Profile Shape Factor Research Articles

Generalized Scaling and Model for Friction in Wall Turbulence.

We present a novel generalized scaling framework and predictive model for wall friction in turbulent flows. The scaling is derived from the dynamical equations, and total mean-flow kinetic energy and the velocity profile shape factor are used as surrogates for dynamical and boundary condition effects. Veracity of the present approach is assessed using data from the literature spanning unprecedented ranges of flow types, Reynolds numbers, accelerations, and history effects. Unlike previous models that solely apply to standard flows, the present framework reconciles nonstandard flows with standard flows and enables accurate estimates of wall friction in numerical simulations and experiments without resolving the viscous sublayer or using the law of the wall.

A high-resolution and observationally constrained OMI NO<sub>2</sub> satellite retrieval

Abstract. This work presents a new high-resolution NO2 dataset derived from the NASA Ozone Monitoring Instrument (OMI) NO2 version 3.0 retrieval that can be used to estimate surface-level concentrations. The standard NASA product uses NO2 vertical profile shape factors from a 1.25° × 1° (∼ 110 km × 110 km) resolution Global Model Initiative (GMI) model simulation to calculate air mass factors, a critical value used to determine observed tropospheric NO2 vertical columns. To better estimate vertical profile shape factors, we use a high-resolution (1.33 km × 1.33 km) Community Multi-scale Air Quality (CMAQ) model simulation constrained by in situ aircraft observations to recalculate tropospheric air mass factors and tropospheric NO2 vertical columns during summertime in the eastern US. In this new product, OMI NO2 tropospheric columns increase by up to 160 % in city centers and decrease by 20–50 % in the rural areas outside of urban areas when compared to the operational NASA product. Our new product shows much better agreement with the Pandora NO2 and Airborne Compact Atmospheric Mapper (ACAM) NO2 spectrometer measurements acquired during the DISCOVER-AQ Maryland field campaign. Furthermore, the correlation between our satellite product and EPA NO2 monitors in urban areas has improved dramatically: r2 = 0.60 in the new product vs. r2 = 0.39 in the operational product, signifying that this new product is a better indicator of surface concentrations than the operational product. Our work emphasizes the need to use both high-resolution and high-fidelity models in order to recalculate satellite data in areas with large spatial heterogeneities in NOx emissions. Although the current work is focused on the eastern US, the methodology developed in this work can be applied to other world regions to produce high-quality region-specific NO2 satellite retrievals.

Closure relations effects on the prediction of the stratified two-phase flow stability via the two-fluid model

The possibility of predicting the exact long wave linear stability boundary via the two-fluid (TF) model for horizontal and inclined stratified two-phase flow is examined. The application of the TF model requires the introduction of empirical closure relations for the velocity profile shape factors and for the wave induced wall and interfacial shear stresses. The latter are recognized as the problematic closure laws. In order to explore the closure relations effects and to suggest the necessary modifications that can improve the stability predictions of the TF model, the results are compared with the exact long wave solution of the Orr–Sommerfeld equations for the two-plate geometry. It is demonstrated that with the shape factors corrections and the inclusion of wave induced stresses effects, the TF model is able to fully reproduce the exact long wave neutral stability curves. The wave induced shear stresses in phase with the wave slope, which give rise to the so called “sheltering force”, were found to have a remarkable destabilizing effect in many cases of horizontal and inclined flows. In such cases, the sheltering effects must be included in the TF model, otherwise the region of smooth stratified flow would be significantly over predicted. Based on the results of the exact analysis, a simple closure relation for the sheltering term in the TF model is provided.

Post-monsoon equilibrium beach profiles and longshore sediment transport rates at Candolim, Miramar and Keri beaches of Goa, India

