Entrainment Flux Research Articles

Video-based measurements of the entrainment, speed and mass flux in a wind-blown eruption column

On May 4 2010 a wind-blown ash plume issued from Eyjafjallajökull volcano in Iceland. Analysis of a 17-minute-long video recording of the eruption suggests that, within 2–2.5 km of the vent, the flow was moving with the wind and rising under buoyancy, following a trajectory directly analogous with laboratory experiments of turbulent buoyant plumes in a cross-flow. The radius of the time-averaged ash cloud grew with height z at a rate r = 0.48 z, corresponding to an entrainment coefficient 0.4, again consistent with laboratory experiments. By analysing the frames in the video and comparing the shape of the plume to that predicted by the model, we estimate that during the 17 minutes recorded, the eruption rate gradually decreased by about 43% from an initial rate of 1.11 × 104 kg s−1 to 0.63 × 104 kg s−1. The analysis reported herein opens the way to assess eruption rates and eruption column processes from video recordings during explosive volcanic eruptions.

Entrainment and mixing of unsteady gravity currents in compound channels

Compound channels are a common hydraulic section of many alluvial and fluvial systems, serving as conduits for the flow of water and sediment. The proper design of these structures requires an understanding of the entrainment and mixing mechanisms in them. This paper presents a three-dimensional numerical study of lock-exchange flow in a compound channel covering the Reynolds numbers (Re) range of 17[Formula: see text]000–39[Formula: see text]000. This study investigates flow structures and mixing patterns for various geometries and flow characteristics. The results show that the entrainment coefficient decreases as the dense flow progresses, and the amplitude of instantaneous mixing fluctuations decreases with an increase in the width of the floodplain and reduced gravity. The averaged flux entrainment profiles show a minimum at [Formula: see text] at different times in the front area. In the head area also, a downward concavity can be seen in the profiles around [Formula: see text]. This study also reveals that changes in floodplain height do not affect the establishment of lobe-and-cleft instability. The wider the floodplain channel, the larger the lobe-and-cleft instability created. Small-scale mixing dominates at high Reynolds numbers, leading to higher fluid mixing.

Impact of Uncertainties in the Atmospheric Boundary Layer Height on the Numerical Simulation of Chemical Species

Uncertainties in the atmospheric boundary layer height (ABL-H) are associated either with the uncertainties in meteorological fields or the definition of the ABL-H. When the ABL-H is involved in ABL parameterization schemes these uncertainties can have impacts on numerical simulation of chemical species. The impacts are examined numerically by employing a 1-D diffusion model with the K-profile scheme and 3-D air quality forecast model with the turbulent kinetic energy (TKE)-based scheme. The dependency on the ABL-H in the two schemes is very different. Sensitivity tests with the 1-D model show that the over-estimated/under-estimated ABL-H leads to the decrease/increase of concentration of tracers under both stable and unstable conditions due to the increase/decrease of the volume of tracers within the ABL. Under unstable conditions, the over-estimated/under-estimated ABL-H also enhances/weakens the vertical diffusivity, and leads to the decrease/increase of the concentration of tracers for the negative/positive vertical gradient of tracer. These impacts result in a little change with height within the ABL. The impacts of the ABL-H through the counter-gradient term and entrainment flux are much smaller than the impact through changing the volume of the ABL and vertical diffusivity in the ABL. Sensitivity tests with the 3-D numerical model with the TKE scheme show that over urban areas the over-estimated/under-estimated ABL-H leads to the increase/decrease of TKE in the whole ABL but does not always lead to stronger/weaker diffusivity and lower/higher concentrations of chemical species.

