Entrainment Flux Research Articles

Mean Profiles of Moisture Fluxes in Snow-Filled Boundary Layers

Profiles of moisture fluxes have been examined for convective boundary layers containing clouds and snow, using data derived from aircraft measurements taken on four dates during the 1983/1984 University of Chicago lake-effect snow project. Flux profiles were derived from vertical stacks of aircraft cross-wind flight legs taken at various heights over Lake Michigan near the downwind shore. It was found that, if ice processes are taken into account, profiles of potential temperature and water content were very similar to those presented in past studies of convective boundary layers strongly heated from below. Profiles of total water content and equivalent potential temperature adjusted for ice were nearly invariant with height, except very near the top of the boundary layer, suggesting that internal boundary-layer mixing processes were rapid relative to the rates at which heat and vapour were transported into the boundary layer through entrainment and surface fluxes. Ice was found to play a significant, measurable role in boundary-layer moisture fluxes. It was estimated that 40 to 57% of the upward vapour flux was returned to the surface in the form of snow, converting about 45 to 64% of the surface latent heat flux into sensible heat in the snow-producing process. Assuming advective fluxes are relatively small (thought to be appropriate after the first few tens of km over the lake as suggested by past studies), the boundary layer was found to warm at a rate faster than could be explained by surface heat fluxes and latent heat releases alone, the remainder of the heating presumably coming from radiational processes and entrainment. Discussions of moisture phase change processes throughout the boundary layer and estimates of errors of these flux measurements are presented.

Entrainment of FCC from fluidized beds — A new correlation for the elutriation rate constants Ki∞ *

Batch and continuous experiments of fluidization have been carried out in columns of diameter 76 and 152 mm. Gas velocities of 0.1–0.8 m/s were used with mixtures of coarse and fine FCC as the feed materials. The total entrainment flux E Z and the elutriation rate constants K i∞ * are found to depend on the gas velocity in the form of E Z ∝ U n and K i∞ * ∝ U m , respectively. The values of n and m depend on the bed compositions and particle size; they become smaller at higher gas velocities. For FCC, n has an average value of 4.0 in the velocity range 0.2–0.4 m/s and tends to a value of 2 at higher gas velocities. The effect of column diameter depends on the gas velocity profiles and is reduced for column diameters above 0.1 m. Empirical correlations to predict K i∞ * and E Z have been developed from the results.

ENTRAINMENT OF FINES FROM FLUIDIZED BEDS WITH AN EXPANDED FREEBOARD

Apart from accomodating cyclones, expanded freeboards are very effective at reducing the particle carryover from fluidized beds by reducing the superficial gas velocity. However, few experimental studies have been done on this aspect of entrainment. Batch experiments on entrainment have been carried out at velocities of 0.2m/s to 0.8 m/s using Group A FCC powders in 76 mm and 152 mm diameter columns and also in a column constructed from a 76 mm diameter section 1.1m high at the bottom having a 152 mm diameter section with a height of 1.3 m above it. This is referred to as the expanded column. Results show that by doubling the diameter of the top section the total entrainment fluxes, Ez , are reduced to about 1% of the original values. The elutriation rate constants, K* i∞ , of fines entrained from fluidized beds with an expanded freeboard are best calculated using as the equilibrium concentrations those in the dense bed, Xbi , but the gas velocities and the cross sectional area used are those based on the larger expanded section of the column.

AN EMPIRICAL APPROACH TO THE PREDICTION OF ELUTRIATION OF FINES FROM FLUIDIZED BEDS AT DIFFERENT FREEBOARD LEVELS

An empirical approach has been developed to predict the total entrainment flux at different levels of freeboard height. The approach is based on the results of experimental investigations carried out in a 152 mm diameter column, with FCC as the feed powder. The powder was fluidized at superficial gas velocities of 0.2 m/s and 0.7 m/s.