Equilibrium profile is one of the conce pts in coastal geomorphology which is a result of the balance of destructive versus constructive forces. Two e quilibrium be ach profile models, viz. Bruun/Dean’s twothirds power mode l and modified Bodge expone ntial model were used to analyse the measured post-monsoon (winter) beach profiles from three beaches in Goa having varying coastal morphology settings. The major factors that affect the equilibrium beach profile, viz. the me dian grain size (D50) and the profile shape factor m, which are inve rsely proportional to each othe r, have been analysed for their application to the study site. Also, the variation of these two parameters with beach slope and grain size is studie d. Longshore sedime nt transport rates (LSTRs) are estimate d at these three beaches from the littoral environme ntal observations. LSTRs show that during winte r months, the net transport is of the orde r of 10.83  10 6 m 3 /year (southe rly transport) and 9.02  10 6 m 3 /year (southerly transport) respectively, at Candolim and Ke ri beaches, whe reas it is about 0.62  10 6 m 3 /year (northerly transport) at Miramar. This article discusses the methods used and results of measure me nts of beach morphology, LSTRs, analysis of equilibrium profiles and influe nce of various paramete rs relate d to equilibrium profiles.

Velocity profile variations in granular flows with changing boundary conditions: insights from experiments

We present results of detailed velocity profile measurements in a large series of granular flow experiments in a dam-break setup. The inclination angle, bead size, and roughness of the running surface were varied. In all experiments, the downstream velocity profiles changed continuously from the head to the tail of the avalanches. On rough running surfaces, an inflection point developed in the velocity profiles. These velocity profiles cannot be modeled by the large class of constitutive laws which relate the shear stress to a power law of the strain rate. The velocity profile shape factor increased from the head to the tail of the avalanches. Its maximum value grew with increasing roughness of the running surface. We conclude that flow features such as velocity profiles are strongly influenced by the boundary condition at the running surface, which depends on the ratio of bead size to the typical roughness length of the surface. Furthermore, we show that varying velocity profile shape factors inside gravitationally driven finite-mass flows give rise to an additional term in the depth-averaged momentum equation, which is normally solved in the simulation software of hazardous geophysical flows. We therefore encourage time dependent velocity profile measurements inside hazardous geophysical flows, to learn about the importance of this “new” term in the mathematical modeling of these flows.

Retrieval of vertical columns of sulfur dioxide from SCIAMACHY and OMI: Air mass factor algorithm development, validation, and error analysis

We develop an improved retrieval of sulfur dioxide (SO2) vertical columns from two satellite instruments (SCIAMACHY and OMI) that measure ultraviolet solar backscatter. For each SCIAMACHY and OMI observation, a local air mass factor (AMF) algorithm converts line‐of‐sight “slant” columns to vertical columns using altitude‐dependent scattering weights computed with a radiative transfer model (LIDORT), weighted by relative vertical SO2 profile (shape factor) determined locally with a global atmospheric chemistry model (GEOS‐Chem). The scattering weights account for viewing geometry, surface albedo, cloud scattering, absorption by ozone, and scattering and absorption by aerosols. Absorption of radiation by mineral dust can reduce seasonal mean instrument sensitivity by 50%. Mean SO2 shape factors simulated with GEOS‐Chem and used in the AMF calculation are highly consistent with airborne in situ measurements (INTEX‐A and INTEX‐B); differences would affect the retrieved SO2 columns by 10%. The retrieved vertical columns are validated with coincident airborne in situ measurements (INTEX‐A, INTEX‐B, and a campaign over east China). The annual mean AMF errors are estimated to be 35–70% in polluted regions (e.g., East Asia and the eastern United States) and less than 10% over clear ocean regions. The overall SO2 error assessment is 45–80% for yearly averages over polluted regions. Seasonal mean SO2 columns retrieved from SCIAMACHY and OMI for 2006 are significantly spatially correlated with those from GEOS‐Chem, in particular over the United States (r = 0.85 for SCIAMACHY and 0.82 for OMI). A sensitivity study confirms the sensitivity of SCIAMACHY and OMI to anthropogenic SO2 emissions.

TheAandmCoefficients in the Bruun/Dean Equilibrium Profile Equation Seen from the Arctic

Abstract The Bruun/Dean relation between water depth and distance from the shore with a constant profile shape factor is widely used to describe shoreface profiles in temperate environments. However, it has been shown that the sediment scale parameter (A) and the profile shape factor (m) are interrelated variables. An analysis of 63 Arctic erosional shoreface profiles shows that both coefficients are highly variable. Relative frequency of the average m value is only 16% by the class width 0.1. No other m value frequency exceeds 21%. Therefore, there is insufficient reason to use average m to characterize Arctic shoreface profile shape. The shape of each profile has a definite combination of A and m values. Coefficients A and m show a distinct inverse relationship, as in temperate climate. A dependence of m values on coastal sediment grain size is seen, and m decreases with increasing grain size. With constant m = 0.67, parameter A obtains a dimension unit m1/3. But A equals the water depth in meters 1 m f...

