Boundary Layer Similarity Research Articles

A Numerical Study on the Lean-Rich Interaction of Methane/Air Flames

Interaction of flames in a lean-rich concentration field is studied numerically adopting a counterflow as a model problem. Detailed kinetic mechanism is adopted in analyzing the structure of various type of flames which can be found in lean-rich interaction. Flow field is simplified to quasi one-dimensional by using boundary layer approximation and similarity formulation. Triple flames are identified and its structure shows that a diffusion flame is located in the middle of two premixed flames. Such a diffusion flame is formed by and CO generated from the rich premixed flame and leaked from the lean premixed flame. The flame position can be identified either from the hydrogen production rate or the heat release rate. Transition from single diffusion flame to triple flame is observed as degree of premixing is increased.

Satellite‐derived surface temperatures with boundary layer temperatures and geostrophic winds to estimate surface energy fluxes

The surface sensible heat flux, H, and the latent heat flux, LE, were determined under unstable conditions for the First ISLSCP (International Satellite Land Surface Climatology Project) Field Experiment (FIFE) site in eastern Kansas. NOAA 9 and 11 AVHRR radiative surface temperatures, corrected for atmospheric effects using the split window technique, were used for the surface temperature in a bulk atmospheric boundary layer similarity formulation for H. Mean vertically integrated mixed layer temperatures, determined from radiosonde data, were also required in this technique. However, unlike previous applications, the present approach avoids the need for direct wind speed measurements by using instead the geostrophic wind speed, VG, as derived from the routine measurements of the surface pressure field. LE was then determined as the residual term of the surface energy balance, using H from the bulk similarity formulation. Under the unstable conditions considered, results for both H and LE were comparable to those found in previous work by means of measured wind speeds with the same FIFE data. It is shown that for slight to moderate instabilities a 1% error in the friction velocity generally produces less than 1% error in H.

Design artifacts in eulerian air quality models: Evaluation of the effects of layer thickness and vertical profile correction on surface ozone concentrations

Previous studies on the regional acid deposition model (RADM) have revealed high bias of surface SO 2 and O 3 concentrations by the model, especially during nighttime hours. Comparison of the RADM results with surface measurements of hourly ozone concentrations from the National Dry Deposition Network (NDDN) sites showed distinct diurnal variations in the model high bias. Here, we investigate what part of this phenomenon is influenced by the coarse vertical resolution of RADM in representing the deposition layer. For certain deposition species in the model, we apply the planetary boundary layer (PBL) similarity theory to predict the high bias of the model results (volume averages) to the surface observations (time series at a point) for the horizontally homogeneous case. Here, we applied the profile corrections to a secondary species O 3, which is one of active reacting species even at night especially with NO. However, we attempted to separate the effect of deposition layer thickness from the effects of other horizontal and vertical resolution such as emissions source distribution during the NOO 3 titration process for a clearer presentation of our hypothesis. The study shows that there are situations when a considerable portion of the high bias of model O 3 concentrations at night is explained by the coarse vertical resolution in the deposition layer. It is shown that the model needs to resolve, at least, the lower half of the PBL in order to predict surface deposition fluxes correctly. Comparison with several NDDN observations shows that for certain NDDN sites the present hypothesis cannot fully explain the model's high bias of daily minimum O 3. In a companion paper, the effect of emission source distribution in representing the NOO 3 titration process will be studied to investigate causes of the model bias further.

Using scintillation at two wavelengths to measure path-averaged heat fluxes in free convection

Local free convection scaling is one of the obvious triumphs of boundary-layer similarity theory. In free convection, there is no dynamic velocity scale; the sensible and latent heat fluxes, therefore, scale directly with the temperature and humidity structure parameters C t 2 and C q 2. By using scintillation to measure the refractive index structure parameter C n 2 at two electromagnetic (EM) wavelengths, we can obtain C t 2 and C q 2 and, thus, in effect, measure path-averaged values of the sensible and latent heat fluxes. Here I describe this so-called two-wavelength method for free convection, derive quantitative guidelines for optimizing the method, and evaluate its potential accuracy. I show that the two-wavelength method works best when one EM wavelength is in the visible or infrared region and the other is in the millimeter or radio region. When the Bowen ratio is between -5 and -0.1 or between 0.1 and 5, the expected accuracy of the measured fluxes is ±10–20% — typical of what is possible with eddy-correlation measurements. With the two-wavelength method, however, the fluxes represent spatial averages.

