Standard deviation of vertical two-point longitudinal velocity differences in the atmospheric boundary layer

The standard deviation of vertical two-point longitudinal velocity fluctuation differences is analyzed experimentally with eleven sets of turbulence measurements obtained at the NASA 150-m ground-winds tower site at Cape Kennedy, Florida. It is concluded that /u _*0 is proportional to (fz/u _*0)^0.22, where the coefficient of proportionality is a function of fz/u _*0 and u _*0/fL ₀. The quantities f and L₀ denote the Coriolis parameter and the surface Monin-Obukhov stability length, respectively; u _*0 is the surface friction velocity; z is the vertical distance between the two points over which the velocity difference is calculated; and zz is the mean height of the mid-point of the interval z above natural grade. The results of the analysis are valid for 20<-u _*0/fL ₀<2000.     

Turbulent Pressure and Velocity Perturbations Induced by Gentle Hills Covered with Sparse and Dense Canopies

How the spatial perturbations of the first and second moments of the velocity and pressure fields differ for flow over a train of gentle hills covered by either sparse or dense vegetation is explored using large-eddy simulation (LES). Two simulations are investigated where the canopy is composed of uniformly arrayed rods each with a height that is comparable to the hill height. In the first simulation, the rod density is chosen so that much of the momentum is absorbed within the canopy volume yet the canopy is not dense enough to induce separation on the lee side of the hill. In the second simulation, the rod density is large enough to induce recirculation inside the canopy on the lee side of the hill. For this separating flow case, zones of intense shear stress originating near the canopy-atmosphere interface persist all the way up to the middle layer, ‘contaminating’ much of the middle and outer layers with shear stress gradients. The implications of these persistent shear-stress gradients on rapid distortion theory and phase relationships between higher order velocity statistics and hill-induced mean velocity perturbations (Δu) are discussed. Within the inner layer, these intense shear zones improve predictions of the spatial perturbation by K-theory, especially for the phase relationships between the shear stress (~ ?Δu/?z) and the velocity variances, where z is the height. For the upper canopy layers, wake production increases with increasing leaf area density resulting in a vertical velocity variance more in phase with Δu than with ?Δu/?z. However, background turbulence and inactive eddies may have dampened this effect for the longitudinal velocity variance. The increase in leaf area density does not significantly affect the phase relationship between mean surface pressure and topography for the two simulations, though the LES results here confirm earlier findings that the minimum mean pressure shifts downstream from the hill crest. The increase in leaf area density and associated flow separation simply stretches this difference further downstream. This shift increases the pressure drag, the dominant term in the overall drag on the hill surface, by some 15%. With regards to the normalized pressure variance, increasing leaf area density increases ${\sigma_p/u_{*}^{2}}$ near the canopy top, where u _* is the longitudinally averaged friction velocity at the canopy top and σ _p is the standard deviation of the pressure fluctuations. This increase is shown to be consistent with a primitive scaling argument on the leading term describing the mean-flow turbulent interaction. This scaling argument also predicts the spatial variations in σ _p above the canopy reasonably well for both simulations, but not inside the canopy.     

Observational results on the influence of stability and wind-wave coupling on momentum transfer and turbulent fluctuations over ocean waves

Turbulence data obtained over ocean waves during the BOMEX experiment of 1969 are presented. Procedures in measurement and analyses are described which include adjustments for possible platform, R/V FLIP, motion. Momentum transfer is shown to have been influenced by both stability and wind-wave coupling. The wind-wave coupling influence is separated from the stability influence and is described in terms of a linear dependence of the deviation from the logarithmic profile on C/u _*, where C is the phase speed corresponding to the wave spectrum peak. As observed by others, a value of C/u _* near 25 is associated with minimal wind-wave coupling influence. For C/u _* greater than 25, momentum transfer is decreased relative to the neutral profile prediction. Expressions are also presented for the wind-wave coupling influence on relative intensities, _u /u _*, _u /u _* and _w/u _*. Values of the relative intensities approximate neutral overland values when the expressions are written such that the wave influence is zero near a C/u _* value of 25.     