Local entrainment across a TNTI and a TTI in a turbulent forced fountain

Local instantaneous exchanges of volume, momentum and buoyancy across turbulent/non-turbulent interfaces (TNTIs) and turbulent/turbulent interfaces (TTIs) are studied using data from direct numerical simulations of a turbulent forced fountain. We apply a novel algorithm that enables independent calculation of the instantaneous local entrainment and detrainment fluxes, and therefore, for the first time, the entrainment and detrainment coefficients according to the fountain model (Bloomfield & Kerr, J. Fluid Mech., vol. 424, 2000, pp. 197–216) are determined explicitly. Across the interface between the fountain and the ambient fluid, which is a TNTI, only volume entrainment occurs, and it is well predicted by the fountain model. Across the interface between the rising upflow and falling downflow within the fountain, which is a TTI, both entrainment and detrainment of volume, momentum and buoyancy occur – with the magnitude of both entrainment and detrainment typically being large compared with the net for all exchanges. However, the model seems to be unable to capture the momentum exchanges due to its ignorance of the pressure. We find that each conditional entrainment and detrainment rate, of volume, momentum and buoyancy, can be described accurately by Gaussian profiles, while the net exchange that is the superposition of the entrainment and detrainment cannot. Moreover, the entrainment exchange rate has its maximum closer to the fountain centreline than that of detrainment, explaining the tendency for net entrainment closer to the fountain centreline and net detrainment further away.

The relative efficiencies of the entrainment of mass, momentum and kinetic energy from a turbulent background

We derive expressions relating the entrainment fluxes of momentum and kinetic energy, relative to the mass flux entrained into a turbulent wake exposed to a turbulent background. These expressions contain correlations between the entrainment velocity and the turbulent fluctuations within the background. We perform high-resolution, simultaneous particle image velocimetry and planar laser-induced fluorescence experiments, and observe these correlations to be negligible in the far wake, such that momentum and kinetic energy are entrained into the wake with the same relative efficiency to mass as from an idealised, non-turbulent background. This is a useful result in the context of modelling, since the entrainment hypothesis (Turner, J. Fluid Mech., vol. 173, 1986, pp. 431–471) can still be used to model the entrainment of momentum and kinetic energy. Nevertheless, the entrainment rate of mass is shown to vary spatially, and with the specific nature of the background turbulence, so this in turn drives a spatial/background-turbulence-specific entrainment rate of momentum/kinetic energy. Contrastingly, in the near wake, whilst momentum is entrained from a turbulent background with the same relative efficiency to mass as for an idealised non-turbulent background, this is not the case for kinetic energy. Owing to the sum of multiple positive, small-valued correlations between the fluctuations in the background and the entrainment velocity, kinetic energy is entrained more efficiently than in the idealised case. This includes entrainment from a non-turbulent background, where small correlations are observed between the irrotational background fluctuations and the entrainment velocity. Evidence is also presented that the entrainment velocity scales with the Kolmogorov velocity scale when the background is turbulent.

The influence of roughness-element-spacing on turbulent entrainment over spanwise heterogeneous roughness

Spanwise heterogeneous surfaces have been found to modulate local turbulent entrainment by inducing large-scale secondary flows (SFs). This work aims to clarify the variations of the local and total entrainment fluxes with the intensity of SF. The SF intensity is controlled by the spanwise spacing between adjacent ridge-type roughness elements s. It is found that, for the two components of turbulent entrainment (nibbling and engulfment), their local fluxes grow rapidly with the SF intensity in the downwash regions; asymmetrically, both fluxes decline slowly and then become relatively stable in the upwash regions. In other words, the downwash flow is more effective in modulating the local entrainment flux than the upwash flow. Therefore, the largest total entrainment flux would be induced at s≈δ, where the SF intensity is the largest (δ is the boundary layer thickness). Moreover, the emergence of the tertiary flow when s≳2δ would lower the local entrainment flux, and reduce the total flux to the same level of the homogeneous roughness. Therefore, it is deduced that a heterogeneous surface with a large roughness-element spacing could not enhance the total entrainment flux.

Base suction, entrainment flux, and wake modes in the vortex formation region at the rear of a three-dimensional blunt bluff body.

A slitted base cavity of constant depth with a varying filling ratio 0≤R_{f}≤100% is experimentally investigated to reduce the form drag of a three-dimensional blunt body (the so-called squareback Ahmed body) at a Reynolds number Re=2.89×10^{5}. The drag reduction is achieved by a decrease of base suction (or, equivalently, the increase of pressure at the base). The plain cavity (R_{f}=100%) reduces the base suction by 22% compared to the case with no cavity (R_{f}=0). All intermediate filling ratio are obtained by the enlargement of the slits, initially having a zero width for the plain cavity case. It is shown that the gradual base suction change can be related to the level of the entrainment flux of the free shear layers developing from the rear separation and to the suppression of the transverse steady asymmetric instability of the wake. The model of the vortex formation region length of Gerrard [J. Fluid Mech. 25, 401 (1966)0022-112010.1017/S0022112066001721] is shown to provide an insightful interpretation of the drag reduction mechanism using ventilated base cavities.