Daytime turbulent exchange between the Amazon forest and the atmosphere

Detailed observations of turbulence just above and below the crown of the Amazon rain forest during the wet season are presented. The forest canopy is shown to remove high‐frequency turbulent fluctuations while passing lower frequencies. Filter characteristics of turbulent transfer into the Amazon rain forest canopy are quantified. In spite of the ubiquitous presence of clouds and frequent rain during this season, the average horizontal wind speed spectrum and the relationship between the horizontal wind speed and its standard deviation are well described by dry convective boundary layer similarity hypotheses originally found to apply in flat terrain. Diurnal changes in the sign of the vertical velocity skewness observed above and inside the canopy are shown to be plausibly explained by considering the skewness budget. Simple empirical formulas that relate observed turbulent heat fluxes to horizontal wind speed and variance are presented. Changes in the amount of turbulent coupling between the forest and the boundary layer associated with deep convective clouds are presented in three case studies. Even small raining clouds are capable of evacuating the canopy of substances normally trapped by persistent static stability near the forest floor. Recovery from these events can take more than an hour, even during midday.

A software library for the calculation of surface fluxes over land and sea

In this paper Fortran-77 routines are described for the calculation of the surface fluxes of heat, moisture, and momentum over horizontally homogeneous flat terrain. Distinction is made between conditions over sea and over land. Different parameterization are implemented where the level of the parameterization depends on the availability of the input data. A so-called flux-profile method is utilised when wind, temperature and humidity observations are available at two heights in the atmospheric surface layer. The minimum input parameters over sea are the water temperature, the air temperature and a single wind speed. Over land these are the wind speed, the air temperature, the aerodynamic roughness length and cloud cover from SYNOP-observations. As such the fluxes can be calculated with routinely available observations at meteorological stations. Therefore, the boundary layer similarity approach for which the surface fluxes are needed, becomes feasible for a wide range of applications.

Specification of the Scale and Magnitude of Thermals Used to Initiate Convection in Cloud Models

Boundary layer similarity techniques are employed to specify the scale and intensity of a thermal perturbation used to initialize a cloud in a numerical cloud model. Techniques are outlined to specify the needed similarity variables from external information. Finally, the cloud model respone using the similarity scaled thermal is analyzed employing variations in the similarity variables giving an indication of the importance of the correct specification of the initiating thermal.

Mixed convection boundary layer similarity solutions: prescribed wall heat flux

The similarity solutions for mixed convection boundary-layer flow when the wall heat flux is prescribed are analysed in detail in terms of a buoyancy parameterα andm the exponent of the free stream flow. It is shown that forα〉0 the solution approaches the free convection limit, and forα〈0, there is a range ofα,αs〈α〈0, over which dual solutions exist. The nature of the bifurcation atα=αs, and how the lower branch of solutions behaves asα→0− are also considered. It is established that the solution becomes singular asm→1/5 and the nature of this singularity is also discussed, where it is shown that two separate cases have to be treated, namely whenα is of 0(1) and whenα is small. Finally it is shown that form large the solution approaches that corresponding to exponential forms for the free stream and prescribed wall heat flux. Taken all together this information enables a complete description of how the solution behaves over all possible ranges of the parametersα andm to be deduced.