Spatial Variability of Turbulent Fluxes in the Roughness Sublayer of an Even-Aged Pine Forest

The spatial variability of turbulent flow statistics in the roughness sublayer (RSL) of a uniform even-aged 14 m (= h) tall loblolly pine forest was investigated experimentally. Using seven existing walkup towers at this stand, high frequency velocity, temperature, water vapour and carbon dioxide concentrations were measured at 15.5 m above the ground surface from October 6 to 10 in 1997. These seven towers were separated by at least 100m from each other. The objective of this study was to examine whether single tower turbulence statistics measurements represent the flow properties of RSL turbulence above a uniform even-aged managed loblolly pine forest as a best-case scenario for natural forested ecosystems. From the intensive space-time series measurements, it was demonstrated that standard deviations of longitudinal and vertical velocities (_u, _w) and temperature (_T) are more planar homogeneous than their vertical flux of momentum (u_* ²) and sensible heat (H) counterparts. Also, the measured H is more horizontally homogeneous when compared to fluxes of other scalar entities such as CO₂ and water vapour. While the spatial variability in fluxes was significant (>15 %), this unique data set confirmed that single tower measurements represent the canonical structure of single-point RSL turbulence statistics, especially flux-variance relationships. Implications to extending the moving-equilibrium hypothesis for RSL flows are discussed. The spatial variability in all RSL flow variables was not constant in time and varied strongly with spatially averaged friction velocity u_*, especially when u_* was small. It is shown that flow properties derived from two-point temporal statistics such as correlation functions are more sensitive to local variability in leaf area density when compared to single point flow statistics. Specifically, that the local relationship between the reciprocal of the vertical velocity integral time scale (I_w) and the arrival frequency of organized structures (/h) predicted from a mixing-layer theory exhibited dependence on the local leaf area index. The broader implications of these findings to the measurement and modelling of RSL flows are also discussed.     

Similarity forms for ground-source surface-layer diffusion

Past work on analyzing ground-source diffusion data in terms of surface-layer similarity theory is reviewed; these analyses assume that _z /L orh/L is a function of u ^* x/L (where h = Q/ dy). It is argued that an alternative scaling, h ^*/L versus x/L, is nearly as universal in that it is very weakly influenced by surface roughness, except for a modest influence in the free convective case (h ^* = Q/u ^* dy); the advantage of this scaling is that it eliminates the need to reassess as vertical diffusion progresses. The Prairie Grass data set is adjusted for the difference in source and sampling heights, and is plotted with this scaling. Simple analytic equations are suggested that fit the resultant data plots for stable and unstable conditions, and suggestions are made towards practical application of these results.On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.     

Turbulent Intensities and Velocity Spectra for Bare and Forested Gentle Hills: Flume Experiments

To investigate how velocity variances and spectra are modified by the simultaneous action of topography and canopy, two flume experiments were carried out on a train of gentle cosine hills differing in surface cover. The first experiment was conducted above a bare surface while the second experiment was conducted within and above a densely arrayed rod canopy. The velocity variances and spectra from these two experiments were compared in the middle, inner, and near-surface layers. In the middle layer, and for the canopy surface, longitudinal and vertical velocity variances () were in phase with the hill-induced spatial mean velocity perturbation (Δu) around the so-called background state (taken here as the longitudinal mean at a given height) as predicted by rapid distortion theory (RDT). However, for the bare surface case, and remained out of phase with Δu by about L/2, where L is the hill half-length. In the canopy layer, wake production was a significant source of turbulent energy for , and its action was to re-align velocity variances with Δu in those layers, a mechanism completely absent for the bare surface case. Such a lower ‘boundary condition’ resulted in longitudinal variations of to be nearly in phase with Δu above the canopy surface. In the inner and middle layers, the spectral distortions by the hill remained significant for the background state of the bare surface case but not for the canopy surface case. In particular, in the inner and middle layers of the bare surface case, the effective exponents derived from the locally measured power spectra diverged from their expected  − 5/3 value for inertial subrange scales. These departures spatially correlated with the hill surface. However, for the canopy surface case, the spectral exponents were near  − 5/3 above the canopy though the minor differences from  − 5/3 were also correlated with the hill surface. Inside the canopy, wake production and energy short-circuiting resulted in significant departures from  − 5/3. These departures from  − 5/3 also appeared correlated with the hill surface through the wake production contribution and its alignment with Δu. Moreover, scales commensurate with Von Karman street vorticies well described wake production scales inside the canopy, confirming the important role of the mean flow in producing wakes. The spectra inside the canopy on the lee side of the hill, where a negative mean flow delineated a recirculation zone, suggested that the wake production scales there were ‘broader’ when compared to their counterpart outside the recirculation zone. Inside the recirculation zone, there was significantly more energy at higher frequencies when compared to regions outside the recirculation zone.     

