Note on turbulent scaling parameters for the convective planetary boundary layer

Scaling velocities relevant for turbulent flows in the planetary boundary layer are discussed. It is suggested that the scaling parameters should be determined by integrated bulk properties of the respective turbulent production terms. According to this concept, a new velocity scale, replacing the friction velocityu*, is proposed depending on bothu* and the geostrophic windu _g . The convective velocity scalew* can be determined by the integral of the buoyancy production term and is therefore an appropriate velocity scale. Examination of Minnesota and Kansas data shows that these data do not give the possibility of verifying whether the new scaling velocity is more appropriate thanu*. This is because the range of variability of atmospheric stability during the field measurements is too small. However, theoretical considerations based on integrated properties of the turbulence, through the depth of the planetary boundary layer, are given in support of the new scaling velocity.     

The Effective Height of a Two-Wavelength Scintillometer System

A scaling factor, S, is derived to account for the difference in path-weighted measurement heights of a combined system consisting of a large-aperture scintillometer (LAS) and a millimetre-wave scintillometer (MWS), operating at wavelengths of 0.88 μm and about 3 mm respectively, and designed to determine the area-averaged latent heat flux. This work extends an earlier derivation of Z _ef , the effective height for the LAS yielding the area-averaged sensible heat flux. The LAS and MWS have different path-weighting functions, therefore, in general, it is expected that the path-weighted beam heights are different, for paths other than with the beam parallel to the land surface. Their difference will depend on the detail of the experimental set-up. The objective is to introduce a scaling factor that transforms the MWS refractive-index structure parameter measurement to the same path-weighted height of the LAS measurement. By applying S as a prelude to the calculation of the temperature and humidity structure parameters, and the sensible and latent heat fluxes, these quantities are made representative of the same measurement height, thus simplifying the application of two-wavelength scintillometry. The equations presented here enable the analysis of LAS-MWS paths such that they can be selected to optimize S towards its ideal value of unity. For this purpose we provide a new analytical approximation of the LAS path-weighting function. The importance of accounting for S is demonstrated by example applications over varying topography as well as for slanted beams.     

Notes on an Internal Boundary-Layer Height Formula

The derivation of the Panofsky–Dutton internal boundary-layer(IBL) height formula has been revisited. We propose that the upwindroughness length (rather than downwind) should be used in theformula and that a turbulent vertical velocity (_w) ratherthan the surface friction velocity (u_*) should be considered asthe appropriate scaling for the rate of propagation ofdisturbances into the turbulent flow. A published set ofwind-tunnel and atmospheric data for neutral stratification hasbeen used to investigate the influence of the magnitude ofroughness change on the IBL height.     

Friction velocity scaling in wind wave generation

This note is devoted to the problem of the appropriate scaling of parameters relevant for sea waves, such as wave height, peak frequency, duration, and fetch. In the past, the growth of sea waves has often been analysed in terms of the wind velocity at a fixed height, despite the fact that many authors have stressed the importance of scaling with the friction velocity. This problem would be immaterial if the ratio between the friction velocity and the wind speed at a fixed height were a constant. There is, however, ample evidence that this ratio increases with wind speed (Smith and Banke, 1975; Smith, 1980), in agreement with dimensional considerations by Charnock (1955) on the friction height. As a result, the scaling problem is an important one. In this note we conjecture that the correct procedure is to scale wave parameters with friction velocity, and we discuss experimental evidence for the correctness of this conjecture. Comparing two independent datasets (JONSWAP and KNMI), we find some evidence supporting our ideas. Further confirmation remains desirable, however, and suggestions are made as to how this might be obtained.     

Three-dimensional simulations and wind-tunnel experiments on airflow over isolated forest stands

Prediction of windthrow risk to individual or groups of retained trees in harvested stands requires an improved understanding of canopy airflow dynamics. Large-eddy simulations were used to simulate wind-tunnel experiments in two and three dimensions to compare with observations for model validation and to address parameter space considerations for the design of subsequent retention pattern experiments. The three-dimensional simulations were similar to the observed wind-tunnel data for the statistical profiles for but there were greater differences in skewness and kurtosis. These results were obtained using a common leaf-area drag formulation without either skin friction or speed dependent drag that enables scaling with U ₀ (ambient wind speed) and h (height of the canopy). This scaling results in a single non-dimensional parameter h/h _c where h _c (x, y, z) is the momentum range resulting from the canopy drag. The validity of the model scaling was tested using two-dimensional simulations. The irrotational component of the flow (potential flow) was found to be important when defining vertical domain limitations and has significant implications for time dependent flow (i.e. turbulent conditions) when considering retention pattern design. The sudden onset of drag associated with the isolated stand presents some unexpected challenges. The horizontal scales of the shearing instabilities were simulated in two dimensions and found to range between 2h for early times to 7h for later times. The early-time horizontal scales are in the range of logical retention pattern scales and as such need to be taken into account as part of the parameter space, i.e. a range of retention pattern lengths need consideration.     

