Convective Boundary Layer Research Articles

MHD Mixed Convection Boundary Layer Casson Nanofluid Flow over an Exponential Stretching Sheet

This paper investigates the effects of radiation, internal heat source and magnetohydrodynamics (MHD) on the mixed convective boundary layer flow of a Casson nanofluid within a porous medium that is saturated and subject to an exponentially stretching sheet. The nanofluid model incorporates Brownian motion and thermophoresis, and the Darcy model is employed for the porous medium. By applying an appropriate similarity transformation, the nonlinear governing boundary layer equations are converted into a set of nonlinear coupled ordinary differential equations. These equations are then solved numerically using the Hermite wavelet method, with simulations conducted through the MATHEMATICA programming language. The analysis covers various aspects including temperature distribution, velocity, solute concentration and several engineering parameters such as skin friction coefficients, the Nusselt number (rate of heat transfer) and the Sherwood number (rate of mass transfer), all evaluated based on dimensionless physical parameters. The results indicate that elevated radiation intensifies temperatures and leads to thicker thermal boundary layers. As the Casson parameter increases, both the velocity and the momentum boundary layer become narrower. Additionally, a more pronounced chemical reaction rate reduces the thickness of the solutal boundary layer. The accuracy and reliability of the numerical Hermite wavelet method are validated through a comparative analysis with previous studies, demonstrating excellent concordance and confirming the robustness of the computational approach.

An Investigation of Convective Boundary Layer Depth and Entrainment Zone Properties Using Dual-Polarization Radar and Balloon-Borne Observations

Abstract Previous work has shown that differential reflectivity (ZDR) observations from National Weather Service dual-polarization Doppler weather radars (WSR-88Ds) provide accurate estimates of convective boundary layer (CBL) depth when compared with depth estimates from 0000 UTC rawinsonde observations. We extend this work by launching small rawinsondes, called Windsonds, to study ZDR signals throughout the daytime hours. Results show that it can be difficult to identify CBL depth from ZDR alone when biological scatterers are absent. The exploration of other radar variables leads to the use of azimuthal ZDR variance to help in identifying CBL characteristics. A variable that combines both ZDR and azimuthal ZDR variance, called DVar, allows for improved signal identification using the quasi-vertical profile (QVP) method. Furthermore, QVP channel width is found to be closely tied to overall entrainment zone (EZ) structure. Results show that the centers and vertical extents of channels of reduced DVar in QVPs correlate well with sounding-observed CBL depth and EZ depth, respectively, across all stages of CBL development and in both clear and cloud-topped CBLs. The QVP approach tends to fail in identifying CBL and EZ depths when the vertical gradient in moisture above the CBL is small. Additionally, we compare observed EZ depth to various EZ parameterizations and show that the parameterizations generally underestimate EZ depth. We conclude that the ability of WSR-88Ds to sample the CBL should be leveraged to increase our knowledge of CBL properties.

Convectively Induced Secondary Circulations and Wind‐Driven Heat Fluxes in the Surface Energy Balance Over Land

AbstractIncreased resolution has enabled kilometer‐scale weather and climate models to partially resolve secondary circulations, including horizontal convective rolls (HCRs) and cold pool gust fronts. Although these circulations are ubiquitous in convective boundary layers over land, their impacts on the surface energy balance are largely unknown. Doppler lidar and surface observations were combined with DOE E3SM land model experiments, revealing increased surface winds (5 m/s) and heat fluxes (50 W/m2) in convergent branches of HCRs. Larger wind‐driven flux responses (up to 150 W/m2) were found along gust fronts. Surface energy balance shifts to accommodate wind‐driven fluxes, reducing ground heat conduction and longwave cooling. Our findings from the US Southern Great Plains are broadly relevant to modeling convective boundary layers. In particular, widely used subgrid wind gust parameterizations were found to be physically inconsistent with resolved secondary circulations and could worsen climate prediction biases at kilometer‐scales.

