THE UNSTABLE MODES OF NATURAL CONVECTION BOUNDARY LAYER

The instability of natural convection boundary layer around a vertical heated flat plate is analyzed theoretically in this paper. The results illustrate that the 'loop' in the neutral curve is not a real loop but a twist of the curve in the frequency-wave number-Grashof number space, and there is only one unstable mode at small Prandtl numbers. Specially, when the Prandtl number is large enough two unstable modes will be found in the 'loop' region. Along the amplifying surface intersection the two unstable modes have the same Grashof number, wave number and frequency but different amplifying rates. Their instability characteristics are analyzed and the criterion for determining the existence of the multi-unstable modes is also discussed.

Development of a Single-Column Model in RegCM4 and Its Preliminary Application for Evaluating PBL Schemes in Simulating the Dry Convection Boundary Layer

A single-column model(SCM)is developed in the regional climate model RegCM4.The evolution of a dry convection boundary layer(DCBL)is used to evaluate this SCM.Moreover,four planetary boundary layer(PBL)schemes,namely the Holtslag-Boville scheme(HB),Yonsei University scheme(YSU),and two University of Washington schemes(UW01,Grenier-Bretherton-Mc Caa scheme and UW09,Bretherton-Park scheme),are compared by using the SCM approach.A large-eddy simulation(LES)of the DCBL is performed as a benchmark to examine how well a PBL parameterization scheme reproduces the LES results,and several diagnostic outputs are compared to evaluate the schemes.The results show that the SCM is properly constructed.In general,with the DCBL case,the YSU scheme performs best for reproducing the LES results,which include well-mixed features and vertical sensible heat fluxes;the simulated wind speed,turbulent kinetic energy,entrainment flux,and height of the entrainment zone are all underestimated in the UW09;the UW01 has all those biases of the UW09 but larger,and the simulated potential temperature is not well mixed;the HB is the least skillful scheme,by which the PBL height,entrainment flux,height of the entrainment zone,and the vertical gradients within the mixed layer are all overestimated,and a inversion layer near the top of the surface layer is wrongly simulated.Although more cases and further testing are required,these simulations show encouraging results towards the use of this SCM framework for evaluating the simulated physical processes by the RegCM4.

Summer atmospheric boundary layer structure in the hinterland of Taklimakan Desert, China

Understanding the characteristics of the structure of desert atmospheric boundary layer and its land surface process is of great importance to the simulations of regional weather and climate. To investigate the atmospheric boundary layer structure and its forming mechanism of Taklimakan Desert, and to improve the accuracy and precision of regional weather and climate simulations, we carried out a GPS radiosonde observation experiment in the hinterland of Taklimakan Desert from 25 June to 3 July, 2015. Utilizing the densely observed sounding data, we analyzed the vertical structures of daytime convective boundary layer and nighttime stable boundary layer in summer over this region, and also discussed the impacts of sand-dust and precipitation events on the desert atmospheric boundary layer structure. In summer, the convective boundary layer in the hinterland of Taklimakan Desert developed profoundly and its maximum height could achieve 4,000 m; the stable boundary layer at nighttime was about 400-800-m thick and the residual mixing layer above it could achieve a thickness over 3,000 m. Sand-dust weather would damage the structures of nighttime stable boundary layer and daytime convective boundary layer, and the dust particle swarm can weak the solar radiation absorbed by the ground surface and further restrain the strong development of convective boundary layer in the daytime. Severe convective precipitation process can change the heat from the ground surface to the atmosphere in a very short time, and similarly can damage the structure of desert atmospheric boundary layer remarkably. Moreover, the height of atmospheric boundary layer was very low when raining. Our study verified the phenomenon that the atmospheric boundary layer with supernormal thickness exists over Taklimakan Desert in summer, which could provide a reference and scientific bases for the regional numerical models to better represent the desert atmospheric boundary layer structure.

Development of the Convective Boundary Layer Capping with a Thick Neutral Layer in Badanjilin:Observations and Simulations

In this study, the development of a convective boundary layer （CBL） in the Badaujilin region was investigated by comparing the observation data of two cases. A deep neutral layer capped a CBL that occurred on 30 August 2009. This case was divided into five sublayers from the surface to higher atmospheric elevations： surface layer, mixed layer, inversion layer, neutral layer, and sub-inversion layer. The development process of the CBL was divided into three stages： S1, S2, and S3. This case was quite different from the development of the three-layer CBL observed on 31 August 2009 because the mixed layer of the five-layer CBL （CBL5） eroded the neutral layer during S2. The specific initial structure of the CBL5 was correlated to the synoptic background of atmosphere during nighttime. The three-stage development process of the CBL5 was confirmed by six simulations using National Center for Atmospheric Research （USA） large-eddy simulation （NCAR-LES）, and some of its characteristics are presented in detail.