A numerical model study of the structure and similarity scaling of the nocturnal boundary layer (NBL)

A one-dimensional numerical model based on the equations of mean motion and turbulent kinetic energy (TKE), with Delage's (1974) mixing-length parameterization has been used to simulate the mean and turbulent structure of the evolving stably stratified nocturnal boundary layer (NBL). The model also includes a predictive equation for the surface temperature and longwave radiational cooling effects.In the absence of advective and gravity wave effects, it is found that the model-simulated structure, after a few hours of evolution, could be ordered fairly well by a similarity scaling (u _*0, _*0, L ₀, and h) based on surface fluxes and the NBL height. Simple expressions are suggested to describe the normalized profiles of momentum and heat fluxes, TKE, eddy-viscosity and energy dissipation. A good ordering of the same variables is also achieved by a local scaling (u _*0, _* and L) based on the height-dependent local fluxes. The normalized TKE, eddy viscosity and energy dissipation are unique functions of z/L and approach constant values as z/L , where L is the local Monin-Obukhov length. These constants are close to the values predicted for the surface layer as z/L , thus suggesting that the Monin-Obukhov similarity theory can be extended to the whole NBL, by using the local (height-dependent) scales in place of surface-layer scales. The observed NBL structure has been shown to follow local similarity (Nieuwstadt, 1984).     

Comments on ‘the characteristics of turbulent velocity components in the surface layer under convective conditions’, by H. A. Panofsky,H. Tennekes,D. H. Lenschow,and J. C. Wyngaard

Panofsky et al. (1977) have presented an analysis which seems to show a clear dependence of the dimensionless turbulence statistics _u /u _* and _v/u _* on the planetary boundary-layer stability parameter z _i/L. However it is possible that much of the apparent relationship results from artificial correlations introduced by the use of inter-related dimensionless parameters. Apparent dependencies of similar statistical quantities on z/L in the surface boundary layer might also be contaminated.This work was supported by the U.S. Department of Energy, and is a contribution of the Multistate Atmospheric Power Production Pollution Study (MAP3S).     

Estimating the Monin-Obukhov length in the stable boundary layer for dispersion calculations

Analysis of data collected during the Prairie Grass, Kansas and Minnesota experiments reveals the following empirical relationship between the Monin-Obukhov length L and the friction velocity u _*: L = Au _* ², A = 1.1 × 10³s²m^-1. This result combined with the formulation for the height of the stable boundary layer h suggested by Zilitinkevich (1972) leads to h u _* ^3/2 f–^1/2 where f is the Coriolis parameter. Data from the Minnesota study (Caughey et al., 1979) provide ample support for this expression.These empirical equations for L and h are useful for routine dispersion estimates during stable conditions.     

The Spatial Variability of Turbulence above a Forest

Summary The spatial variability of turbulence above a forest has been examined. Two measurement towers were erected 800 m apart within a heterogeneous mixed forest located in the north east of the Netherlands. The measurements of u ^* /u were analysed and subsequently used to test a surface layer model. The model simulated the magnitude of the measurements reasonably well, but measured trends were not always reproduced by the model. The variable (du/dz)/u did not adapt as quickly to the new surface as u ^* /u. This is in agreement with Schmid (1994), and can be explained by a local decrease in mixing length. It is recommended to adapt the mixing length near a surface transition to improve the accuracy of surface layer models of heterogeneous landscapes. Received September 8, 1997 Revised April 15, 1998     

Displaced-Beam Small Aperture Scintillometer Test. Part I: The Wintex Data-Set

The friction velocity (u_*) and the sensible heat flux density (H) determined with a displaced-beam small aperture scintillometer (DBSAS) and a hot-film eddy correlation system are compared. Random errors in the DBSAS are relatively small, compared to scatter found with two eddy-correlation systems. Assuming that the hot-film system yields the true fluxes, theDBSAS appears to overestimate u_* when u_* is less than 0.2 m s^-1 and to underestimate u_* at high wind speeds. This implies that the DBSAS measurements of theinner scale length of turbulence, l₀, a direct measure for the dissipation rate of kinetic turbulent energy, are biased. Possible causes for these results are discussedin detail. A correction procedure is presented to account for effects of random noise and of so-called inactive turbulence or sensor vibrations. The errors in u_* cause errors in the DBSAS measurements of the structure parameter of temperature C_T ². The derived H appears to be less sensitive to errors in l₀ and C_T ², because errors in these quantities tend to cancel out.     