Estimation of boundary layer humidity fluxes and statistics from airborne differential absorption lidar (DIAL)

The water vapor differential absorption lidar (DIAL) of the German Aerospace Research Establishment (DLR) was flown aboard the National Center for Atmospheric Research (NCAR) Electra research aircraft during the Boreal Ecosystem‐Atmosphere Study (BOREAS). The downward looking lidar system measured two‐dimensional fields of aerosol backscatter and water vapor mixing ratio in the convective boundary layer (CBL) and across the CBL top (zt). We show a case study of DIAL observations of vertical profiles of mean water vapor, water vapor variance, skewness, and integral scale in the CBL. In the entrainment zone (EZ) and down to about 0.3 zi the DIAL observations agree with in situ observations and mixed‐layer similarity theory. Below, the water vapor optical depth becomes large and the DIAL signal‐to‐noise ratio degrades. Knowing the water vapor surface flux and the convective velocity scale w* from in situ aircraft measurements, we derive entrainment fluxes by applying the mixed‐layer gradient (MLG) and mixed‐layer variance (MLV) methods to DIAL mixing ratio gradient and variance profiles. Entrainment flux estimates are sensitive to our estimate of zt. They are shown to be rather insensitive to the input surface flux and to the DIAL data spatial resolution within the investigated range. The estimates break down above about 0.9 zt as the flux‐gradient and flux‐variance relationships were developed to describe the large‐scale mixing in the mid‐CBL. The agreement with in situ entrainment flux estimations is within 30% for the MLV method. On a flight leg with significant mesoscale variability the entrainment flux turns out to be 70% higher than the in situ value. This is in good agreement with the fact that large‐eddy simulations (LES) of mean water vapor profiles and variances, upon which the MLG and MLV methods are based, do not include mesoscale variability. The additional water vapor variance from mesoscales may then lead to the overestimate of the flux. Deviations from the in situ observations may also be due to poor LES resolution of small‐scale mixing in the EZ, similarly coarse resolution of the DIAL data, or a capping inversion in the LES model (8 K) which is significantly stronger than the observed inversion (3–4 K).

The effects on water mass formation of surface mixed layer timedependence and entrainment fluxes

An air-sea buoyancy flux out of the ocean between the surface outcroppings of different isopycnals must be balanced by a convergence of advective and diffusive fluxes of buoyancy across those isopycnals (Walin, 1982; Tziperman, 1986; Garrett et al., 1995). For steady conditions, the diapycnal diffusive flux due to vertical mixing in the surface mixed layer is very small, so that the advective buoyancy flux dominates (Speer, 1993; Garrett et al., 1995). The associated advective buoyancy flux can then be used to estimate the volume flux of water out of the base of the surface mixed layer. The resulting thermodynamic algorithm provides a valuable estimate of water mass formation in the ocean. In contrast, for the time-dependent real ocean with horizontal and vertical gradients of the horizontal buoyancy gradient, diurnal and seasonal mixed layer deepening and entrainment in the presence of a buoyancy jump at the base of the mixed layer contributes to the annual volume flux out of the base of the deepest (wintertime) mixed layer. The mismatch between the predictions of the ideal algorithm and measured rates of water mass formation (Speer, 1997) may thus be partly due to mixed layer processes rather than diapycnal mixing in the thermocline.

Role of entrainment in surface‐atmosphere interactions over the boreal forest

We present a description of the evolution of the convective boundary layer (CBL) over the boreal forests of Saskatchewan and Manitoba, as observed by the National Center for Atmospheric Research (NCAR) Electra research aircraft during the 1994 Boreal Ecosystem‐Atmosphere Study (BOREAS). All observations were made between 1530 and 2230 UT (0930–1630 local solar time (LST)). We show that the CBL flux divergence often led to drying of the CBL over the course of the day, with the greatest drying (approaching 0.5 g kg−1 h−1) observed in the morning, 1000–1200 LST, and decreasing over time to nearly no drying (0–0.1 g kg−1 h−1) by midafternoon (1500–1600 LST). The maximum warming (0.45 K h−1 ) also occurred in the morning and decreased slightly to about 0.4 Kh−1 by midafternoon. The CBL vapor pressure deficit (VPD) increased over the course of the day. A significant portion of this increase can be explained by the vertical flux divergence, though horizontal advection also appears to be important. We suggest a linkage among boundary layer growth, the vertical flux divergences, and boundary layer cloud formation, with cloud activity peaking at midday in response to rapid CBL growth, then decreasing somewhat later in the day in response to CBL warming and decreased growth. We also see evidence of feedback between increasing VPD and stomatal control. We use eddy‐covariance flux measurements from the Electra to compute the virtual temperature entrainment ratio Ar. The computed mean value of 0.08±0.12 is somewhat lower than the commonly assumed value of 0.2, as well as with other estimates from BOREAS. This value is very sensitive to the determination of CBL depth. We find that Ar increases with an increasing jump in mean wind across the CBL top. The entrainment flux of water vapor is found to be most dependent on time of day (negative correlation). The ratio of entrainment to surface flux of water vapor is 1.57±0.25. Airborne lidar observations of the CBL top reveal a CBL top “thickness” that is smaller than would be expected from simple theory but consistent with past lidar observations. The normalized thickness is found to have a very consistent value , where 12 cases were examined. A new method of computing the variability of the CBL top is illustrated, and we show that this variance in the CBL depth also scales with the depth but that the value of this normalized variance differs substantially from the “thickness” defined in past literature.