A Diagnostic Analysis on the Effect of the Residual Layer in Convective Boundary Layer Development near Mongolia Using 20th Century Reanalysis Data

Although the residual layer has already been noted in the classical diurnal cycle of the atmospheric boundary layer, its effect on the development of the convective boundary layer has not been well studied. In this study, based on 3-hourly 20th century reanalysis data, the residual layer is considered as a common layer capping the convective boundary layer. It is identified dally by investigating the development of the convective boundary layer. The region of interest is bounded by （30^-60~N, 80^-120~E）, where a residual layer deeper than 2000 m has been reported using radiosondes. The lapse rate and wind shear within the residual layer are compared with the surface sensible heat flux by investigating their climatological means, interannual variations and daily variations. The lapse rate of the residual layer and the convective boundary layer depth correspond well in their seasonal variations and climatological mean patterns. On the interannual scale, the correlation coefficient between their regional averaged （40°-50°N, 90°-110°E） variations is higher than that between the surface sensible heat flux and convective boundary layer depth. On the daily scale, the correlation between the lapse rate and the convective boundary layer depth in most months is still statistically significant during 1970-2012. Therefore, we suggest that the existence of a deep neutral residual layer is crucial to the formation of a deep convective boundary layer near the Mongolian regions.

A Laboratory Modeling of the Velocity Field in the Convective Boundary Layer with the Particle Image Velocimetry Technique

Based on the research of the convective boundary layer (CBL) temperature field in a convective tank, this paper studies the characteristics of the CBL velocity field in the convective tank. Aluminium powder (400 orders) is used as a tracer particle in the application of the particle image velocimetry (PIV) technique. The experiment demonstrates: the velocity distribution in the mixed layer clearly possesses the characteristics of CBL thermals; the velocity distribution in the top zone of the mixed layer shows entrainment layer characteristics; the vertical distribution of turbulent characteristic variables is reasonable, which is similar to field observations and other tank results; the error analysis demonstrates the validity of aluminium powder, which implies the reliability of the results.

Footprint Characteristics of Scalar Concentration in the Convective Boundary Layer

Footprint characteristics for passive scalar concentration in the convective boundary layer （CBL） are investigated. A backward Lagrangian stochastic （LS） dispersion model and a large eddy simulation （LES） model are used in the investigation. Typical characteristics of the CBL and their responses to the surface heterogeneity are resolved from the LES. Then the turbulence fields are used to drive the backward LS dispersion. To remedy the spoiled description of the turbulence near the surface, MoninObukhov similarity is applied to the lowest LES level and the surface for the modeling of the backward LS dispersion. Simulation results show that the footprint within approximately 1 km upwind predominates in the total contribution. But influence from farther distances also exists and is even slightly greater than that from closer locations. Surface heterogeneity may change the footprint pattern to a certain degree. A comparison to three analytical models provides a validation of the footprint simulations, which shows the possible influence of along-wind turbulence and the large eddies in the CBL, as well as the surface heterogeneity.

MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions

This article concentrates on the steady magnetohydrodynamic （MHD） flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper （Cu）, Silver （Ag）, Alumina （A1203） and Titanium Oxide （TiO2）. Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.

Mixed convection in gravity-driven nano-liquid film containing both nanoparticles and gyrotactic microorganisms

Analysis of a gravity-induced film flow of a fluid containing both nanoparticles and gyrotactic microorganisms along a convectively heated vertical surface is presented.The Buongiorno model is applied. Two kinds of boundary conditions, the passive and the active boundary conditions, are considered to investigate this film flow phenomenon.Through a set of similarity variables, the ordinary differential equations that describe the conservation of the momentum, the thermal energy, the nanoparticles, and the microorganisms are derived and then solved numerically by an efficient finite difference technique.The effects of various physical parameters on the profiles of momentum, thermal energy,nanoparticles, microorganisms, local skin friction, local Nusselt number, local wall mass flux, and local wall motile microorganisms flux are investigated. It is expected that the passively controlled nanofluid model can be much more easily achieved and applied in real circumstances than the actively controlled model.

