Surface Friction Velocity Research Articles

Vertical dispersion of ground-level releases in the surface boundary layer

By assuming that the eddy diffusivity of mass is proportional to that of heat, this paper derives simple expressions for the asymptotic behavior of cross-wind integrated ground-level concentrations under neutral, stable, and unstable conditions. We show that: • C∗y ∼ x∗−1 under neutral conditions; • ∼ x∗−13 under stable conditions; • ∼ x∗−2 under unstable conditions; where C∗y = Cyu∗ |L|Q and x∗ = x/|L|, and Cy is the cross-wind integrated concentration, u∗ is the surface friction velocity, L is the Monin-Obukhov length, and Q is the pollutant release rate. We show that simple interpolations between the asymptotic limits provide excellent fits to the Prairie Grass (Barad, 1958, Paper No. 59, Geophysics Research Directorate, MA) diffusion data. Our analysis of surface dispersion in unstable conditions indicates that the concentration decrease with distance is not consistent with that predicted by free convection theory (Yaglom, 1972, Atmos. Ocean Phys.8, 333–340). Under asymptotically unstable conditions, the concentration falls off as x−2 rather than as x−32 predicted by the theory.

A model-dependent method for inverting vertical profiles of scattering to obtain particle size spectra in boundary layers

A method for obtaining particle size spectra from vertical profiles of scattering strength in planetary boundary layers is presented. It is assumed that the boundary layer is horizontally homogeneous, and that the vertical turbulent diffusion of particles can be modeled from a knowledge of the surface friction velocity. Equilibrium boundary layer profiles for each class of suspended particles are assumed to be established resulting from the balance between vertical turbulent diffusion and gravitational settling. The forward problem thus models the depth-dependent scattering as the sum across size classes weighted by number density and scattering cross-section in accordance with established scattering theory. Constrained inverses produce the size spectra. Results of inversions from synthetic ocean data are presented for optical transmissometry and acoustic backscattering. Inversions of acoustic field data from the HEBBLE experiment are also presented. Finally, the applications of the work presented for the design of ocean boundary layer experiments, its application in other fields, and the directions for future research are discussed.

The impact of soil moisture on dispersion-related characteristics

This study investigates the impact of soil moisture availability on dispersion-related characteristics: surface friction velocity (u*), characteristic scales of temperature and humidity (T* andq*), the planetary boundary layer height (h) and atmospheric stability classified by Monin-Obukhov length (L), Kazanski-Monin parameter (μ) and convective velocity scale (w*) during daytime convective condition using a one-dimensional primitive equation with a refined soil model.

Statistical properties of the sea surface sound dipole source

A broadband measurement (40–4000 Hz) of the vertical directional spectrum of the underwater ambient acoustic field was made in an acoustically isolated area where the ambient is dominated by well‐documented local sea conditions. Measurements, made over a 1‐year period, sampled a wide range of sea conditions and made possible a statistical analysis of the effects of the sea surface condition on the acoustic field. Having the total directional spectrum, unperturbed by long‐distance sources, allowed the partitioning of the measurement into multiple source types, each type distinguished by its unique vertical directional pattern. An important component of the sea‐surface‐generated radiation is a diffuse distribution of vertical dipole sources. A unique property of the present data analysis is that the dipole source strength “area density” is found by matching only that part of the total measured pressure field exhibiting a dipole pattern. This is accomplished by parametric spectral estmation procedures. The frequency spectrum of the dipole source strength is found to be a bandpass function whose parameters are statistically related to the wind‐generated surface friction velocity. The results of the analysis contribute an important element to an accurate modeling of the space‐time statistics of sea surface sound.