MHD Free Convection Boundary Layer Flow on a Horizontal Circular Cylinder in a Williamson Hybrid Ferrofluid with Viscous Dissipation

The present research examined the flow of a horizontal circular cylinder immersed in a Williamson hybrid ferrofluid via free convection boundary layer flow. The fluid flow is modelled by means of governing partial differential equations that incorporate viscous dissipation and magnetohydrodynamic (MHD) effects. Prior to being converted into a more practical partial differential equation, these dimensional equations are reduced to a non-dimensional form by utilising appropriate dimensionless variables. The Keller-box approach is then used to solve these equations with fewer dependent variables numerically. Graphical representations are generated, and the impacts of different interested factors are analysed using MATLAB software. According to the results, the hybrid ferrofluid outperformed ferrofluid with the same particle volume fraction in terms of skin friction and convective heat transfer capabilities.

Instability of a vertical free convection boundary layer flow: Asymptotically from a perfectly flat one to a highly curved one

Instability of a vertical free convection boundary layer flow: Asymptotically from a perfectly flat one to a highly curved one

Dual characteristics of mixed convection flow of three-particle aqueous nanofluid upon a shrinking porous plate

Purpose This study aims to analyze the thermo-hydrodynamic characteristics for the mixed convection boundary layer flow of three-particle aqueous nanofluid on a shrinking porous plate with the influences of thermal radiation and magnetic field. Design/methodology/approach The basic equations have been normalized with the help of similarity transformations. The obtained equations have been solved numerically using the shooting method in conjunction with the sixth-order Runge–Kutta technique. Numerical results for the velocity and temperature are illustrated with varying relevant parameters. Findings The results reveal that the local drag coefficient increases with higher values of the magnetic field parameter, nanoparticle volume fraction and suction parameter. On the other hand, boosting the radiation parameter and nanoparticle concentration notably enhances heat transfer. Furthermore, it is noted that the suction parameter and magnetic field parameter both lead to an increase in velocity and promote the occurrence of dual solutions within the problem conditions. Research limitations/implications The limitations are that the model is appropriate for thermal equilibrium of base fluid and nanoparticles, and constant thermo-physical properties. Originality/value To the best of the authors' knowledge, no study has taken an attempt to predict the flow and heat transfer characteristics of unsteady mixed convection ternary hybrid nanofluid flow over a shrinking sheet, particularly under the influence of magnetic field and radiation. The findings obtained here may hold particular significance for those interested in the underlying theoretical and practical implications.

Initiation of a Supercell by Convectively Generated Gravity Waves in the Simulated Kaiyuan Tornadic Event of 3 July 2019

Abstract An EF4-rated supercell tornado occurred on 3 July 2019 in Kaiyuan, China, causing heavy casualties. A three-level nested-grid high-resolution numerical simulation is used to investigate the initiation of the tornadic supercell. Automatic weather station (AWS) data, FY-4A visible satellite data, and Doppler radar data are used to verify the model simulation. The most important aspects of the simulated pre-supercell mesoscale convective system (MCS) and the initiation of the supercell agree with observations. Detailed investigation of the model results reveals that the initial cells form first above a convective boundary layer (CBL) on the dry side of a surface dryline. Above the CBL is a moist layer in terms of relative humidity and the layer is stable. Convectively generated gravity waves (GWs) emanating from the MCS and propagating southward along the stable layer above the CBL provide localized forcing for the actual triggering of initial cells at specific locations. The associated perturbation potential temperature and vertical velocity patterns confirm that the GWs trigger a series of cloud bands. The additional lifting by the updraft of a horizontal convective roll in the CBL underneath the GW updraft works together to promote faster growth of the initial cell that later becomes the supercell. Examination of the Scorer parameter profiles shows favorable conditions for vertical trapping of GWs along the wave guide in the stable layer, preventing the radiation of wave energy to the upper levels.