An aircraft study of turbulence dissipation rate and temperature structure function in the unstable marine atmospheric boundary layer

The dissipation rate of turbulent kinetic energy, , and the temperature structure function parameter, C _T ², have been measured over water from the near surface (Z = 3 m) to the top of the boundary layer. The near surface values of and C _T ² were used to calculate the velocity and temperature Monin-Obukhov scaling parameters u _* and T _*. The data collected during unstable lapse rates were used to evaluate the feasibility of extrapolating the values of and C _T ² as a function of height with empirical scaling formulae. The dissipation rate scaling formula of Wyngaard et al. (l971 a) gave a good fit to an average of the data for Z < 0.8 Z _i. In the surface layer the scaling formula of Wyngaard et al. (1971b) disagreed with the C _T ² values by as much as 50%. This disagreement is due to an unexpected reduction in the measured values of C _T ² forZ < 30 m. At this point it is not clear if the discrepancy is a unique property of the marine boundary layer or if it is simply some unknown instrumental or analytical problem. The mixed layer scaling results were similar to the overland results of Kaimal et al. (1976).     

A wind tunnel study of turbulent flow around single and multiple windbreaks, part I: Velocity fields

This paper describes wind-tunnel experiments on the flow around single and multiple porous windbreaks (height H), sheltering a model plant canopy (height H/3). The mean wind is normal to the windbreaks, which span the width of the wind tunnel. The incident turbulent flow simulates the adiabatic atmospheric surface layer. Five configurations are examined: single breaks of three solidities (low, medium, high; solidity = 1 - porosity), and medium-solidity multiple breaks of streamwise spacing 12H and 6H. The experimental emphases are on the interactions of the windbreak flow with the underlying plant canopy; the effects of solidity; the differences in shelter between single and multiple windbreaks; and the scaling properties of the flow. Principal results are: (1) the "quiet zones" behind each windbreak are smaller in multiple than single arrays, because of the higher turbulence level in the very rough-wall internal boundary layer which develops over the multiple arrays. Nevertheless, the overall shelter effectiveness is higher for multiple arrays than single windbreaks because of the "nonlocal shelter" induced by the array as a whole. (2) The flow approaching the windbreak decelerates above the canopy but accelerates within the canopy, particularly when the windbreak solidity is high. (3) A strong mixing layer forms just downwind of the top of each windbreak, showing some of the turbulence and scaling properties of the classical mixing layer formed between uniform, coflowing streams. (4) No dramatic increase in turbulence levels in the canopy is evident at the point where the deepening mixing layer contacts the canopy (around x/H = 3) but the characteristic inflection in the canopy wind profile is eliminated at this point.     

Turbulence spectra in the near-neutral surface layer over the Loess Plateau in China

We present the power spectra of wind velocity and the cospectra of momentum and heat fluxes observed for different wind directions over flat terrain and a large valley on the Loess Plateau. The power spectra of longitudinal (u) and lateral (v) wind speeds satisfy the −5/3 power law in the inertial subrange, but do not vary as observed in previous studies within the low frequency range. The u spectrum measured at 32 m height for flow from the valley shows a power deficit at intermediate frequencies, while the v spectrum at 32 m downwind of the valley reaches another peak in the low frequency range at the same frequency as the u spectrum. The corresponding peak wavelength is consistent with the observed length scale of the convective outer layer at the site. The v spectrum for flat terrain shows a spectral gap at mid frequencies while obeying inner layer scaling in its inertial subrange, suggesting two sources of turbulence in the surface layer. All the spectra and cospectra from the valley direction show a height dependency over the three levels.     

On the memory of wind standard deviation for upstream roughness

Big eddies in the outer part of the atmospheric boundary layer contribute to the variance of the horizontal velocity fluctuations near the surface. Because of the slow adjustment of these eddies to new boundary conditions, they carry the roughness characteristics of a large upstream terrain. A scaling relation is proposed that accounts for the memory effects in the big eddies. It is concluded that the standard deviation of the horizontal wind ( _u ) measured at a given height is representative for the shear stress at greater height. This gives at least qualitative support to existing work where u is used for exposure correction of mean wind.     