Nighttime free convection characteristics within a plant canopy

An intensive measurement campaign within and above a maize row canopy was carried out to investigate flow characteristics within this vegetation. Attention was given to finding adequate scaling parameters of the within-canopy windspeed and air temperature profiles under above-canopy stable stratification.During clear and calm nights the within-canopy condition differs considerably from the abovecanopy state. In contrast to the daytime, the windspeed and temperature profiles do not scale with the above-canopy friction velocity,u ^* , and the scaling temperature,T ^* , respectively. A free convection flow regime is generated, forced by the soil heat flux at the canopy floor and by cooling at the top of the canopy. However, the windspeed and temperature profiles appear to scale well with the free convective velocity scale,w ^* , and the free convective temperature scale,T ^f , respectively. The free convective state within the canopy agrees well with the free convection criterion Gr>16Re²(u ^* ), where Gr is the Grashof number and Re(u ^* ) the Reynolds number, a criterion often used in technical flow problems. Also it is shown that under within-canopy free convection, there is a unique relation between the Grashof number, Gr, and the Reynolds number if the latter is based on the free convective velocity scale.Under within-canopy free convective conditions, it appears that within the canopy the fluxes of heat and water vapour can be estimated well with the relatively simple variance technique. Under these conditions, the Grashof, or Rayleigh number, represents a measure for the kinetic energy of the turbulence within the canopy.     

Fluxes of gases and particles above a deciduous forest in wintertime

Eddy-correlation measurements of the vertical fluxes of ozone, carbon dioxide, fine particles with diameter near 0.1 m, and particulate sulfur, as well as of momentum, heat and water vapor, have been taken above a tall leafless deciduous forest in wintertime. During the experimental period of one week, ozone deposition velocities varied from about 0.1 cm s^–1 at night to more than 0.4 cm s^-1 during the daytime, with the largest variations associated primarily with changes in solar irradiation. Most of the ozone removal took place in the upper canopy. Carbon dioxide fluxes were directed upward due to respiration and exhibited a strong dependence on air temperature and solar heating. The fluxes were approximately zero at air temperatures less than 5 °C and approached 0.8 mg m^–2 s^–1 when temperatures exceeded 15 °C during the daytime. Fine-particle deposition rates were large at times, with deposition velocities near 0.8 cm s^–1 when turbulence levels were high, but fluxes directed upward were found above the canopy when the surface beneath was covered with snow. Diffusional processes seemed to dominate fine-particle transfer across quasilaminar layers and subsequent deposition to the upper canopy. Deposition velocities for particulate sulfur were highly variable and averaged to a value small in magnitude as compared to similar measurements taken previously over a pine forest in summer.     

Roughness effects on urban turbulence parameters

Urban roughness lengths are estimated from measurements of u and u _* at one level under neutral conditions, assuming a logarithmic form for the vertical profile of wind velocity. At a given location in the urban area, estimated values show considerable directional variation. The dependence of some turbulence parameters on the urban roughness lengths is experimentally investigated during near-neutral conditions. The ratios _i /u _* decrease with roughness whereas the turbulence intensities _i /u increase with it. The dependence on roughness is not the same for all components.     

Tilt errors and precipitation effects in trivane measurements of turbulent fluxes over open water

For 390 ten-minute samples of turbulent flux, made with a trivane above a lake, the vertical alignment is determined within 0.1 ° through azimuth-dependent averaging. One degree of instrumental misalignment is found to produce an average tilt error of 9 ± 4% for momentum flux, and 4 ± 2% for heat flux. The tilt error in the vertical momentum flux depends mainly ons _u/u_*, and cannot be much diminished with impunity by high-pass pre-filtering of the turbulence signals. The effects of rain on trivane measurements of vertical velocity are shown to be negligible at high wind speeds, and adaptable to correction in any case.The normalized vertical velocity variance,s _w/u_*, appears to be proportional to the square root ofz/L for unstable stratification. For a wind speed range of 2 to 15 m s^–1, the eddy correlation stresses measured at 4- and 8-m heights can be reasonably well estimated by using a constant drag coefficientC _d=1.3 X 10^-3, while cup anemometer profile measurements give an overestimate of eddy stress at high wind speeds. A good stress estimate is also obtained from the elevation variance; it is suggested that trivane measurement of this variance might be made from a mobile platform, e.g., a moderately stabilized spar buoy.     

Effect of atmospheric stability on the growth of surface gravity waves

In this paper we study the effect of atmospheric stability on the growth of surface gravity waves. To that end we numerically solved the Taylor-Goldstein equation for wind profiles which deviate from a logarithmic form because stratification affects the turbulent momentum transport. Using Charnock's relation for the roughness height z ₀ of the wind profile, it is argued that the growth rate of the wave depends on the dimensionless phase velocity c/u _* (where u _* is the friction velocity) and a measure of the effect of atmospheric stability, namely the dimensionless Obukhov length gL/u _* ², whereas it only depends weakly on gz _t /u _* ² (where z _t is the roughness height of the temperature profile). Remarkably for a given value of u _* /c, the growth rate is larger for a stable stratification (L > 0) than for an unstable one (L < 0). We explain why this is the case. If, on the other hand, one considers the growth rate as a function of c/U ₁₀ (where U ₁₀ is the windspeed at 10 m), the situation reverses for c/U ₁₀ < 1. For practical application in wave prediction models, we propose a new parameterization of the growth rate of the waves which is an improvement of the Snyder et al. (1981) proposal because the effect of stability is taken into account.     