Development of a Multi‐Scale Meteorological Large‐Eddy Simulation Model for Urban Thermal Environmental Studies: The “City‐LES” Model Version 2.0

AbstractTo bridge the gaps between meteorological large‐eddy simulation (LES) models and computational fluid dynamics (CFD) models for microscale urban climate simulations, the present study has developed a meteorological LES model for urban areas. This model simulates urban climates across both mesoscale (city scale) and microscale (city‐block scale). The paper offers an overview of this LES model, which distinguishes itself from standard numerical weather prediction models by resolving buildings and trees at the microscale simulations. It also differs from standard CFD models by accounting for atmospheric stratification and physical processes. Noteworthy features of this model include: (a) the calculation of long‐ and short‐wave radiations in three dimensions, incorporating multiple reflections within urban canopy layers using the radiosity method, and accounting for building and tree shadows in the simulations; (b) the provision of various heat stress indices (Universal Thermal Climate Index, Wet Bulb Globe Temperature, MRT, THI); (c) the assessment of the efficacy of heat stress mitigation measures such as dry‐mist spraying, roadside trees, cool pavements, and green/cool roofs strategies; (d) the capability to run on supercomputers, with the code parallelized in a three‐dimensional manner, and the model can also run on a graphics processing unit cluster. Following the introduction of this model, the study confirms its basic performance through various numerical experiments, including simulations of thermals in the convective boundary layer, coherent structure of turbulence over urban canopy, and thermal environment and heat stress indices in urban districts. The model developed in this study is intended to serve as a community tool for addressing both fundamental and applied studies in urban climatology.

Statistical Postprocessing of Week-1 and Week-2 Precipitation Forecasts over Taiwan

Abstract The predictability of precipitation is hindered by finer-scale processes not captured explicitly in global numerical models, such as convective interactions, cloud microphysics, and boundary layer dynamics. However, there is growing demand across various sectors for medium- (3–10-day) and extended-range (10–30-day) quantitative precipitation forecasts (QPFs) and probabilistic QPFs (PQPFs). This study uses a novel statistical postprocessing technique, APPM, that combines analog postprocessing (AP) with probability matching (PM) to produce week-1 and week-2 accumulated precipitation forecasts over Taiwan. AP searches for historical predictions that closely resemble the current forecast and create an AP ensemble using the observed high-resolution precipitation patterns corresponding to these forecast analogs. Frequency counting and PM are then separately applied to the AP ensemble to produce calibrated and downscaled PQPFs and bias-reduced QPFs, respectively. Evaluation over a 22-yr (1999–2020) period shows that raw ensemble forecasts from the GEFS of NOAA/NWS/Environmental Modeling Center, collected for the subseasonal experiment, are underdispersive with a wet bias. In contrast, the AP ensemble spread well represents forecast uncertainty, leading to substantially more reliable and skillful probabilistic forecasts. Furthermore, the AP-based PQPF demonstrates superior discrimination ability and yields notably greater economic benefits for a wider range of users, with the maximum economic value increasing by 30%–50% for the week-2 forecast. Compared to the raw ensemble mean forecast, the calibrated QPF exhibits lower mean absolute error and explains 3–8 times more variance in observations. Overall, the APPM technique significantly improves week-1 and week-2 QPFs and PQPFs over Taiwan. Significance Statement There are two significant challenges in improving precipitation forecasts beyond a few days in Taiwan. First, large-scale numerical models often struggle with accurately predicting precipitation locations, magnitudes, and providing sufficient detail. Second, probabilistic precipitation forecasts have been unreliable, failing to convey accurate uncertainty information to users. In response to these challenges, this study has developed a relatively simple yet effective technique that corrects the spatiotemporal distribution of predicted precipitation and downscales the forecasts from a 1° to 1-km spatial resolution. Our results demonstrate that this technique significantly alleviates these two issues, resulting in more accurate precipitation forecasts and more reliable probabilistic precipitation forecasts within a 2-week timeframe.