Characterizing the dispersive state of convective boundary layers for applied dispersion modeling

Estimates from semiempirical models that characterize surface heat flux, mixing depth, and profiles of temperature, wind, and turbulence are compared with observations from atmospheric field studies conducted in Colorado, Illinois, Indiana, and Minnesota. Sodar observations are compared with tower measurements at the Colorado site, for wind and turbulence profiles. The median surface heat flux, as calculated using surface-layer flux-profile relationships and an energy budget model, was consistently overestimated by 20 to 80%. Several mixing-depth models were evaluated: (1) integration of the hourly surface heat flux and friction velocity, (2) solving for the time rate of change of profiles of virtual potential temperature, and (3) an interpolation scheme used by the U.S. Environmental Protection Agency in regulatory dispersion models. For the late afternoon, 80 to 90% of the estimates from the first and third models were within 40% of the observed values. For the morning hours after sunrise, all were less accurate. Temperature estimates from surface-layer flux-profile relationships compared well with observations within the mixed layer, but were too low for the inversion layer aloft. Wind profiles were derived using surface-layer flux-profile relationships, a windprofile power-law based on Pasquill stability category, and sodar measurements. The sodar measurements were superior to both types of model estimates. Turbulence profiles were derived from sodar measurements and from semiempirical similarity relationships based on mixing depth and Obukhov length. The scatter in the comparisons with the sodar observations is twice that seen in the comparisons with empirical profile relationships. Overall, it appears that uncertainty of as low as 20 to 30% in the characterization of the diffusion meteorology is the exception rather than the rule.

On the impact of thermal stability on some rough flow effects over mobile surfaces

Calculations are made of the effects of thermal stability under a range of conditions, over the sea and land, on the physical factors (including the critical wind speed) affecting dust-storm generation, snow drift, and rough sea conditions. The computational procedure involves the surface friction velocity, u*, and its relation with the aerodynamic roughness over aerodynamically rough, mobile surfaces. The results indicated that even at relatively high wind speeds, thermal effects under extreme advection situations may be significant, particularly for those properties of the agitated surface dependent on u*3 and u*4.

Measuring the vertical directional spectra caused by sea surface sound

The objective of the measurements discussed here is the development of a database of directional spectra obtained in an acoustically isolated area (Tongue of the Ocean, the Bahamas) where the acoustic ambient is principally controlled by the local (observable) sea surface conditions. The purpose of the database is the identification of a model of the space‐time statistics of sea surface sound. A wideband (40‐ to 4000‐Hz) vertical acoustic linear antenna system was used. Data logging took place in a remote autonomously operating subsurface buoy system. Recording restrictions limited each of the seven octavely nested apertures of the sensor system to four wavelengths. However, quite adequate spatial resolution of the directional spectral estimates was obtained using a physically based parametric model of the random process. The results of the initial 2‐month deployment (wind speed range of 2–16 m/s) are discussed here. The measured directional spectra are displayed as a function of frequency, elevation angle, and surface friction velocity. The sea surface sound source structure is discussed.

Ambient and transient bubble spectral densities in quiescent seas and under spilling breakers

Recently published observations, using laser holography near the ocean surface, have shown that the densities of 10 to 15 micron radius bubbles can be as high as 106 (per cubic meter per micron radius increment) within 3 m of the surface of quiescent seas, thereby supporting the acoustically derived values of two decades ago. The accumulated evidence suggests that these quiescent microbubble densities off the coast of California are proportional to a−4 for radius range 10 < a < 60 microns and a−2.5 for larger bubbles. A calibrated, floating, multi‐frequency, acoustical resonator has now been used to obtain the bubble spectrum for 9 radii from 30 to 240 microns, 25 cm under breaking waves in the open sea. At this depth, bubbles larger than 60 microns have a radius dependence approximately a−2.5 and smaller bubble densities vary approximately as a a−4. Our densities are in good agreement with recently published laboratory studies of bubbles, using laser scattering under wind‐blown surfaces with about the same surface frictional velocity U*. Older, photographically derived densities at ocean depth 75 cm are close to the new data only over the limited range 50 to 100 microns. Past inconsistencies between acoustical results and optical results were apparently due to an inability of some optical techniques to identify small bubbles in the difficult ocean environment.