Tuning the electron temperature of a nitrogen plasma by adding helium and argon

Using the global model and its concomitant profile shape factor and recent experimental ionization cross section, calculation of the electron temperature, Te, is carried out as a function of the mixing ratio in two-species N2/Ar and N2/He plasmas. The result is compared with measured values determined by the line-ratio technique in an inductively coupled plasma. The overall trend of the variation of the measured electron temperature is well described by the model: they agree in the N2/He plasma and the calculated Te becomes increasingly lower at higher argon partial pressure, up to ∼20% for a pure argon plasma. A second method uses an empirically determined profile shape factor for a pure nitrogen plasma and calculates the change of electron temperature due to the addition of inert gas. Except for the pure helium case, the difference between the measured and calculated value is <10% in the entire range of mixing ratio.

A computational investigation of unsteady turbulent wake–boundary-layer interaction

The relative motion of rotor and stator blade rows in a turbomachine generates periodically unsteady flow on the blades due to travelling wake perturbations. To better understand the attendant wake–boundary-layer interaction a calculation procedure was developed to model the behaviour of this complex unsteady flow. Due to nonlinear interactions with the boundary layer, the travelling discrete frequency wakes were found to decrease the velocity profile shape factor. For the range of reduced frequencies examined ( ϖ=0.33–9.33) the skin-friction coefficient was found to be frequency dependent. The calculated results for both steady and unsteady velocity profiles, and for skin friction compared well with experimental data. Although the agreement between measured and calculated velocity phase shift was poor, in both experimental and model results the negative phase shift throughout the boundary layer due to the travelling-wave fluctuations has been captured.

Influence of profile shape factors on intrinsic Si-MESFET device capacitances under diffusion mechanism

An accurate model for the device capacitances of ion-implanted MESFETs using Pearson distribution annealing is reported. The effects of profile shape factors on the intrinsic gate-source and gate-drain capacitances are analyzed in the pre- and post-anneal conditions. An established reduction in capacitances with Pearson's higher moments approach leads to optimization of devices performances.

Volume Balance Irrigation Advance Equation: Variation of Surface Shape Factor

In application of the volume balance (VB) models, it is generally assumed that the average depth of surface water is constant. This basic assumption may cause significant errors in computing advance. In this paper an accurate algebraic VB equation is developed to predict the advance phase in surface irrigation. In the suggested analysis the average surface water depth is considered to be variable in time. By systematic analysis of accurate kinematic-wave (KW) numerical solutions, the behavior of the surface profile shape factor used in the VB equation is examined. A new equation describing the time dependence of the surface shape factor is derived. Comparison tests indicated that the suggested variable surface shape factor VB equation produces essentially the same results as the KW numerical method. The suggested equation is improved for the case of level or low sloping borders.

Effect of sandpaper roughness and stream turbulence on the laminar layer and its transition

AbstractThe work reported here was an experimental study of the combined influence of a sandpaper rough surface and a stream turbulence upon laminar and transitional boundary layers. Data correlations were obtained using the previously determined parameter of an equivalent Nikuradse size of roughness. These correlations are derived for the development of the laminar layer in thickness and profile shape factor, for the onset and the length of transition and for the distribution of intermittency through transition. Further fundamental differences in flow behaviour from those in a rough pipe have been found to add to those already reported.