On a Correlation Model for Laser Scanners: A Large Eddy Simulation Experiment

Large Eddy Simulations (LES) allow the generation of spatio-temporal fields of the refractivity index for various meteorological conditions and provide a unique way to simulate turbulence-distorted phase measurements as those from geodetic sensors. This approach enables a statistical quantification of the von Kármán model’s adequacy in describing the phase spectrum and the assessment of the validity of common assumptions such as isotropy or the Taylor frozen hypothesis. This contribution shows that the outer scale length, defined using the Taylor frozen hypothesis as the saturation frequency of the phase spectrum, can be statistically estimated, along with an error fit factor between the model and its estimation. It is found that this parameter strongly varies with height and meteorological conditions (convective or wind-driven boundary layer). The simulations further highlight the linear dependency with the variance of the turbulent phase fluctuations but no dependency on the local outer scale length as defined by Tatarskii. An application of these results within a geodetic context is proposed, where an understanding and solid estimation of the outer scale length is mandatory in avoiding biased decisions during statistical deformation analysis. The LES presented in this contribution support derivations for an improved stochastic model of terrestrial laser scanners.

Understanding Coherent Turbulence and the Roll‐Cell Transition With Lagrangian Coherent Structures and Frame‐Indifferent Fluxes

AbstractWe present the first analysis of frame‐indifferent (objective) fluxes and material vortices in Large Eddy Simulations of atmospheric boundary layer turbulence. We extract rotating fluid features that maintain structural coherence over time for near‐neutral, transitional, and convective boundary layers. In contrast to traditional analysis of coherent structures in turbulent boundary layers, we provide the first identification of vortex boundaries that are mathematically defined to behave as tracer transport barriers. Furthermore, these vortices are indifferent to the choice of observer reference frame and can be identified without user‐dependent velocity field decompositions. We find a strong agreement between the geometric qualities of the coherent structures we extract using our new method and classical descriptions of horizontal rolls and convective cells arising from decades of observational studies. We also quantify trends in individual vortex contributions to turbulent and advective fluxes of heat under varying atmospheric stability. Using recently developed tools from the theory of transport barrier fields, we compare diffusive momentum and heat barrier fields with the presence of rolls and cells, and determine a strong connection between heat and momentum orthogonality with the physical drivers of roll‐cell transformation. This newly employed frame‐indifferent characterization of coherent turbulent structures can be directly applied to numerical model output, and thus provides a new Lagrangian approach to understand complex scale‐dependent processes and their associated dynamics.

Implications of energy balance non-closure on carbon dioxide flux uncertainties: Insights from large eddy simulations in convective boundary layers

The non-closure of surface energy balance, often encountered in eddy covariance (EC) measurements, raises a critical query: does this non-closure lead to underestimated scalar fluxes, particularly CO2 flux (Fc), when using the same theoretical framework in EC? To address this question, we utilize high-resolution large-eddy simulations (LESs) to explore correlations between energy flux imbalances and Fc imbalances in convective boundary layers, considering both homogeneous and idealized heterogeneous surfaces. Our findings reveal that the unsteady CO2 or storage represents a leading factor influencing Fc imbalance, especially notable when the entrainment ratio for Fc is large. Even in scenarios with uniform surface Fcs, heterogeneous thermally-generated turbulence resulting from variable surface sensible heat flux (H) can induce substantial horizontal flux divergence, magnifying Fc imbalance. While a linear correlation between the energy flux imbalance and Fc imbalance arises under shared causative mechanisms (e.g., storage), complex correlations emerge if their influencing factors differ, contingent upon surface heterogeneity and site location. This complexity underscores the limitations in applying the closing methods for energy flux imbalance to the Fc imbalance.

The Development of Rotation in Simulated Dust-Devil-Like Vortices

Abstract The analysis uses a numerical simulation of an initially resting, dry, atmosphere, in which uniform surface heating leads to the development of a growing convective boundary layer (CBL). As soon as convective mixing sets in, regions of weak vertical vorticity develop at the lowest model level. Using forward trajectories, this vorticity is shown to originate from horizontal baroclinic production and subsequent reorientation into the vertical within the descending branches of the convective cells. The requirement for vertical vorticity production in the downdraft cells is shown to be a non-axisymmetric horizontal footprint of the downdraft regions. The resulting vertical vorticity is not initially associated with rotation. However, as the CBL matures, like-signed vortex patches merge, the vertical vorticity magnitude increases due to stretching, and deformation in the vortex core decreases, leading to the development of vortices. The ultimate origin of the vortices is thus initially horizontal vorticity that has been produced baroclinically, and that has subsequently been reoriented into the vertical in sinking air.