Turbulence, waves and mixing at shear-free density interfaces. Part 1. A theoretical model

This paper presents a theoretical model of turbulence and mixing at a shear-free stable density interface. In one case (single-sided stirring) the interface separates a layer of fluid of density ρ in turbulent motion, with r.m.s. velocity uH and lengthscale LH, from a non-turbulent layer with density ρ+Δρ, while in the second case (double-sided stirring) the lower layer is also in turbulent motion. In both cases, the external Richardson number Ri=ΔbLH/ u2H (where Δb is the buoyancy jump across the interface) is assumed to be large. Based on the hypotheses that the effect of the interface on the turbulence is as if it were suddenly imposed (which is equivalent to generating irrotational motions) and that linear waves are generated in the interface, the techniques of rapid distortion theory are used to analyse the linear aspects of the distortion of turbulence and of the interfacial motions. New physical concepts are introduced to account for the nonlinear aspects.To describe the spectra and variations of the r.m.s. fluctuations of velocity and displacements, a statistically steady linear model is used for frequencies above a critical frequency ωr/μc, where ωr(=Δb/2uH) is the maximum resonant frequency and μc<1. As in other nonlinear systems, observations below this critical frequency show the existence of long waves on the interface that can grow, break and cause mixing between the two fluid layers. A nonlinear model is constructed based on the fact that these breaking waves have steep slopes (which determines the form of the displacement spectrum) and on the physical argument that the energy of the vertical motions of these dissipative nonlinear waves should be comparable to that of the forced linear waves, which leads to an approximately constant value for the parameter μc. The model predictions of the vertical r.m.s. interfacial velocity, the interfacial wave amplitude and the velocity spectra agree closely with new and published experimental results.An exact unsteady inviscid linear analysis is used to derive the growth rate of the full spectrum, which asymptotically leads to the growth of resonant waves and to the energy transfer from the turbulent region to the wave motion of the stratified layer. Mean energy flux into the stratified layer, averaged over a typical wave cycle, is used to estimate the boundary entrainment velocity for the single-sided stirring case and the flux entrainment velocity for the double-sided stirring case, by making the assumption that the ratio of buoyancy flux to dissipation rate in forced stratified layers is constant with Ri and has the same value as in other stratified turbulent flows. The calculations are in good agreement with laboratory measurements conducted in mixing boxes and in wind tunnels. The contribution of Kelvin–Helmholtz instabilities induced by the velocity of turbulent eddies parallel to the interface is estimated to be insignificant compared to that of internal waves excited by turbulence.

Turbulent Bursting-Based Sediment Entrainment Function

One of the basic impediments to a clear understanding of a variety of fundamental problems in the context of sediment transport has been the lack of a well-grounded formulation of bed sediment entrainment. This is dealt with herein, physically based on the mechanism that bed sediment particles are actually entrained by the bursting process inherent in wall turbulent flows. A simple theoretical model for sediment entrainment from flat, loose bed is established using the averaged bursting period scaled on inner variables and the spatial scales of turbulent bursts. Sediment entrainment is shown to depend strongly on bed-shear velocity. The theoretical entrainment flux is compared to available laboratory data sets covering both hydraulically smooth and transitional bed situations. Generally good agreement is obtained, representing the best performance of the present model in relation to existing entrainment functions. It appears to characterize a rather encouraging aspect for a new approach to sediment transport, given the enhanced understanding of turbulent bursting.