Turbulence measurements above a pine forest

Eddy fluxes of momentum, sensible and latent heat, and turbulence spectra measured over the Thetford Forest during 10 days in the Spring of 1973 are described. The measured total heat flux (H + E) for 122 20-min periods agreed closely on average with independent estimates from an energy balance method. There was evidence that the energy balance data gave small systematic overestimates of available energy during the hours before noon, compensated by slight underestimates for the remainder of the day. A comparison of measured wind speeds and friction velocities in neutral stability confirmed the validity of the aerodynamic method for estimating momentum fluxes at heights of a few roughness lengths above the canopy. In stable conditions the log-linear wind profileU = (u _*/k)(ln ((z -d)/z _o) + (z -d -z _o)/L) with = 3.4 ± 0.4 provided a good fit to the data. Spectra in unstable conditions were generally more sharply peaked than those measured by other workers over smoother terrain: differences were less marked in the case of vertical velocity in stable conditions. Temperature spectra in these stable conditions showed high energy at relatively low wavenumbers, andwT cospectra showed a cospectral gap; both of these results were associated with an intermittent sawtooth structure in the temperature fluctuations.Now at the Meteorological Office, Bracknell     

Calculation of velocity skewness in real and artificial plant canopies

Wind velocities within a plant canopy are much more strongly skewed than those of the air flow above. We have examined the governing Eulerian equations for the velocity products u _i, u _j u_k using data from a wind tunnel study with an artificial canopy consisting of an array of 5 cm lengths of monofilament fishing line, and from measurements in corn (Zea mays L).Simple parameterizations for pressure-velocity correlations, and for the quadruple velocity products allowed reasonably accurate calculations of the third moments using measured profiles of the mean velocity, variance and covariance fields. Comparisons of individual terms in the rate equations for ovu _i, u _j u _krevealed that diffusion (from above) and mean shear were most important in creating large skewness in the canopy. A drag term also contributed but was of lesser importance. These terms were balanced by return-to-isotropy and a turbulence interaction term. A quasi-Gaussian approximation considerably underestimated the magnitude of the fourth moments within the canopy.     

Turbulence measurements during mistral winds with a 1-dimensional sonic anemometer

Fluctuations in the vertical wind velocity and air temperature were measured with a 1-dimensional sonic anemometer and fine thermocouple over a flat agricultural site in the Rhone Valley, France. Strong Mistral winds with speeds up to 20 m s^–1 kept atmospheric conditions very close to neutral and ensured stationarity. Friction velocities estimated both by eddy correlation (sonic plus Gill Bivane) and inertialdissipation (sonic only) methods agreed within 1 and 5 % respectively of traditional profile measurements over the measured range of 0.2 to 1.2 m s^–1. The coefficient of eddy transport for heat exceeded that of momentum by a factor of 1.38 (± 0.05), a result almost identical to that obtained in the Kansas experiment (Businger et al., 1971). For - 0.15 >= z/L >= 0.05, the ratio _w /u _* was 1.69 and 1.34 for unstable and stable conditions, respectively. For ¦z/L¦ >= 0.05, the ratio /T _* was 1.40 independent of whether neutrality was approached from either stable or unstable conditions.     

Spectral Short-circuiting and Wake Production within the Canopy Trunk Space of an Alpine Hardwood Forest

Using synchronous multi-level high frequency velocity measurements, the turbulence spectra within the trunk space of an alpine hardwood forest were analysed. The spectral short-circuiting of the energy cascade for each velocity component was well reproduced by a simplified spectral model that retained return-to-isotropy and component-wise work done by turbulence against the drag and wake production. However, the use of an anisotropic drag coefficient was necessary to reproduce these measured component-wise spectra. The degree of anisotropy in the vertical drag was shown to vary with the element Reynolds number. The wake production frequency in the measured spectra was shown to be consistent with the vortex shedding frequency at constant Strouhal number given by f _vs = 0.21ū/d, where d can be related to the stem diameter at breast height (dbh) and ū is the local mean velocity. The energetic scales, determined from the inflection point instability at the canopy–atmosphere interface, appear to persist into the trunk space when , where C _du is the longitudinal drag coefficient, a _cr is the crown-layer leaf area density, h _c is the canopy height, and β is the dimensionless momentum absorption at the canopy top.