A Variant of the Local Similarity Theory and Approximations of Vertical Profiles of Turbulent Moments of the Atmospheric Convective Boundary Layer

The approximation of the turbulent moments of the atmospheric convective layer is based on a variant of the local similarity theory using the concepts of the semi-empirical theory of Prandtl turbulence. In the proposed variant of the local similarity theory, the second moment of vertical velocity and the “spectral” Prandtl mixing length are used as basic parameters. This approach allows us to extend Prandtl’s theory to turbulent moments of vertical velocity and buoyancy and additionally offer more than ten new approximations. The comparison of the proposed approximation with other variants of the theory of local similarity is considered. It is shown that the selected basic parameters significantly improve the agreement between the local similarity approximations and experimental data. The approximations are consistent with observations in the turbulent convective layer of the atmosphere, the upper boundary of which nearly corresponds to the lower boundary of the temperature inversion. Analytical approximations of local similarity can find applications in the construction of high-order moment closures in the vortex of resolving numerical turbulence models, as well as in the construction of “mass-flux” parametrization.

An Automated Approach to Estimating Convective Boundary Layer Depth from Dual-Polarization WSR-88D Radar Observations

Abstract Convective boundary layer (CBL) depth can be estimated from dual-polarization WSR-88D radars using the product differential reflectivity ZDR because the CBL top is collocated with a local ZDR minimum produced by Bragg scatter at the interface of the CBL and the free troposphere. Quasi-vertical profiles (QVPs) of ZDR are produced for each radar volume scan and profiles from successive times are stitched together to form a time–height plot of ZDR from sunrise to sunset. QVPs of ZDR often show a low-ZDR channel that starts near the ground and rises during the morning and early afternoon, identifying the CBL top. Unfortunately, results show that this channel within the QVP can occasionally be misleading. This motivated creation of a new variable DVar, which combines ZDR with its azimuthal variance and is particularly helpful at identifying the CBL top during the morning hours. Two methods are developed to track the CBL top from QVPs of ZDR and DVar. Although each method has strengths and weaknesses, the best results are found when the two methods are combined using inverse variance weighting. The ability to detect CBL depth from routine WSR-88D radar scans rather than from rawinsondes or lidar instruments would vastly improve our understanding of CBL depth variations in the daytime by increasing the temporal and spatial frequencies of the observations. Significance Statement The daytime convective boundary layer (CBL) can increase in depth from a few hundred to a few thousand meters between sunrise and sunset and is strongly connected to temperature changes at Earth’s surface. Unfortunately, current observations of CBL depth primarily consist of measurements from twice daily rawinsonde launches at 97 locations across the United States. As a result, CBL depth observations lack fine spatial and temporal resolution and miss the daily cycle of CBL growth. This study seeks to fill the gaps in CBL depth observations by developing an automated method to estimate CBL depth from dual-polarization WSR-88D radar observations with a temporal resolution as fine as 5–10 min. These observations will greatly enhance our ability to observe and monitor CBL depth in real time.

Mixed Convection Boundary Layer Flow on A Vertical Flat Plate in Al203-Ag/Water Hybrid Nanofluid with Viscous Dissipation Effects

Mixed Convection Boundary Layer Flow on A Vertical Flat Plate in Al203-Ag/Water Hybrid Nanofluid with Viscous Dissipation Effects

Local nonsimilar solution and heat analysis of mixed convective flow across whole spherical shape with nonisothermal surface temperature

This study investigates the behavior of a mixed convective boundary layer flowing around a rigid spherical shape with non-isothermal wall temperature. The fluid assumed in this examination exhibits both incompressibility and viscosity. The major purpose is to examine the impact of the non-uniform surface temperature on the flow patterns, including velocity outlines and temperature outlines. An examination is conducted on the modified conservation equations of the boundary layer flow utilizing the local non-similarity method. The MATLAB built-in code bvp4c is used to find computational solutions. The outcomes are then shown for both air and water, specifically at a temperature of 21°C. The influence of several factors, such as the mixed convective variable [Formula: see text] and the exponent [Formula: see text] in the wall temperature function [Formula: see text]), is shown in velocity and temperature profiles. In addition, the study computes the local frictional force factor and local wall heat transport factor and compares these values with results from earlier research. Significantly, the study expands upon data made around the lower stagnating point to include other sites within the sphere, thereby offering a thorough comprehension of the whole flowing field.