The turbulent structure of the internal boundary layer near the shore

The mean structure within the internal boundary layer (IBL) near the shore, which develop from the coast in the presence of a sea breeze, has been described in Part I of this study (Ogawa and Ohara, 1984). This paper presents the results of the similarity and energy budget analysis for the purpose of parameterization of the turbulent structure within the IBL. The analysis of the turbulent kinetic energy balance, turbulent intensities and spectra show that the wind is strongly affected by mechanical turbulence in comparison with the past results in a fully developed convective layer where thermal convection dominated. The standard deviations of the wind velocities normalized by the friction velocity u _* (surface-layer scaling parameter) are functions only of the normalized height z/Z _i within 160 m of the shoreline, where Z _i is the IBL. On the other hand, the standard deviations of temperature normalized by _* (mixing-layer scaling parameter) have less scatter with distance than those normalized by T _* (surface-layer scaling parameter). The data showed that both u _* (not a mixed-layer parameter), and Z _i (not a surface-layer parameter) are necessary to describe the turbulent characteristics of the IBL near the shore.Deceased March, 1984.     

Outlier Problem in Evaluating Similarity Functions in the Stable Atmospheric Boundary Layer

The gradient-based similarity approach removes turbulent fluxes as governing parameters and replaces them with vertical gradients of mean wind speed and potential temperature. As a result, the gradient Richardson number, Ri, appears as a stability parameter instead of the Monin–Obukhov stability parameter z/L (L is the Obukhov length). The gradient-based scaling is more appropriate for moderate and very stable conditions when the gradients are large and their errors are relatively small whereas z/L becomes ambiguous in these conditions because turbulent fluxes are small. However, the gradient-based formulation is faced with a problem related to the influence of Ri outliers: outliers with high values of Ri can exist in conditions that are really near-neutral. These outliers are mapped into the very stable range in plots in which Ri is the independent variable and may lead to spurious dependencies for bin-averaged data (spurious bin-averaging). This effect is quite large for functions that are steep for the gradient-based scaling. The present study uses the Surface Heat Budget of the Arctic Ocean (SHEBA) data to examine the problem and proposes two methods, conditional analysis and independent binning, to limit the influence of outliers on bin-averaging. A disadvantage of the conditional analysis is associated with eliminating outliers based on criteria that could be considered as subjective. The independent bin-averaging method does not have this disadvantage, but the scatter of the bin-averaged points is higher than for the conditional analysis, rendering data analysis and interpretation difficult.     

Local similarity relationships in a horizontally inhomogeneous boundary layer

Local similarity theory, an analogy to the Monin-Obukhov similarity theory, is successfully applied to airborne observations in a coastal area of South Australia. The boundary layer over this highly non-uniform surface is characterized by extensive variations in its thermal stratification and turbulence characteristics. However, the behaviour of some statistical parameters of second- and higher moments seems to be determined mainly by local forcing, while horizontal advection plays a less important role. For these parameters, local scaling is effective. It is shown that the dimensionless variances of vertical velocity and potential temperature are functions of z/ only, where is the local Monin-Obukhov length and z is the height above ground. The dimensionless variance of horizontal velocity components is found to depend on h/, where h is the height of the oundary layer. Similarity relationships for some triple correlations are also discussed. The empirically determined local similarity relationships are found to agree with those obtained from surface-layer similarity. Finally, to illustrate the complexity of the local forcing, distributions of vertical energy and momentum fluxes, from which the local scaling parameters are derived, are shown.     

Bulk Transfer Relations for the Roughness Sublayer

In the roughness sublayer (RSL), Monin–Obukhov surface layer similarity theory fails. This is problematic for atmospheric modelling applications over domains that include rough terrain such as forests or cities, since in these situations numerical models often have the lowest model level located within the RSL. Based on empirical RSL profile functions for momentum and scalar quantities, and scaling the height with the RSL height z _*, we derive a simple bulk transfer relation that accounts for RSL effects. To verify the validity of our approach, these relations are employed together with wind speed and temperature profiles measured over boreal forest during the BOREAS experimental campaign to estimate momentum and heat fluxes. It is demonstrated that, when compared with observed flux values, the inclusion of RSL effects in the transfer relations yields a considerable improvement in the estimated fluxes.     

The characteristics of turbulent velocity components in the surface layer under convective conditions

It is proposed that the ratios of the standard deviations of the horizontal velocity components to the friction velocity in the surface layer under convective conditions depend only onz _i /L wherez _i is the height of the lowest inversion andL is the Monin-Obukhov length. This hypothesis is tested by using observations from several data sets over uniform surfaces and appears to fit the data well. Empirical curves are fitted to the observations which have the property that at largez _i /-L, the standard deviations become proportional tow _*, the convective scaling velocity.Fluctuations of vertical velocity obtained from the same experiments scale withz/L, wherez is the height above the surface, in good agreement with Monin-Obukhov theory.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The influence of atmospheric stratification on the growth of water waves