A mesoscale simulation of land surface heterogeneity from HAPEX-Sahel

A mesoscale version of the UK Meteorological Office Unified Model has been used to study the evolution of the planetary boundary layer over heterogeneous terrain in the HAPEX-Sahel region. The model simulates a typical diurnal cycle during the dry down period of the intensive observation period on 8 October 1992. The model has a grid length of 10 km, with a domain covering a region of approximately 1000 km 2, centred on the HAPEX experiment. Satellite images are used to generate a mesoscale land cover map over the region. To initialise the soil moisture, a simple soil moisture accounting model was developed. This generates soil moisture patterns from daily rainfall estimates over the entire mesoscale domain. Where possible, the land surface scheme has been calibrated with measurements taken during the experiment. Moisture availability is the principle component in determining the partition of energy at the surface. The mean midday Bowen ratio of the square is 0.82. However, spatial contrasts in soil moisture availability lead to a range of midday sensible heat fluxes of between 100 W m −2 and 280 W m −2. The pattern of surface fluxes is closely related to the mesoscale variation of the seasonal rainfall. Comparisons of the model output with surface meteorology, surface fluxes, sonde and aircraft measurements are encouraging. Both model and climate observations show similar gradients at the surface across the square. Features of the aircraft measurements are well represented by the model. Anomalous increases in latent heat flux with height measured by the aircraft are also found in the model. This may be related to high entrainment fluxes at the inversion separating contrasting air flows. Heat and moisture budget calculations show the importance of large scale flow in the evolution of the boundary layer. Periods of low level south-westerly flow for example produce considerably larger inputs of moisture into the planetary boundary layer than surface evaporation. In this study, the influence of surface flux variability on the boundary layer is limited. However, scaling surface fluxes up to larger scales must take some account of the considerable variation in soil moisture.

Surface layer response to weak winds, westerly bursts, and rain squalls in the western Pacific warm pool

In November–December 1992, we measured microstructure, the hydrographic field, and the velocity field in the western equatorial Pacific near 1°43′S and 156°E as the first part of the Tropical Ocean ‐ Global Atmosphere ‐ Coupled Ocean Atmosphere Response Experiment. During our stay, we observed two westerly wind bursts with maximum speeds of about 10 m s−1, rainfalls of about 20 mm h−1, and nearly 2 weeks of calm and dry weather. During wind bursts, mixing in the upper 1 MPa was dramatic and rapid, and the major turbulence in the thermocline was produced by near‐inertial shears following the wind bursts, during which dissipation rates and Richardson numbers were comparable to those in the central Pacific. By the end of the October–November westerly burst, the averaged eddy diffusivity of momentum in the mixed layer was about 10−2 m2 s−1. Below the mixed layer, a layer about 0.50–0.75 MPa thick with high shear and strain along with a high dissipation rate persisted even after the wind burst. During calm days, mixing was primarily driven by nighttime convection and was confined to the upper 0.1 or 0.2 MPa. In general, no diurnal deep cycle in dissipation rate was found below the mixed layer, unlike in the central equatorial Pacific. Entrainment below the mixed layer occurred when both wind work and convection were large. On average, the entrainment heat flux at the base of the mixed layer was about 6 (±2) W m−2. Salinity gradients were important to density between 0.3 and 0.6 MPa. However, the salinity stratification did not control entrainment mixing. During calm and dry weather, the mixed layer heat content was governed by the vertical divergence of the radiative flux, that is, the net surface heat flux minus the radiative flux out the bottom of the layer. Both the entrainment flux and the advective flux (which was estimated as the residual term) were smaller than uncertainties in the surface heat flux. During the October–November wind burst, however, the advective term was one of the most dominant terms in the heat budget. Although the entrainment heat flux was small over short timescales, it may be important in long‐term budgets because the long‐term net surface heating could also be small.