The variational approach to study the mixed convection boundary layer flow over a permeable Riga plate

AbstractThe physical problem of steady state, laminar, mixed convection (Ri) with double‐diffusive (N) in an electrically low conducting fluid past a semi‐infinite electromagnetic () influenced flat plate with internal uniform heat generation (Q) in the presence of suction/injection (H) by considering viscous dissipation (Ec), thermophoresis (Nt) and thermal diffusion effects (Sr) is mathematically modeled as a simultaneous system of nonlinear partial differential equations. To achieve the solution of the problem numerically, Gyarmati's variational principle known as the “Governing Principle of Dissipative Processes” on the basis of nonequilibrium thermodynamic processes in the theory of continua, is adopted. This research work correlates the phenomenon of fluid around submersibles/space vehicles and provides related insights. To estimate the transportation fluid fields within the boundary layer, the appropriate trial polynomials have been employed, and functionals for the integral variational principle are determined. Next, the Euler–Lagrange equations of the functionals are obtained as a system of polynomial equations involving boundary layer thicknesses of momentum, temperature, and concentration. The expressions of local shear stress, local Nusselt, and local Sherwood numbers have been derived and the effects of various physical factors involved in the problem are explored. A comparison with the previously published results in the literature is provided to confirm the validity of the solution procedure. The results depict that injection () and opposing buoyancy () decrease the skin friction about 38% in sea water and 11% in ionized air when compared to impermeable plate for . The aiding buoyancy () plays a dominant role in heat and mass transfers, respectively, with the massive gradients of 340% and 763% in magnitude for the heavier fluid sea water flow while 47% and 3% for the lighter fluid ionized air flow when . The buoyancy parameters (Ri, N) decrease the heat transfer, but increase the mass transfer.

Large-scale semi-organized rolls in a sheared convective turbulence: Mean-field simulations

Based on a mean-field theory of a non-rotating turbulent convection [T. Elperin et al., Phys. Rev. E 66, 066305, (2002)], we perform mean-field simulations (MFS) of sheared convection that takes into account an effect of modification of the turbulent heat flux by the non-uniform large-scale motions. This effect is caused by the production of additional essentially anisotropic velocity fluctuations generated by tangling of the mean-velocity gradients by small-scale turbulent motions due to the influence of the inertial forces during the lifetime of turbulent eddies. These anisotropic velocity fluctuations contribute to the turbulent heat flux. As the result of this effect, there is an excitation of large-scale convective-shear instability, which causes the formation of large-scale semi-organized structures in the form of rolls. The lifetimes and spatial scales of these structures are much larger compared to the turbulent scales. By means of MFS performed for stress-free and no-slip vertical boundary conditions, we determine the spatial and temporal characteristics of these structures. Our study demonstrates that the modification of the turbulent heat flux by non-uniform flows leads to a strong reduction of the critical effective Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the formation of the large-scale rolls. During the nonlinear stage of the convective-shear instability, there is a transition from a two-layer vertical structure with two rolls in the vertical direction before the system reaches steady-state to a one-layer vertical structure with one roll after the system reaches steady state. This effect is observed for all effective Rayleigh numbers. We find that inside the convective rolls, the spatial distribution of the mean potential temperature includes regions with a positive vertical gradient of the potential temperature caused by the mean heat flux of the convective rolls. This study might be useful for understanding the origin of large-scale rolls observed in atmospheric convective boundary layers, as well as in numerical simulations and laboratory experiments.

The role of adding carbon nanoparticles to free convective boundary layer viscoelastic fluid flow past a vertical porous cone surface: application in wastewater treatment

The role of adding carbon nanoparticles to free convective boundary layer viscoelastic fluid flow past a vertical porous cone surface: application in wastewater treatment