A Methodology for Estimating the Energy and Moisture Budget of the Convective Boundary Layer Using Continuous Ground-Based Infrared Spectrometer Observations

Abstract Land–atmosphere interactions play a critical role in both the atmospheric water and energy cycles. Changes in soil moisture and vegetation alter the partitioning of surface water and energy fluxes, influencing diurnal evolution of the planetary boundary layer (PBL). The mixing-diagram framework has proven useful in understanding the evolution of the heat and moisture budget within the convective boundary layer (CBL). We demonstrate that observations from the Department of Energy Atmospheric Radiation Measurement (ARM) Southern Great Plains site provide all of the needed inputs needed for the mixing-diagram framework, allowing us to quantify the impact from the surface fluxes, advection, radiative heating, encroachment, and entrainment on the evolution of the CBL. Profiles of temperature and humidity retrieved from the ground-based infrared spectrometer [Atmospheric Emitted Radiance Interferometer (AERI)] are a critical component in this analysis. Large-eddy simulation results demonstrate that mean mixed-layer values derived are shown to be critical to close the energy and moisture budgets. A novel approach demonstrated here is the use of network of AERIs and Doppler lidars to quantify the advective fluxes of heat and moisture. The framework enables the estimation of the entrainment fluxes as a residual, providing a way to observe the entrainment fluxes without using multiple lidar systems. The high temporal resolution of the AERI observations enables the morning, midday, and afternoon evolution of the CBL to be quantified. This work provides a new way to use observations in this framework to evaluate weather and climate models. Significance Statement The energy and moisture budget of the planetary boundary layer (PBL) is influenced by multiple sources, and accurately representing this evolution in numerical models is critical for weather forecasts and climate predictions. The mixing-diagram approach, driven by profiling observations as illustrated here, provides a powerful way to quantify the contributions from each of these sources. In particular, the energy and moisture mixed into the PBL from above the PBL can be determined accurately from ground-based remote sensors using this approach.

Entrainment at multi-scales in shear-dominated and Rayleigh–Taylor turbulence

A partially turbulent flow continuously incorporates irrotational fluid into the turbulent region, a phenomenon known as entrainment. Although entrainment locally acts at viscous scales, the thin interface separating the turbulent from the irrotational region is extremely convoluted, and twisted in such a way that renders the global entrainment flux scale-independent. Despite turbulent entrainment being widely recognized as a multi-scale process, the theoretical basis for quantifying the entrainment flux at multi-scales is lacking. In this paper we derive an equation that allows us to quantify the local entrainment velocity at multi-scales. This is done by defining the local entrainment velocity as the propagation speed of an iso-surface of filtered enstrophy relative to the coarse-grained velocity field, and using the filtered enstrophy budget to split the total velocity into its individual components, i.e. viscous, inviscid, baroclinic and sub-filter. The equation is used to investigate the entrainment at multi-scales in simulated turbulent mixing layers, where turbulence is sustained by either a mean shear or an unstable buoyancy gradient (Rayleigh–Taylor turbulence).

Turbulent structure of the Arctic boundary layer in early summer driven by stability, wind shear and cloud-top radiative cooling: ACLOUD airborne observations