An evaluation of neutral and convective planetary boundary-layer parameterizations relative to large eddy simulations

This paper compares a number of one-dimensional closure models for the planetary boundary layer (PBL) that are currently in use in large-scale atmospheric models. Using the results of a large-eddy simulation (LES) model as the standard of comparison, the PBL models are evaluated over a range of stratifications from free convective to neutral and a range of surface shear stresses. Capping inversion strengths for the convective cases range from weakly to strongly capped. Six prototypical PBL models are evaluated in this study, which focuses on the accuracy of the boundary-layer fluxes of momentum, heat, and two passive scalars. One scalar mimics humidity and the other is a top-down scalar entrained into the boundary layer from above. A set of measures based on the layer-averaged differences of these fluxes from the LES solutions is developed. In addition to the methodological framework and suite of LES solutions, the main result of the evaluation is the recognition that all of the examined PBL parameterizations have difficulty reproducing the entrainment at the top of the PBL, as given by the LES, in most parameter regimes. Some of the PBL models are relatively accurate in their entrainment flux in a subset of parameter regimes. The sensitivity of the PBL models to vertical resolution is explored, and substantive differences are observed in the performance of the PBL models, relative to LES, at low resolution typical of large scale atmospheric models.

A determinate model of thrust-augmenting ejectors

A theoretical analysis of the compressible flow through a constant-area jet-engine ejector in which a primary jet mixes with ambient fluid from a uniform free stream is pursued. The problem is reduced to a determinate mathematical one by prescribing the ratios of stagnation properties between the primary and secondary flows. For some selections of properties and parameters more than one solution is possible and the meaning of these solutions is discussed by means of asymptotic expansions. Our results further show that while under stationary conditions the thrust-augmentation ratio assumes a value of 2 in the large area-ratio limit, for a free-stream Mach number greater than 0.6 very little thrust augmentation is left. Due to the assumptions made, the analysis provides idealized values for the thrust-augmentation ratio and the mass flux entrainment factor.

Microphysical and Turbulent Structure of Nocturnal Stratocumulus as Observed during ASTEX

Abstract Measurements of the microphysical and turbulence structure of stratocumulus made during the Atlantic Stratocumulus Transition Experiment are presented. The measurements made from a C-130 aircraft, belonging to the Meteorological Research Flight, on the night of 12–13 June 1992 show that the convection in the boundary layer is driven both by longwave radiative cooling at cloud top and by the surface buoyancy flux. The turbulence kinetic energy budget, velocity and temperature variance, and vertical fluxes are calculated to discover how the turbulence structure varies with height. The vertical velocity variance profile is found to resemble that of a clear convective boundary layer. The entrainment velocity and entrainment fluxes are estimated. The results show that the entrainment is very efficient in the case studied. As a result, the buoyancy production of turbulent kinetic energy in the cloud layer is considerably reduced. Horizontally averaged droplet spectra are calculated to study the relativ...

Warm Weddell Deep Water west of Maud Rise

A pool of relatively warm (>1.0°C) Weddell Deep Water (WDW) immediately west of Maud Rise appears to be a quasi‐stationary feature. The “warm pool” is derived from the flow of warm WDW around the flanks of Maud Rise. An austral spring 1989 expedition of the R/V Akademik Fedorov obtained detailed measurements of the warm pool. It displays the general regional relationship of temperature maximum (t‐max) warmth to shallowness of the pycnocline, as well as mixed layer oxygen concentration well below full saturation. Depression of oxygen values is a product of injection of WDW into the mixed layer during the ice‐covered winter period. Associated with this transfer are high vertical fluxes of heat and salt which limit the thickness of the sea ice cover. In the winter the atmosphere is sufficiently cold to remove the WDW heat without massive sea ice melting, though the regional ice thickness is restricted. In the spring the atmospheric conditions cannot remove the ocean heat, and ice melting ensues before the atmospheric heat budget alone can account for the ice melt. This is clearly seen in the warm pool as very low mixed layer oxygen, which is a reflection of high WDW entrainment and vertical heat flux and is normally associated with high mixed layer salinity. Here it is coupled instead with reduced salinity, a result of approximately 0.5 m of ice melt. The Fedorov data confirm the role of oceanic heat flux in early removal of Southern Ocean sea ice at the end of winter, in that the region of highest WDW entertainment is associated with greater amounts of melt water.