An energy balance approach to determine regional evapotranspiration based on planetary boundary layer similarity theory and regularly recorded data

An energy balance procedure was developed to determine regional evapotranspiration using only regularly recorded solar radiation and rawinsonde data. The major input terms in the basic energy balance equation are daily surface net radiation and sensible heat flux. Net radiation was determined by empirical and semiempirical radiation balance equations and the sensible heat flux term from an aerodynamic mass transfer equation derived from concepts of planetary boundary layer similarity theory. The procedure gave better results for a small (100 ha) agricultural watersheds than a comparable procedure based on purely aerodynamic mass transfer considerations, especially on 1‐ and 2‐day periods. For a larger (1000 ha) hydrologic watershed the model achieved acceptable accuracy for monthly estimates of regional evapotranspiration. On this time scale, comparison with observation yielded slopes from 0.97 to 1.14 with correlations between 0.90 and 0.91. For the monthly comparison, the purely aerodynamical model achieved virtually the same accuracy. These results were obtained using the same data set that was used to calibrate the model. When independent data were used, the accuracy for the monthly estimate degraded (slope 0.75, correlation 0.40). For bimonthly estimates, accuracy improved (slope 0.92, correlation 0.73).

Evaluation of surface wind and flux analysis techniques using conventional data in marine cyclones

Abstract Data from seven storms from the Storm Transfer and Response Experiment in November 1980 have been used to evaluate the relative accuracy of surface wind and flux fields based on two analysis procedures. Two essentially independent techniques were used; objective analysis which is based on composite data taken at several synoptic intervals to enhance the number of observations and processing carefully hand-analyzed (subjective) surface pressure analyses into wind and flux fields using a planetary boundary layer (PBL) similarity model. Scale and accuracy limits imposed by instrument accuracy, sampling error, and gridding and analysis procedures are evaluated for each of these techniques by comparison with independent data and with each other. Wind field differences between the objective composite analysis and the PBL model predictions are found to be comparable to the measurement-related uncertainty in the observations. Unresolved variability in the 10–100 km scale of the dynamic and thermodynamic variables produces the main source of error in both the objective and model wind fields. Additional wind field differences are contributed by PBL and gradient wind assumptions used in the PBL model. Wind differences between either of the two analyses and individual observations are about ±3 m s−1 and ±30° in the mean, and can be greater than ±5 m s−1 and ±50° for small regions. Comparable differences are found between the two wind field analyses. The wind and thermodynamic field differences combine to produce substantial differences in the derived fields. Mean differences of ±19W m−2 and ±41 W m−2 for the fluxes of sensible and latent heat, respectively, represent differences of about 50% of the mean fluxes, with local differences as much as double or triple the magnitude of these means. Fronts are equally well represented by the two analyses, but values of divergence and curl of surface stress may differ by a factor of 2 or more in regions of fronts. These local differences in the derived fields result primarily from the large wind field differences in these inadequately resolved regions.

Laminar thermal boundary layer on a continuous accelerated sheet extruded in an ambient fluid

Exact boundary layer similarity solutions are developed for flow, friction and heat transfer on a continuously accelerated sheet extruded in an ambient fluid of a lower temperature.

Natural convection in stratified porous media heated from the side.

Natural convection in horizontally stratified porous media heated from the side is studied analytically and numerically. The analysis assumes the boundary layer approximation and similarity solutions are obtained for temperature distributions, velocity profiles and the heat transfer characteristics. The analytical solutions can approximately describe the effect of layering in permeability on the convective behavior, except near the interface where the flow changes abruptly. It is also shown that they compare well with the numerical solutions for overall heat transfer behavior.

A class of backward free-convective boundary-layer similarity solutions

This paper presents a class of backward free-convective boundary-layer similarity solutions. It is shown that these boundary layers can be produced along slender downward-projecting slabs of prescribed thickness variation, which are infinitely long. It is pointed out that these solutions can be used to describe free convective flows along vertical fins which have received attention in the literature before. An important result is that the temperature along a downward-projecting fin of constant thickness varies in proportion to the inverse of the seventh power of the shifted longitudinal coordinate.

Exact and approximate solutions of a chemically reacting nonequilibrium flow problem

By studying a two-dimensional flow problem, the consequences of employing approximation methods in ignition problems are elucidated. Asymptotic and local similarity solutions are obtained for flows over an adiabatic plate and over a perfectly conducting plate. The governing partial differential equations are transformed into a single integral equation in Von Mises space which is amenable to solutions by the Laplace method and by the assumption of a slowly varying function. To apply the technique of local similarity to the present problem, the usual boundary layer similarity transformation is used. The results are compared with an available exact numerical solution.