A method for the retrieval of atomic oxygen density and temperature profiles from ground‐based measurements of the O+(²D ‐ ²P) 7320‐Å twilight airglow

This paper describes a technique for the retrieval of altitude profiles of the atomic oxygen concentration (n = [O]) and temperature (T) from ground‐based measurements of the O+(²D ‐ ²P) doublet at 7320 and 7330 Å in the twilight airglow. The technique is based on previously demonstrated knowledge that at solar zenith angles (SZA) characteristic of twilight conditions, the upper state of the 7320‐Å doublet transition is produced by photoionization and photoelectron impact ionization of atomic oxygen and lost mainly by radiative decay, thereby providing a sensitive dependence on [O]. We apply inverse problem theory to retrieve the exospheric temperature (T∞), the atomic oxygen concentration at 120 km (n120), the temperature at 120 km (T120) and the temperature profile shape factor (S) using a Bates‐Walker representation of n given approximately by n = (n120T120/T) exp[−z] where T = T∞ ‐ (T∞ ‐ T120)exp[−S(h ‐ h120)], z is the reduced height, and h is the altitude. The algorithm is tested and theoretically verified using synthetic data sets where random errors of measurements are characterized by Poisson noise due primarily to sky background. In the tests that we report here the solar EUV flux is specified. In a separate paper we will report how the solar EUV ionization rate can be independently derived from various twilight emissions. By comparing retrieved with known input values, it is demonstrated that for the altitude range 200 to 500 km the atomic oxygen concentration [O] can be retrieved with relative errors ≃15% and systematic errors of about 25% if the solar EUV is given. Sensitivity of the results to noise, sample size (degrees of freedom), and absolute calibration are quantitatively evaluated. In addition, to demonstrate the validity of the technique experimentally, we utilized the Atmosphere Explorer E (AE‐E) in situ measurements of the solar EUV flux and [O], with the latter taken when perigee was over Arecibo on an occasion when the observatory airglow spectrometer was simultaneously measuring the 7320‐Å emission from the ground during twilight. The results show excellent agreement with the measured [O] values which were ∼ 50% lower than the mass spectrometer incoherent scatter (MSIS‐86) model values at ∼ 300 km on that day, thereby demonstrating the value of the method for monitoring day‐to‐day variations in [O] and the temperature.

Atomic and carrier profiles of 1-, 2-, 4-, and 6-MeV 30Si implanted into GaAs

3 0Si has been implanted in GaAs at energies of 1, 2, 4, and 6 MeV. We have measured atomic concentration profiles using secondary ion mass spectroscopy (SIMS) and carrier concentration profiles using an electrolytic capacitance-voltage procedure. Theoretical atomic profiles have been calculated using the computer code TRIM-86. The range statistics and profile shape factors: Rm, Rp, ΔRp, skewness (γ1), kurtosis (β2), and maximum Si density (Nmax) have been determined from the SIMS data. The first two moments (Rp and ΔRp) were also obtained from the carrier profiles and the theoretical profiles. The range and standard deviation obtained by the separate techniques have a maximum difference of only 15%, and the difference is usually less than 10%. This is less than the mutual experimental uncertainty of 17%. The samples were activated using a furnace anneal (800 °C, 15 min) with a Si3N4 cap and using rapid thermal anneal (1000 °C, 10 s) with and without a cap. No redistribution of Si was observed for any of the anneal conditions.

Electron density measurements from cutoff of electron cyclotron emission in the DIII-D tokamak

Cutoff of microwave emission at the second harmonic of the electron cyclotron frequency has been used to infer the local electron density profile in the DIII-D tokamak. Modeling the density profile during the uncontrolled density increase associated with the transition to H-mode operation permits the profile shape factor and line average to be estimated. In special cases, the density fluctuations associated with sawteeth can also be inferred. Independent corroboration of the standard density diagnostics has been performed with this technique.

Kinematic overland flow — Generalization of Rose's approximate solution, Part II

The approximate kinematic overland flow equation derived by Rose et al. and generalized by Moore includes a water surface profile shape factor C. Rose et al. assumed a constant C = 0.625. The variation of C as a function of normalized discharge q∗ is examined during various phases of the overland flow hydrograph rise and recession under constant and time-varying rainfall excess. The possible range of C values is bounded by rising and falling limb boundary curves. These vary linearly from C = 1, q∗ = 0 to C = 0.625, q∗ = 1 (steady state or equilibrium) during the hydrograph rise and linearly from C = 0.625, q∗ = 1 to C = 0.4, q∗ = 0 during the recession. At any time during an event the value of C depends on both the value of q∗ and its previous pattern of variation or history. Analytical equations are presented that allow C to be estimated during a runoff event, thus permitting improved predictions of overland flow on plane surfaces using the approximate theory without any increase in computational complexity.