Coherent structure of the convective boundary layer derived from large-eddy simulations

Turbulence in the convective boundary layer (CBL) uniformly heated from below and topped by a layer of uniformly stratified fluid is investigated for zero mean horizontal flow using large-eddy simulations (LES). The Rayleigh number is effectively infinite, the Froude number of the stable layer is 0.09 and the surface roughness height relative to the height of the convective layer is varied between 10−6 and 10−2. The LES uses a finite-difference method to integrate the three-dimensional grid-volume-averaged Navier–Stokes equations for a Boussinesq fluid. Subgrid-scale (SGS) fluxes are determined from algebraically approximated second-order closure (SOC) transport equations for which all essential coefficients are determined from the inertial-range theory. The surface boundary condition uses the Monin–Obukhov relationships. A radiation boundary condition at the top of the computational domain prevents spurious reflections of gravity waves. The simulation uses 160 × 160 × 48 grid cells. In the asymptotic state, the results in terms of vertical mean profiles of turbulence statistics generally agree very well with results available from laboratory and atmospheric field experiments. We found less agreement with respect to horizontal velocity fluctuations, pressure fluctuations and dissipation rates, which previous investigations tend to overestimate. Horizontal spectra exhibit an inertial subrange. The entrainment heat flux at the top of the CBL is carried by cold updraughts and warm downdraughts in the form of wisps at scales comparable with the height of the boundary layer. Plots of instantaneous flow fields show a spoke pattern in the lower quarter of the CBL which feeds large-scale updraughts penetrating into the stable layer aloft. The spoke pattern has also been found in a few previous investigations. Small-scale plumes near the surface and remote from strong updraughts do not merge together but decay while rising through large-scale downdraughts. The structure of updraughts and downdraughts is identified by three-dimensional correlation functions and conditionally averaged fields. The mean circulation extends vertically over the whole boundary layer. We find that updraughts are composed of quasi-steady large-scale plumes together with transient rising thermals which grow in size by lateral entrainment. The skewness of the vertical velocity fluctuations is generally positive but becomes negative in the lowest mesh cells when the dissipation rate exceeds the production rate due to buoyancy near the surface, as is the case for very rough surfaces. The LES results are used to determine the root-mean-square value of the surface friction velocity and the mean temperature difference between the surface and the mixed layer as a function of the roughness height. The results corroborate a simple model of the heat transfer in the surface layer.

Velocity profiles, the resistance law and the dissipation rate of mean flow kinetic energy in a neutrally and stably stratified planetary boundary layer

The logarithmic + polynomial approximation is suggested for vertical profiles of velocity components in a planetary boundary layer (PBL) at neutral and stable stratification. The resistance law functions A and B are determined on the basis of this approximation, using integral relations derived from the momentum equations, the Monin-Obukhov asymptotic formula for the wind profile in a stably stratified near-surface layer and the known expressions for the PBL depth. This result gives a realistic and convenient method for calculating the surface friction velocity and direction and the total dissipation rate of mean flow kinetic energy in terms of geostrophic velocity, buoyancy flux at the surface, the roughness parameter and the Coriolis parameter. In the course of these derivations a review is given of current views on the main problems of the neutral and stable PBL.

Turbulent diffusivity and diurnal variations in the atmospheric boundary layer

Diurnal variations of the vertical profiles of wind and temperature have been surveyed, and the diffusivity and the dimensionless gradient function in the atmospheric boundary layer have been estimated. Even in the middle of the atmospheric boundary layer (e.g., below a height of 442 m), the vertical wind profile normalized by the surface friction velocity has approximately a universal profile function different from that in the surface boundary layer. Under strong stability conditions, the dimensionless gradient function has a value of about 9.