A nanofluid MHD flow with heat and mass transfers over a sheet by nonlinear boundary conditions: Heat and mass transfers enhancement

In this paper,we have numerically examined the steady boundary layer of a viscous incompressible nanofluid and its heat and mass transfers above a horizontal flat sheet.The boundary conditions considered were a nonlinear magnetic field,a nonlinear velocity and convection.Such nonlinearity in hydrodynamic and heat transfer boundary conditions and also in the magnetic field has not been addressed with the great details in the literature.In this investigation,both the Brownian motion and thermophoretic diffusion have been considered.A similarity solution is achieved and the resulting ordinary differential equations (nonlinear) are worked numerically out.Upon validation,the following hydrodynamic and heat and mass transfers parameters were found:the reduced Sherwood and Nusselt numbers,the reduced skin friction coefficient,and the temperature and nanoparticle volume fraction profiles.All these parameters are found affected by the Lewis,Biot and Prandtl numbers,the stretching,thermophoretic diffusion,Brownian motion and magnetic parameters.The detailed trends observed in this paper are carefully analyzed to provide useful design suggestions.

A Laboratory Study of the Turbulent Velocity Characteristics in the Convective Boundary Layer

Based on the measurement of the velocity field in the convective boundary layer （CBL） in a convection water tank with the particle image velocimetry （PIV） technique, this paper studies the characteristics of the CBL turbulent velocity in a modified convection tank. The experiment results show that the velocity distribution in the mixed layer clearly possesses the characteristics of the CBL thermals, and the turbulent eddies can be seen obviously. The comparison of the vertical distribution of the turbulent velocity variables indicates that the modeling in the new tank is better than in the old one. The experiment data show that the thermal＇s motion in the entrainment zone sometimes fluctuates obviously due to the intermittence of turbulence. Analyses show that this fluctuation can influence the agreement of the measurement data with the parameterization scheme, in which the convective Richardson number is used to characterize the entrainment zone depth. The normalized square velocity wi^2/w＊^2. at the top of the mixed layer seems to be time-dependent, and has a decreasing trend during the experiments. This implies that the vertical turbulent velocity at the top of the mixed layer may not be proportional to the convective velocity （w＊）.

Convective heat and mass transfer in MHD mixed convection flow of Jeffrey nanofluid over a radially stretching surface with thermal radiation

Mixed convection flow of magnetohydrodynamic(MHD) Jeffrey nanofluid over a radially stretching surface with radiative surface is studied. Radial sheet is considered to be convectively heated. Convective boundary conditions through heat and mass are employed. The governing boundary layer equations are transformed into ordinary differential equations. Convergent series solutions of the resulting problems are derived. Emphasis has been focused on studying the effects of mixed convection, thermal radiation, magnetic field and nanoparticles on the velocity, temperature and concentration fields. Numerical values of the physical parameters involved in the problem are computed for the local Nusselt and Sherwood numbers are computed.

Secondary flows in statistically unstable turbulent boundary layers with spanwise heterogeneous roughness

Large-scale secondary motions are known to occur in turbulent flows over surfaces with spanwise roughness heterogeneity.Numerical studies often use adjacent high-and low-roughness longitudinal strips to investigate these secondary rolls in boundary layers without any thermal stratification.In the present study,the effect of unstable thermal stratification on secondary rolls in a very high-Reynolds-number turbulent flow with spanwise-heterogeneous roughness is investigated by means of large-eddy simulation.The strength of the unstable stratification is systematically changed from L/h=−20 to L/h=−1,where L and h are Monin-Obukhov length and boundary-layer height,respectively.This range covers the transition from neutral stratification to unstable stratification.The results show that the positive buoyancy associated with the unstable thermal stratification acts against the roughness-induced secondary rolls.In the case of unstable stratification,secondary rolls are completely canceled out by buoyancy and replaced by new stronger convection-induced rolls rotating in opposite directions.