Range and shape factors, damage, regrowth, and redistribution for Ag implants in (100) and (111) Si

The nature of regrowth of implantation-damaged (100) and (111) Si was investigated by measuring the depth distribution of implanted Ag atoms following annealing at 550 °C for fluences of 1×1012 to 1×1015 cm−2. Cross-section transmission electron microscope measurements were made for a few conditions to compare damage depth distributions. Other factors studied were anneal time, Si growth technique, Ag atom densities, and the transition region between amorphous and crystalline Si. Ranges and profile shape factors are reported for 150, 300, 450, and 600 keV Ag implants into Si.

Atomic Profiles of High Energy (MeV) Si Implanted into GaAs

ABSTRACTHigh energy Si implantation into GaAs is of interest for the fabrication of fully implanted monolithic microwave integrated circuits. 30Si has been implanted into LEC GaAs at energies of 1, 2, 4, and 6 MeV. We have measured atomic concentration profiles using SIMS and carrier concentration profiles using an electrolytic CV procedure. Theoretical atomic profiles have been calculated using TRIM-86. Excellent SIMS dynamic range and low background (<1014/cm3) was achieved for the profiles by the use of 30Si. The range statistics and profile shape factors: Rm, Rp, ΔRp, skewness (Y1), kurtosis (B2), and maximum Si density (Nmax) have been determined from the SIMS data by applying a Pearson IV computer fitting routine. The first two moments (Rp and ΔRp) were also obtained from the carrier profiles and the theoretical profiles. The range and standard deviation obtained from each profile have a maximum difference of only 15%, and the difference is usually less than 10%. This is less than the mutual experimental uncertainty of 17%. The samples were activated using a furnace anneal (800°C, 15 min) with a Si3N4 cap and using rapid thermal anneal (1000°C, 10s) with and without a Si3N4 cap. No redistribution of Si was observed for any of the anneal conditions within experimental error.

A model study of pure katabatic flows

A time-dependent 2-dimensional model of pure katabatic flow over a simple finite-length slope is described. This numerical model, based on a turbulent kinetic energy closure, accounts for the effects of radiative cooling and turbulent friction at the surface, and entrainment of air aloft from a quiescent stably stratified ambient atmosphere. The model provides information on the temporal and spatial evolution and structure of katabatic flows. Numerical solution of the governing equations facilitates explicit determination of the coefficient of entrainment, slope Richardson number, profile-shape factors, and depth, velocity, and buoyancy-deficit scales of the flow. The steady-state results of the model, showing the variations of these parameters as functions of downslope distance, slope angle, and ambient stratification, are presented and discussed. For near-neutral stratification, the calculated entrainment coefficient varies as a function only of the slope Richardson number, in agreement with laboratory data. As ambient stratification increases, it profoundly affects the structure of the flow by reducing its depth, speed and entrainment rate. The results and parameterizations presented here can be used as inputs to hydraulic models of drainage flow and pollutant transport. DOI: 10.1111/j.1600-0870.1987.tb00289.x

Depth distributions of hydrogen-implanted and annealed silicon

We have measured the redistribution of hydrogen as a function of annealing temperature in (100) and (111) Si implanted at 250 keV to a fluence of 1×1016 cm−2. The hydrogen profiles were measured using secondary ion mass spectrometry. Hydrogen (1H or 2H) begins to redistribute in hydrogen-implantation-damaged silicon between 300 and 325 °C, moving toward the surface through the implantation-damaged region at a density above 1018 cm−3. The implanted hydrogen begins to diffuse deeper into the undamaged bulk silicon at about 200 °C, but at densities below 1017 cm−3. The initial redistribution of hydrogen toward the surface is shown not to be associated with the regrowth of damage. A second phase of hydrogen redistribution, in which the density of the hydrogen distribution decreases, begins at about 550 °C, which is the temperature of the beginning of regrowth of damage. The density of the implanted hydrogen has decreased below∼1016 cm−3 by 800 °C, for initial implanted hydrogen densities of 1021 cm−3 or less. We also report range and profile shape factors for 1H and 2H atom depth distributions implanted into silicon for a few cases of ion energy and fluence.