A comparison of surface friction velocities estimated by dissipation and iterative bulk aerodynamic methods during gale

Energy dissipation method and an Iterative Bulk Aerodynamic Method (IBAM) are used to estimate friction velocity (u*) for a wide wind speed range (5.66 to 21.6 ms−1) with convective atmospheric conditions over the ocean during the Genesis of Atlantic Lows Experiment (GALE). Values of u* obtained by the IBAM are in reasonably good agreement with those from the dissipation method. The iterative bulk method appears to do well for wind speeds up to about 21 ms−1.

A model study for ambient air quality analysis using routine meteorological observations

In the present study, more realistic and easily adaptable input parameters have been used with a view to investigating the long-range air quality analysis for the dispersion of air pollutants emitted from an area source with a multiple box model. The model formulation has been discussed at length for the ground level sources when convective conditions prevail. The routine meteorological observations have been used for the computation of sensible surface heat flux, friction velocity and mixing depth. A radiation model provides the estimates of the sensible surface heat flux. Based on the similarity theory, an iterative procedure has been adopted for the estimation of friction velocity which provides a coupling of radiation computation and the surface layer of the planetary boundary layer through surface heat flux expression. The important parameters—wind speed and eddy diffusivity profiles—have been derived and have been used to obtain the concentration patterns as hourly averages. The procedure could be easily adopted where observed meteorological parameters may be used for studying the dispersal of pollutants from the ground level sources.

Estimating Small Grain Equivalents of Shrub-Dominated Rangelands for Wind Erosion Control

ABSTRACT Awind erosion equation, which estimates average annual erosion, requires that all vegetative cover be expressed as dry biomass per unit area of flat small grain equivalent (SG)e. For a standing vegetative canopy, the (SG)e depends on the magnitude of the friction velocity reaching an underlying erodible surface. The soil surface friction velocity, and thus (SG)^, was shown to be a function of aerodynamic roughness length of the canopy and the product of a drag coefficient and plant area index. Aerodynamic roughness, as well as canopy silhouette area and mass distribution, were measured in sand sagebrush {Artemisia filifolia Nutt.) and yucca {Yucca elata Englem.) canopies. Estimating equations were developed to predict (SG)^ of the sagebrush and yucca canopies using either above-ground dry biomass or plant area index as inputs. Additional estimating equations were developed to predict plant area or plant mass from simple geometric measurements of yucca and sagebrush. Finally, for shrub or stubble canopies in which (SG)e prediction parameters have not been measured, a way to approximate the prediction parameters using an estimate of canopy aerodynamic roughness length was developed.

A comparison of methods for estimating u* from given uz and air‐sea temperature differences

This paper presents an objective assessment of four methods for estimating sea surface friction velocity u* from wind speed at height z, uz, and air‐sea temperature difference. The methods are compared by using the computed friction velocity as the normalization factor in parametric correlations of wind‐wave parameters with the wind and wave measurements made by NOMAD buoys in the Great Lakes. The results show that (1) wind profile parameters obtained from the four methods are generally comparable, (2) parametric correlations with parameters normalized by u* lead to significantly decreased percentage deviations over correlations normalized by uz, and (3) correlations based on u* derived from the four methods show nearly identical percentage deviations. The conclusions are that (1) u* normalization acts to eliminate the effect of atmospheric stability and (2) any of the four methods can be used effectively in practical applications.

Aircraft estimates of the geostrophic drag coefficient and the rossby similarity functions A and B over the sea

Estimates of the geostrophic drag coefficient and the Rossby similarity functions, A and B obtained from data collected by an instrumented aircraft over the sea are presented. The average value of the geostrophic drag coefficient is 0.027 and is independent of the geostrophic windspeed. The dependence of the similarity functions A and B on boundary-layer parameters is investigated. The function A is found to depend on baroclinicity parameters, while B depends on the parameter u*/fh (where u* is the surface friction velocity, f is the Coriolis parameter, and h is the boundary-layer depth). Using the geostrophic drag coefficient found here and the results of surface drag coefficient studies, a relationship between geostrophic windspeed and surface windspeed is obtained which shows good agreement with empirical data.

