiative transfer models, developed within the framework of turbulent core accretion (TCA) theory, to estimate key protostellar properties. Here, we release the sedcreator python package that carries out these methods. The SEDs are generally well fitted by the TCA models, from which we infer initial core masses M c ranging from 20–430 M ⊙, clump mass surface densities Σcl ∼ 0.3–1.7 g cm−2, and current protostellar masses m * ∼ 3–50 M ⊙. From a uniform analysis of the 40 sources in the full SOMA survey to date, we find that massive protostars form across a wide range of clump mass surface density environments, placing constraints on theories that predict a minimum threshold Σcl for massive star formation. However, the upper end of the m *−Σcl distribution follows trends predicted by models of internal protostellar feedback that find greater star formation efficiency in higher Σcl conditions. We also investigate protostellar far-IR variability by comparison with IRAS data, finding no significant variation over an ∼40 yr baseline.

Numerical study on the pulsating energy evolution in the cavitating flow around a mini Cascade

Cavitation is arguably a highly turbulent phenomenon in the liquid flow system. The cavitating flow around a mini cascade was carried out to investigate the turbulent characteristics and pulsation mechanisms. The results demonstrate that cavitation can significantly affect the turbulence velocity fluctuation and turbulence anisotropy, and intensively alter the local turbulent energy. To better provide an understanding of fundamental mechanisms dictating time-averaged pulsating energy, the inhomogeneity of the local concentration of pulsating energy at the vapor–liquid interface and the turbulent vortex core involves different fundamental mechanisms are expounded thoroughly through the ability of the time-averaged turbulent kinetic energy and the time-averaged pulsating entropy. The pulsating energy of cavitating flow around the mini cascade is basically obtained from the time-averaged flow, while the surrounding dissipative mechanisms are driven by the diffusion and dissipation terms. Further, the new definition of viscous diffusion term is derived based on the resolved turbulent kinetic energy, which can also clearly delineate the diffusion effect of turbulent kinetic energy produced by the molecule viscosity. Finally, the turbulent kinetic energy and pulsating enstrophy transport mechanisms inside the shedding vortex are revealed as significant characteristics of the interaction between vortex dynamics and turbulence–cavitation.

Numerical simulation and experimental validation for investigating the novel hydraulicbarrier-hydrocyclone in industrial beneficiation process

In the face of the dwindling reserves of high-quality phosphate rock resources in the world, beneficiation and purification of low-grade phosphate ore is a possible solution to alleviate the growing scarcity for strategic phosphorus resources. Hydrocyclone is one of the common equipment for solid–solid separation in liquid medium, which is suitable for mineral beneficiation processing. The study investigated the industrial beneficiation of low-grade phosphate ore by novel hydraulicbarrier-hydrocyclone. The results from computational fluid dynamics (CFD) simulation revealed that Semi-through hydraulicbarrier (S-Hb) hydrocyclone had the optimal performance, making short-circuit flow reduced to 7.17% and eliminating fish hook effect, so that the classification efficiency increased by 5% and separation sharpness reached 0.9516. The reasons leading to performance intensification were elaborated in accordance with the optimization and integration of hydrodynamics multiphase flow field by hydraulicbarrier, including the pressure, velocity, turbulent kinetic energy distribution and air core development, as well as streamline analysis, etc. The results from practical industrial experiment indicated that the P2O5 grade was increased to 23.6wt.% from an initial grade of 17.5wt.%, meeting the medium-grade phosphate ore specifications, and the SiO2 content was decreased from 29.0wt.% to 4.2wt.%, meanwhile, the proportional error was 0.74% about cutting size compared to simulation results, indicating excellent consistency. The investigation offered an economically viable route to beneficiate the low-grade phosphate ore, cogently supporting sustainable development of phosphorus resources in chemical engineering.

Application of Prandtl, von Kármán, and lattice Boltzmann methods to investigations of turbulent slip incompressible flow in a flat channel

The paper focuses on the modeling of turbulent slip incompressible flow in a flat channel. Slippage on the channel wall can be caused by two reasons. The first reason is microchannels when the mean free path of molecules exceeds a certain value, which is characterized by the Knudsen number. The second reason is hydrophobic surfaces, which are used to reduce hydraulic resistance. Two models of turbulence were used to derive analytical solutions of fully developed flow. The first model is the Prandtl model (model of mixing length). The second model is the von Kármán model (model of similarity of pulsation velocities). Analytical models were built in a two-layer approximation: a laminar sublayer and a turbulent core. Both models showed a good agreement with the lattice Boltzmann method. An increase in the Knudsen number leads to an increase in the flow rate and a decrease in shear stress on the walls, which reduces the friction factor. This is due to the weakening of the interaction between the flow and the wall, which also leads to a decrease in the shear stress on the walls. As the Reynolds number increases, this effect becomes more noticeable.

Effects of crosswinds and tip configurations on the initial phase of wingtip vortex evolution

Wingtip vortex is the initial phase of aircraft wake flow that jeopardizes flight safety. Previous studies have focused on the effect of incidence angle on tip vortex flow; thus, investigations on tip vortex in the roll-up stage under crosswind conditions are limited. In the present study, two NACA0012 wings with different tip shapes (round and square) were numerically analyzed to explore the effects of wingtip configurations on tip vortex. In addition, the effects of crosswinds on wingtip vortex evolution were also investigated. It was found that sharp edges of the square wingtip generated a multi-vortex system, resulting in a larger turbulent wake vortex core radius. The lift and vortex strength of the square wingtip were 23% higher and only 12% stronger than those of the round wingtip, respectively. Furthermore, crosswinds changed both the pressure distribution and the vortex structure. Crosswinds made the flow field unstable; hence, upwind lower edge vortices of the square wingtip burst earlier and merged faster. Consequently, the tightness of the upwind vortex of the square wingtip increased, and the corresponding vortex strength was enhanced. The downwind vortex of the square wingtip was weakened by 2.7% under a crosswind velocity of 4 m/s, whereas the downwind tip vortex of the round wingtip was strengthened under the same conditions.

Mechanism for turbulence proliferation in subcritical flows

The subcritical transition to turbulence, as occurs in pipe flow, is believed to generically be a phase transition in the directed percolation universality class. At its heart is a balance between the decay rate and proliferation rate of localized turbulent structures, called puffs in pipe flow. Here, we propose the first-ever dynamical mechanism for puff proliferation—the process by which a puff splits into two. In the first stage of our mechanism, a puff expands into a slug. In the second stage, a laminar gap is formed within the turbulent core. The notion of a split-edge state, mediating the transition from a single puff to a two-puff state, is introduced and its form is predicted. The role of fluctuations in the two stages of the transition, and how splits could be suppressed with increasing Reynolds number, are discussed. Using numerical simulations, the mechanism is validated within the stochastic Barkley model. Concrete predictions to test the proposed mechanism in pipe and other wall-bounded flows, and implications for the universality of the directed percolation picture, are discussed.