Effect of bubble coalescence on entrainment in gas fluidized beds

An entrainment flux model for freely bubbling gas-solid fluidized beds was described. The model was based on particle trajectories in the freeboard wit

Turbulent fountains in a closed chamber

An experimental and numerical investigation of the density distribution produced in a container by a negatively buoyant jet has been undertaken to evaluate the effect of the forced vertical motion of the environment. Vertical motion results from inflows and exhausts above and below the jet. Three distinct cases were identified. In the first, a velocity in the environment opposed the jet and produced a steady flow. This configuration was used to measure the entrainment flux along the length of the fountain. This configuration is similar to a jet impinging on an interface for which the entrainment depends on the local Froude number. The experiments covered a wider range of local Froude numbers than previously published and have produced results which are different from those in the literature. In the second case, the environment was at rest except for the motion induced by the fountain. An interface formed at the base of the fountain and moved quickly to the top. Once there, it advanced slowly due to entrainment through the end of the fountain and the length of the fountain increased. The final case is a co-flowing environment. No interface formed if the environment velocity was greater than the advance velocity of the end of the fountain. However, one formed for a smaller environment velocity and the end of the fountain was observed to undergo a quasi-periodic jump phenomenon. The top of the fountain would advance with the environment particles for a short time and then snap back to the elevation of a fountain in an infinite environment. A new interface formed and the cycle repeated.

A Modified First-Order Model for Scalar Diffusion in the Convective Boundary Layer

Abstract A modified first-order model is proposed for scalar diffusion in the convective boundary layer. In addition to the eddy diffusivity term, the model includes a term proportional to the second derivative of the mean scalar. The coefficient of the new term is closely related to the skewness of the vertical velocity component and to the inhomogeneity of the turbulent field. The model is used to explain the difference in eddy diffusivity between the top-down and bottom-up diffusion as well as the countergradient transport of the bottom-up scalar. The model is different from the approach of top-down and bottom-up decomposition in the respect that the former does not assume a linear profile of scalar flux or does not depend on the ratio of the entrainment flux to the surface flux. Unlike a previous countergradient term, the proposed term does not need to be combined with the top-down and bottom-up decomposition. The model equation is numerically solved to obtain the scalar gradient profile for three typ...

Dynamics above a dense equatorial rain forest from the surface boundary layer to the free atmosphere

During the Dynamique et Chimie de l'Atmosphère en Forêt Equatoriale (DECAFE) campaign, dynamical and thermodynamical measurements were made at Impfondo (1°37′N, 18°04′W), over the dense rain forest of northern Congo during the dry season (February 1988). During the measurement period the experimental site was located south of the intertropical convergence zone ground track which manages the dynamics of the large scale. Above the experimental site, the atmospheric low layers are supplied by monsoon air coming from the Guinean gulf; the upper layers (>1500 m) are supplied by warm and dry air (trade winds) coming from the northern desert region and the savanna. Our experimental approach consists of analyzing the heat and moisture content in the low troposphere from vertical soundings made by a tethered balloon (0–400 m) and an aircraft (0–4000 m). The analysis of the evolution of the observed planetary boundary layer (PBL) is made with a mixed layer one‐dimensional model which is forced to represent correctly the observed PBL height growth. The simulated and observed budgets of the heat and moisture in the PBL are balanced by adding dry air to the simulated PBL in the afternoon. This drying out can be maintained only by high levels of entrainment flux at the PBL top. An entrainment velocity of 3 cm s−1 enables the balancing of the moisture budget. This entrainment velocity seems compatible with physicochemical transfers as those of methane and ozone.

Origin and manifestation of flow-combustion interactions in a premixed shear layer

The interactions between the flow field and the combustion process in a premixed shear layer are investigated using the results of numerical simulation. The reaction is governed by a finite-rate Arrhenius kinetics, the flow is compressible and at high Reynolds number, heat release is moderate and molecular heat and mass diffusivities are finite. The thickness of the reaction zone and that of the vorticity layer are approximately the same. Lagrangian simulations are obtained using the vortex and transport element methods. Results indicate that at the early stages, a reacting shear layer behaves like a laminar flame. During the growth of the roll-up eddy, the rate of burning is strongly enhanced by the entrainment fluxes that lead to the swelling of the reaction zone, and the total rate of product formation can be approximated by the unstrained laminar burning velocity times the flame length measured along the line of maximum reaction rate. Following the burning of the eddy core, the strain field along the eddy boundaries causes a noticeable thinning of the reaction zone and reduces the rate of burning. Baroclinic vorticity generation due to the acceleration of fluid elements in the density gradient is the most important mechanism by which combustion affects the flow field. It augments the overall volumetric entrainment into the eddy core, and causes an entrainment asymmetry with a bias towards the products. The generated vorticity extends the growth period of the eddy and imparts on it an extra mean convective motion.