Abstract. Clouds are assumed to play an important role in the Arctic amplification process. This motivated a detailed investigation of cloud processes, including radiative and turbulent fluxes. Data from the aircraft campaign ACLOUD were analyzed with a focus on the mean and turbulent structure of the cloudy boundary layer over the Fram Strait marginal sea ice zone in late spring and early summer 2017. Vertical profiles of turbulence moments are presented from contrasting atmospheric boundary layers (ABLs) from 4 d. They differ by the magnitude of wind speed, boundary-layer height, stability, the strength of the cloud-top radiative cooling and the number of cloud layers. Turbulence statistics up to third-order moments are presented, which were obtained from horizontal-level flights and from slanted profiles. It is shown that both of these flight patterns complement each other and form a data set that resolves the vertical structure of the ABL turbulence well. The comparison of the 4 d shows that especially during weak wind, even in shallow Arctic ABLs with mixing ratios below 3 g kg−1, cloud-top cooling can serve as a main source of turbulent kinetic energy (TKE). Well-mixed ABLs are generated where TKE is increased and vertical velocity variance shows pronounced maxima in the cloud layer. Negative vertical velocity skewness points then to upside-down convection. Turbulent heat fluxes are directed upward in the cloud layer as a result of cold downdrafts. In two cases with single-layer stratocumulus, turbulent transport of heat flux and of temperature variance are both negative in the cloud layer, suggesting an important role of large eddies. In contrast, in a case with weak cloud-top cooling, these quantities are positive in the ABL due to the heating from the surface. Based on observations and results of a mixed-layer model it is shown that the maxima of turbulent fluxes are, however, smaller than the jump of the net terrestrial radiation flux across the upper part of a cloud due to the (i) shallowness of the mixed layer and (ii) the presence of a downward entrainment heat flux. The mixed-layer model also shows that the buoyancy production of TKE is substantially smaller in stratocumulus over the Arctic sea ice compared to subtropics due to a smaller surface moisture flux and smaller decrease in specific humidity (or even humidity inversions) right above the cloud top. In a case of strong wind, wind shear shapes the ABL turbulent structure, especially over rough sea ice, despite the presence of a strong cloud-top cooling. In the presence of mid-level clouds, cloud-top radiative cooling and thus also TKE in the lowermost cloud layer are strongly reduced, and the ABL turbulent structure becomes governed by stability, i.e., by the surface–air temperature difference and wind speed. A comparison of slightly unstable and weakly stable cases shows a strong reduction of TKE due to increased stability even though the absolute value of wind speed was similar. In summary, the presented study documents vertical profiles of the ABL turbulence with a high resolution in a wide range of conditions. It can serve as a basis for turbulence closure evaluation and process studies in Arctic clouds.

Numerical and Physical Simulation of Flux Entrainment Mechanism in Mechanical Stirring Processes

Numerical and Physical Simulation of Flux Entrainment Mechanism in Mechanical Stirring Processes

Characteristics of a pre-monsoon dryline atmospheric boundary layer over the rain shadow region: A case study

A dryline is the zone of distinct moisture gradient separating warm, moist, and hot, dry air masses. It is usually associated with mesoscale phenomena and plays a significant role in atmospheric boundary layer (ABL) dynamics including initiation of convection/thunderstorms. In the tropical Indian region, these dryline conditions are normally associated with the pre-monsoon season. In the present study, dryline characteristics over a rain shadow region in the Indian subcontinent were investigated utilizing observations and Weather Research and Forecasting (WRF) model from 28 to 30 May 2019. Based upon Wind Profiler Radar and MicroWave Radiometer Profiler measurements, the ABL characteristics were investigated. Interestingly, the ABL height was found to evolve up to 5 km with the horizontal wind vectors oscillating between north-westerly and north-easterly flow. During the intense ABL deepening, stronger downdraft cores were observed in comparison with the updraft cores. The stronger downdrafts entrained free-tropospheric dry air thereby further deepening the ABL. Based upon the entrainment velocity estimates at the ABL top and the variations in potential temperature, the dynamic entrainment fluxes were estimated and further implemented for evaluating two slab models to recreate the ABL growth. With this analysis, we demonstrate the significant contribution of entrainment fluxes on ABL growth during dryline conditions.