Axisymmetric Powell-Eyring fluid flow with convective boundary condition: optimal analysis

The effects of axisymmetric flow of a Powell-Eyring fluid over an impermeable radially stretching surface are presented. Characteristics of the heat transfer process are analyzed with a more realistic condition named the convective boundary condition. Governing equations for the flow problem are derived by the boundary layer approximations. The modeled highly coupled partial differential system is converted into a system of ordinary differential equations with acceptable similarity transformations. The convergent series solutions for the resulting system are constructed and analyzed. Optimal values are obtained and presented in a numerical form using an optimal homotopy analysis method （OHAM）. The rheological characteristics of different parameters of the velocity and temperature profiles are presented graphically. Tabular variations of the skin friction coefficient and the Nusselt number are also calculated. It is observed that the temperature distribution shows opposite behavior for Prandtl and Biot numbers. Furthermore, the rate of heating/cooling is higher for both the Prandtl and Biot numbers.

Heat transfer in a porous saturated wavy channel with asymmetric convective boundary conditions

The viscous flow in a wavy channel with convective boundary conditions is investigated. The channel is filled with a porous viscous fluid. Two cases of equal and different external convection coefficients on the walls are taken into account. Effect of viscous dissipation is also considered. The governing equations are derived employing long wavelength and low Reynolds number approximations. Exact closed form solutions are obtained for the simplified equations. Important physical features for peristaltic flow caused by the wavy wave are pumping, trapping and heat transfer rate at the channel walls. These are discussed one by one in depth and detail through graphical illustrations. Special attention has been given to the effects of convective boundary conditions. The results show that for Bi1≠Bi2, there exists a critical value of Brinkman number Brc at which the temperatures of both the walls become equal. And, for Bi1>Bi2 and Br>Brc, the temperature of the cold wall exceeds the temperature of hot wall.

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

Heat transfer analysis in the flow of Walters' B fluid with a convective boundary condition

Radiative heat transfer in the steady two-dimensional flow of Walters＇ B fluid with a non-uniform heat source/sink is investigated. An incompressible fluid is bounded by a stretching porous surface. The convective boundary condition is used for the thermal boundary layer problem. The relevant equations are first simplified under usual boundary layer assumptions and then transformed into a similar form by suitable transformations. Explicit series solutions of velocity and temperature are derived by the homotopy analysis method （HAM）. The dimensionless velocity and temperature gradients at the wall are calculated and discussed.

Nonlinear three-dimensional stretched flow of an Oldroyd-B fluid with convective condition, thermal radiation, and mixed convection

The effect of non-linear convection in a laminar three-dimensional Oldroyd-B fluid flow is addressed. The heat transfer phenomenon is explored by considering the non-linear thermal radiation and heat generation/absorption. The boundary layer as- sumptions are taken into account to govern the mathematical model of the flow analy- sis. Some suitable similarity variables are introduced to transform the partial differen- tial equations into ordinary differential systems. fifth-order techniques with the shooting method The Runge-Kutta-Fehlberg fourth- and are used to obtain the solutions of the dimensionless velocities and temperature. The effects of various physical parameters on the fluid velocities and temperature are plotted and examined. A comparison with the exact and homotopy perturbation solutions is made for the viscous fluid case, and an excellent match is noted. The numerical values of the wall shear stresses and the heat transfer rate at the wall are tabulated and investigated. The enhancement in the values of the Deborah number shows a reverse behavior on the liquid velocities. The results show that the temperature and the thermal boundary layer are reduced when the non- linear convection parameter increases. The values of the Nusselt number are higher in the non-linear radiation situation than those in the linear radiation situation.

Three-dimensional flow of Oldroyd-B fluid over surface with convective boundary conditions

The present study addresses the three-dimensional flow of an Oldroyd-B fluid over a stretching surface with convective boundary conditions. The problem formulation is presented using the conservation laws of mass, momentum, and energy. The solutions to the dimensionless problems are computed. The convergence of series solutions by the homotopy analysis method （HAM） is discussed graphically and numerically. The graphs are plotted for various parameters of the temperature profile. The series solutions are verified by providing a comparison in a limiting case. The numerical values of the local Nusselt number are analyzed.

On similarity profiles predicted in the convective marine boundary layer

On the basis of the ideal of local scale similarity theory, the profile equations of wind, temperature and humidity for the eonvective marine boundary layer have been obtained. The marine boundary layer measurements were made over the western Pacific Ocean as past of the Tropical Ocean and Global Atmosphere (TOGA) Programme during Nov. 1986-Feb. 1987. The similarity profiles predicledfor wind. temperature and humidity in the MBL are in good agreement with the observational data.