A study of sodar observed shear echo structures in relation to wind velocity and other turbulence parameters

The various types of sodar structures observed on land during nocturnal stable conditions have been studied in relation to the changes in meteorological parameters of surface wind speed, frictional velocity and Richardson’s number. The data for the period May 1977 to April 1982 have been used for these studies. It has been found that surface winds contribute to the tall spiky surface based layer structures while the behavior of the frictional velocity and Richardson's number give information about the formation and break up of the eddies in the stable layers of height upto 100m and more respectively.

Nonlinear Properties of Random Gravity Waves in Water of Finite Depth

Abstract The weakly nonlinear theory for a stationary and homogeneous field of random gravity waves in water of finite depth is developed to the third order. This describes the second-order nonlinearities as a bound wavefield that can be expressed in terms of the freely propagating first-order waves. Expressions are obtained for the second-order spectrum and for the first nonlinear correction to the free-wave phase velocity. Calculations of these nonlinearities are made for a specified spectral form (the TMA spectrum) and also for some spectra derived from measurements. Three influences are considered: (i) the directional distribution, which spreads the interacting waves and, if narrow, will enhance the bound-wave contribution to the spectrum; (ii) the growth stage, or maturity, which is quantified by the ratio of the phase velocity at the peak frequency to the surface friction velocity and, if small, will increase the nonlinearity considerably; and (iii) the depth. Although the nonlinearity increases for...

Simple model and climatological aspects of the structure of the convective boundary layer

A model which estimates the parameters in the convective boundary layer using routine meteorological observation data is developed. The data required are net radiation, air temperature, wind speed, and a radiosonde sounding. The model includes the estimation schemes of surface heat flux and friction velocity, and a mixed layer height model modified from the jump model. The field observation of the boundary layer was carried out at Tsukuba, Japan. Estimated data by the model fit well with field observation data. Seasonal and diurnal variations of the convective boundary layer are estimated by the model with the data obtained over a period of 3 years at Tsukuba. Results are as follows. Convection is most intensive in spring. There are two peaks on the seasonal variation pattern of the mixed layer height, with a maximum in spring and secondary peak in autumn. Notably, it is not so high in the summer, despite strong solar radiation. It is known that the potential temperature gradient is large in summer and small in winter, with this feature being related to air mass types. The potential temperature gradient of continental air mass is small and that of maritime air mass is large. Together with the surface heat flux, the occurrence frequency of types of air mass is one of the important factors in explaining seasonal variation of the structure of the convective boundary layer.

Characteristics of turbulent structures in the unstable atmospheric surface layer

An atmospheric surface-layer (ASL) experiment conducted at a meteorological site in the Oostelijk-Flevoland polder of the Netherlands is described. Turbulent fluctuations of wind velocity, air temperature and static pressure were measured, using three 10 m towers. Simultaneous turbulent signals at several heights on the towers were used to investigate the properties of the turbulent structures which contribute most significantly to the turbulent vertical transports in the unstable ASL. These turbulent structures produce between 30 and 50% of the mean turbulent vertical transport of horizontal alongwind momentum and they contribute to between 40 and 50% of the mean turbulent vertical heat transport; in both cases this occurs during 15 to 20% of the total observation time. The translation speed of the turbulent structures equals the wind speed averaged over the depth of the ASL, which scales on the surface friction velocity. The inclination angle of the temperature interface at the upstream edge of the turbulent structures to the surface is significantly smaller than that of the internal shear layer, which is associated with the temperature interface. The turbulent structures in the unstable ASL are determined by a large-scale temperature field: Convective motions, which encompass the whole depth of the planetary boundary layer (PBL), penetrate into the ASL. The curvature of the vertical profile of mean horizontal alongwind velocity forces the alignment of the convective cells in the flow direction (Kuettner, 1971), which have an average length of several hundreds of metres and an average width of a few tens of metres. This mechanism leads to the formation of turbulent structures, which extend throughout the depth of the ASL.