“Turbulent/non-turbulent interface” in a low-Reynolds-number transitional boundary layer over a multi-element airfoil

Akin to the turbulent/non-turbulent interface, which envelops a fully developed turbulence, the iso-vorticity interface that separates the irrotational fluids from the free stream is investigated in a transitional boundary layer over a multi-element airfoil. Geometrically, the interface is steady and flat at the initial transitional stage. With the progress of transition, the interface fluctuates more and more violently. Statistically, the evolution of interface properties, including the fluctuation of interface height σI, the fractal dimension Df, and the thickness of interface δI, are tracked along the streamwise direction. It is revealed that all the three quantities grow with transition. Both σI and δI become invariant at the latter half part of the airfoil where the transition is completed. Counter-intuitively, the growth of Df stops at a more upstream location, indicating the fractal property of turbulence is already existing during transition. Instantaneously, the above-mentioned quantities are found to be related to the periodical vortices inside the boundary layer. The vortex will elevate/sink the above interface by the induced ejection/sweep flow and increases Df at slightly downstream of the vortex. Furthermore, it is highlighted that the variations of interface properties will greatly influence the entrainment by two opposite effects: the length of interface LI and the vorticity gradient across the interface; and it is found that the entrainment flux is mainly controlled by LI. This suggests that the recently reported dominance of LI on entrainment for wall-bounded turbulence could be a universal phenomenon in boundary layers, despite the flow states and wall configurations.

Vertical aerosol particle exchange in the marine boundary layer estimated from helicopter-borne measurements in the Azores region

Abstract. Aerosol particles are important for radiation effects, cloud formation, and therefore the climate system. A detailed understanding of the spatial distribution of aerosol particles within the atmospheric boundary layer, which depends on sources and sinks, as well as long-range transport and vertical exchange, is important. Especially in marine regions, where the climate effect of clouds is comparably high, long-range transport with subsequent vertical mixing dominates over local aerosol sources. In this study, three different methods were applied to estimate the vertical aerosol particle flux in the marine boundary layer (MBL) and the vertical exchange between the MBL and the free troposphere (FT): eddy covariance (EC), flux–gradient similarity (K theory), and the mixed-layer gradient method (MLG). For the first time, MBL aerosol fluxes derived from these three methods were compared in the framework of the “Azores Stratocumulus Measurements of Radiation, Turbulence and Aerosols” (ACORES) field campaign in the Azores region in the northeastern Atlantic Ocean in July 2017. Meteorological parameters and aerosol and cloud properties were measured in the marine troposphere using the helicopter-borne measurement platform ACTOS (Airborne Cloud Turbulence Observation System). All three methods were applied to estimate the net particle exchange between MBL and FT. In many cases, the entrainment fluxes of the MLG method agreed within the range of uncertainty with the EC and K-theory flux estimates close to the top of the MBL, while the surface flux estimates of the different methods diverged. It was not possible to measure directly above the surface with the helicopter-borne payload, which might be a source of uncertainty in the surface fluxes. The observed particle fluxes at the top of the MBL ranged from 0 to 10×106 m−2 s−1 both in the upward and the downward direction, and the associated uncertainties were on the same order of magnitude. Even though the uncertainties of all three methods are considerable, the results of this study contribute to an improved understanding of the transport of particles between the MBL and FT and their distribution in the MBL.

Aerosol-boundary layer interaction modulated entrainment process

Aerosol-boundary layer interactions play an important role in affecting atmospheric thermodynamics and air pollution. As a key factor in dictating the development of the boundary layer, the entrainment process in the context of aerosol-boundary layer interactions is still poorly understood. Using comprehensive field observations made at a superstation in Beijing, we gain insight into the response of the entrainment process to aerosols. We found that high aerosol loading can significantly suppress the entrainment rate, breaking the conventional linear relationship between sensible heat fluxes and entrainment fluxes. Related to aerosol vertical distributions, aerosol heating effects can alter vertical heat fluxes, leading to a strong interaction between aerosols and the entrainment process in the upper boundary layer. Such aerosol-entrainment coupling can inhibit boundary layer development and explains the great sensitivity of observed entrainment rates to aerosols than can traditional calculations. The notable impact of aerosols on the entrainment process raises holistic thinking about the dynamic framework of the boundary layer in a polluted atmosphere, which may have a significant bearing on the dispersion of air pollutants and the land-atmosphere coupling.