The atmospheric surface layer over sea has a density stratification which varies with moisture content and air/sea temperature difference. This influences the growth of water waves. To study the effect quantitatively, the Reynolds equations are solved numerically. For given wind speed and surface roughness, wave growth is found to be more rapid in unstably stratified conditions than in stable conditions. This is due to an increase in turbulence, primarily caused by an increase of mixing length.Under the assumption of a Charnock relation between surface roughness and friction velocity, it is found that for large inverse wave age (u _*/c>0.07), the effect of stratification on wave growth is weell described by Monin-Obukhov scaling of the friction velocity. For smaller values ofu _*/c, Monin-Obukhov scaling overpredicts.The effect on duration-limited wave growth is studied with the third-generation WAM surface wave model driven by 10 m winds. Effects of stratification on the significant wave height are found to be of the order of 10%. The results are comparable to those of a recent reanalysis of field measurements, although the measured stratification effect is somewhat stronger. Implementation of a stratification-dependent growth in wave models is recommended, as it can lead to small but significant improvements in wave forecasts when accurate air and sea temperatures are available.     

Similarity functions D for water vapor in the unstable atmospheric boundary layer

An analysis was performed of experimental data obtained at fixed ship stations during AMTEX 1974 and 1975. This allowed the calculation of the bulk transfer relationships for water vapor and sensible heat in the atmospheric boundary layer for different interpretations of the thickness scale of the boundary layer. It was found that scaling based on the observed thickness, which herein was taken as the height of the lowest value in the potential temperature profile under unstable conditions, produces least scatter in the calculations. The results obtained for the similarity function c( _i ) of the bulk heat transfer coefficient are in good agreement with the results of previous studies. As observed earlier (Brutsaert and Mawdsley, 1976; Mawdsley and Brutsaert, 1977), under unstable conditions the similarity functions D() of the bulk water vapor transfer coefficient are smaller than the corresponding C() functions for sensible heat. In the case of inversion height scaling, the results can be represented by d( _i ) = 0.65 c( _i ).     

One-dimensional turbulence: Part 2. Staircases in double-diffusive convection

One-Dimensional Turbulence (ODT), a turbulence model implemented as an unsteady simulation, is applied to the diffusive regime of double-diffusive convection. For this application, no parameter adjustment or other empiricism is required. Computed component fluxes across heat–salt and salt–sugar interfaces are consistent with the Linden–Shirtcliffe picture, applicable at intermediate density ratios, and Newell's model of interface evolution at high density ratios. The experimentally observed onset of a variable regime at density ratios below 2 is reproduced. Simulations of interface formation in a bottom-heated salt-stabilized medium indicate that Fernando's scaling for interface stabilization height may also apply to the height of initial interface formation. The simulations generate staircases resembling those seen in laboratory experiments, and suggest a refinement of a scaling inferred from experiments. Computed results for a thermally forced configuration and an unforced, vertically homogeneous configuration are compared.     

A numerical study of the convective boundary layer

Computations of the buoyantly unstable Ekman layer are performed at low Reynolds number. The turbulent fields are obtained directly by solving the three-dimensional time-dependent Navier-Stokes equations (using the Boussinesq approximation to account for buoyancy effects), and no turbulence model is needed. Two levels of heating are considered, one quite vigorous, the other more moderate. Statistics for the vigorously heated case are found to agree reasonably well with laboratory, field, and large-eddy simulation results, when Deardorff's mixed-layer scaling is used. No indication of large-scale longitudinal roll cells is found in this convection-dominated flow, for which the inversion height to Obukhov length scale ratio –z _i /L _*=26. However, when heating is more moderate (so that –z _i /L _*=2), evidence of coherent rolls is present. About 10% of the total turbulent kinetic energy and turbulent heat flux, and 20% of the Reynolds shear stress, are estimated to be a direct consequence of the observed cells.     

Markov Chain Simulations of Vertical Dispersion in the Neutral Surface Layer for Surface and Elevated Releases

Vertical dispersion in the neutral surface layer is investigated using a Markov Chain simulation procedure. The conceptual basis of the procedure is discussed and computation procedures outlined. Wind and turbulence parameterizations appropriate to the neutral surface layer are considered with emphasis on the Lagrangian time scale. Computations for a surface release are compared with field data. Good agreement is found for the variation of surface concentration and cloud height to distances 500 m downwind of the source. The functional form of the vertical concentration profile is examined and an exponential with exponent ∼1.6 is found to give the best fit with simulations. For elevated releases, it is demonstrated that an initial dip of the mass mean height from the simulation can be normalized for various release heights using a non-dimensionalized downwind coordinate incorporating advective wind speed and wind shear. The vertical distribution standard deviation (σ_z), as employed in Gaussian models, shows a fair degree of independence with source height but close examination reveals an optimum source height for maximum σ_z at a given downwind distance,x. This source height increases with downwind distance. Also the simulations indicate that vertical wind shear is more important than vertical variation of Lagrangian time scale close to the source, with a reverse effect farther downwind.