MHD flow past a semi-infinite flat plate with heat transfer

Exact numerical solutions to the boundary layer similarity equations of MHD flow and heat transfer past a semi-infinite flat plate of an incompressible viscous fluid have been presented. The velocity of the fluid U and the magnetic field H 0 at a distance from the plate are both assumed to be uniform and parallel to the plate which is considered as isothermal. Velocity, magnetic and temperature fields have been shown graphically whereas the numerical values of ƒ′(0) and {− θ′(0)} are entered in tables. We observe that both ƒ′(0) and {− θ′(0)} decrease with increasing S (magnetic field parameter) and increase with increasing λ (ratio of magnetic diffusivity and viscous diffusivity).

On the unified approach to the boundary layer similarity problems of fluid mechanics

Transformed momentum and energy boundary layer equations are presented in such a form that constitutes the unified base from which the basic boundary layer similar solutions can be developed. This is verified on a number of classical viscous fluid flow application.

A proposed method for estimating diffusion in a freely convective boundary layer by acoustic sounding

An acoustic sounder system can be configured to provide estimates of the vertical profile of wind velocity and the dissipation rates of kinetic and potential energy. A method based on the concepts of boundary-layer similarity theory is outlined by which the characteristic velocity, w ∗ , in a freely convective boundary layer is deduced from the inversion height and a combination of any two of the mean wind speeds in the layer, the dissipation rate of turbulent kinetic energy and that of turbulent potential energy. These variables, in conjunction with the mean wind velocity and source discharge rate are used to establish the normalized heights, downwind and crosswind distances and the crosswind integrated concentrations of passive contaminants, as well as the distance to and magnitude of the maximum ground concentration of initially buoyant or momentum-driven contaminants. The normalized lateral and vertical spreading is deduced from empirically established laboratory relationships for non-buoyant participates. A preliminary analysis is presented for the feasibility of a similar application to the near-neutral and stable planetary boundary layer.

Eddy exchange coefficients in numerical models of the planetary boundary layer

Specification of the eddy exchange coefficients is perhaps one of the most difficult problems in the numerical modeling of the planetary boundary layer. These coefficients have been computed from finite-difference analogs to analytical expressions associated with surface boundary-layer similarity theory, which is based on observations in an equilibrium surface layer. This procedure leads to erroneous results in the region above the surface layer and in a non-equilibrium surface layer. In addition, differencing problems arise in regions of small vertical wind shear. A new turbulence transport model has been obtained through the closure procedures for the transport equations of the Reynolds stress and the turbulent length scale. The new approach could be used to calculate Reynolds stresses and eddy exchange coefficients throughout a non-neutral planetary boundary layer under non-equilibrium conditions.

Application of acoustic sounding to estimating fusion in an atmospheric boundary layer

An acoustic sounder system can be configured to provide estimates of the vertical profile of velocity and dissipation rate of kinetic and potential energy. A method based on the concepts of boundary-layer similarity theory is outlined by which the characteristic velocity in a freely convective boundary layer is deduced from the inversion height and the asymptotic value of the dissipation rate of kinetic energy near the inversion. These values, in conjunction with the mean velocity, are used to establish the normalized heights, downwind and cross-wind distances, and cross-wind integrated concentrations. The normalized lateral and vertical standard deviations are then deduced from empirically established laboratory relationships for nonbuoyant particulates. Preliminary analysis indicate a similar methodology may be applicable to the stable boundary layer.

An application of boundary-layer similarity theories to an aircraft accident investigation

The vertical distribution of turbulence in the planetary boundary layer at the time and place of an aircraft accident is examined. Estimates of the surface stress are determined by means of the boundary-layer resistance laws with a correction for baroclinity. The response of the aircraft to turbulence during its approach, and the exceedance characteristics of the turbulence are given for an empirical spectrum of vertical velocity. Also, a simulation is made of the vertical velocity along the approach path.