Nonlinearly interacting entrainment due to shear and convection in the surface ocean

Large-eddy simulations were performed to investigate the entrainment buoyancy flux at the mixed layer base due to nonlinearly interacting shear-driven turbulence (ST) and convective turbulence (CT). The fluxes due to pure ST and pure CT were first evaluated, and their scalings were derived. The entrainment flux due to coexisting ST and CT was then evaluated and compared to the scaling-based fluxes due to the pure turbulences. It was found that nonlinear effects reduce the entrainment flux by 30 % when the turbulent kinetic energy production rates of ST and CT are comparable. The mixing parameterization schemes used in ocean general circulation models (OGCMs) fail to accurately reproduce the mixing due to the pure turbulences and/or the nonlinear effects, and thus the mixed layer depth (MLD). Because analysis using global datasets suggests that nonlinear effects are large at the mid-latitudes, these results indicate that the nonlinear effects might be responsible for the deep MLD biases in OGCMs and that mixing parameterization schemes need to be improved to correctly represent ocean surface mixing due to shear and convection, as well as waves, in OGCMs.

Mathematical Modeling of Mold Flow Field and Mold Flux Entrainment Assisted With High-Temperature Quantitative Velocity Measurement and Water Modeling

Mathematical Modeling of Mold Flow Field and Mold Flux Entrainment Assisted With High-Temperature Quantitative Velocity Measurement and Water Modeling

Identification of the atmospheric boundary layer structure through vertical distribution of PM2.5 obtained by unmanned aerial vehicle measurements

Variations in the atmospheric boundary layer (ABL) structure present a close relationship with the vertical diffusion of air pollutants. However, the effect of the ABL structure on the vertical distribution of air pollutants is rarely investigated in detail, especially through in-situ measurement. In this study, from November 26th to December 20th, 2017, an unmanned aerial vehicle (UAV) outfitted with sensors was used to monitor meteorological factors and pollutants concentrations (including PM2.5, O3, and BC) in the suburbs of Shanghai. According to the vertical profiles of PM2.5 concentrations, the gradient and the lidar backscatter methods were used to determine the parameters of the ABL structure. Results indicate that the maximum height of the atmospheric boundary layer occurred at noon exceeding 1000 m, and the maximum thickness of the atmospheric entrainment layer occurred at twilight exceeding 360 m during the field campaign. Additionally, the relationships between the structure of ABL and pollutant concentrations were analyzed and quantified. In contrast to the height of the ABL, the concentrations of ground-level aerosol pollutants show a stronger correlation with the thickness of the atmospheric entrainment layer. It also confirms that the entrainment flux ratio was an important factor affecting ground-level ozone concentrations. In summary, the in-situ measurements can provide experimental support for modeling the ABL structure and provide insights for the control of aerosol pollution.

Impact of wind farm wakes on flow structures in and around downstream wind farms

We performed large-eddy simulations in a neutral atmospheric boundary layer to study the interaction between two identical wind farms with 72 turbines each. We demonstrate that the wind farm wake created by the upstream farm affects the entire flow in and around the downstream farm. The vertical entrainment fluxes above the downstream wind farm are strengthened, resulting in a faster wind farm wake recovery behind the downstream farm. These findings illustrate that interaction between extended wind farms affects flow structures beyond the wind farm scale. Furthermore, we demonstrate that wind farm wakes can reduce the power production of turbines throughout the downstream wind farms. We additionally observe that a staggered wind farm extracts more energy from the flow and thus creates a stronger wind farm wake than an aligned wind farm.

Characteristics of sliver defects caused by mould flux entrainment on the surface of the hot-dip galvanised automobile exposed panel

ABSTRACT The characteristics of sliver defects caused by entrained mold fluxes were analyzed after nonaqueous electrolysis. There are three types of entrained mold fluxes, namely the granular, flaky and blocky. When the entrained mold fluxes are small, they are granular or flaky. When the entrained mold fluxes are large, they are blocky or flaky. From the start part of the defect zone, the area fraction of the entrained mold fluxes per unit area decreases exponentially with the length of defect. After the mold fluxes are entrained into the molten steel, SiO2 will react with Al and Ti, resulting in the changes in compositions of mould powders. On the cross-section, the zinc layer thickness in the defect zone, is 22–35 μm, thicker than that in the non-defect zone. Near the entrained mold fluxes, the randomness of grain orientation and the inhomogeneity of grain size are increased and the local grains are refined.