Observation of lake breeze penetration and subsequent development of the thermal internal boundary layer for the Nanticoke II Shoreline Diffusion Experiment

The turbulent structure of the lake breeze penetration and subsequent development of the thermal internal boundary layer (TIBL) was observed using a kytoon-mounted ultrasonic anemometer-thermometer. The lake breeze penetrated with an upward rolling motion associated with the upward flow near the lake breeze front. After the lake breeze front passed, the behaviors of the velocity and temperature at the top of the lake breeze layer were similar to those found in convective boundary layers (CBL). Comparing _gq/_*, _u /w _* and _w /w _* between the present observation of TIBL development after the passage of the lake breeze front and CBL data from the literature, the /_* values showed reasonable agreement; however, _u /w _* and _w /W_* had smaller values in the TIBL than in the CBL at higher altitudes. This is due to the differences in the mean velocity profiles. While the CBL has a uniform velocity profile, the TIBL has a peak at lower elevation due to the lake breeze penetration; the velocity then decreases with height.Present address: The Institute of Behavioral Science, 1-35-7 Yoyogi, Tokyo 151, Japan.     

On characteristics of wind direction fluctuations in the surface layer

It is shown that the ratio of standard deviation of lateral velocity to the friction velocity, /u _*, and therefore wind direction fluctuations, are sensitive to mesoscale terrain properties. Under neutral conditions, /u _* is almost 40% larger in rolling terrain than over a horizontal surface. In the lee of a low mountain, the fluctuations may be 2.5 times as strong as over horizontal terrain. In contrast, vertical velocity fluctuations are little influenced by mesoscale terrain features.Now with Air Weather Service, Offutt AFB, Omaha, Nebraska.     

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.     

Statistics of Surface-Layer Turbulence Over Terrain with Metre-Scale Heterogeneity

Refuge has patchy vegetation in sandy soil. During midday and at night, the surface sources and sinks for heat and moisture may thus be different. Although the Sevilleta is broad and level, its metre-scale heterogeneity could therefore violate an assumption on which Monin-Obukhov similarity theory (MOST) relies. To test the applicability of MOST in such a setting, we measured the standard deviations of vertical (_w) and longitudinal velocity (_u), temperature (_t), and humidity (_q), the temperature-humidity covariance (¯tq), and the temperature skewness (S_t). Dividing the former five quantities by the appropriate flux scales (u_*, _*, and q_*) yielded the nondimensional statistics _w/u_*, _u/u_*, _t/|t_*|, _q/|q_*|, and ¯tq/t_*q_*. _w/u_*, _t/|t_*|, and S_t have magnitudes and variations with stability similar to those reported in the literature and, thus, seem to obey MOST. Though _u/u_* is often presumed not to obey MOST, our _u/u_* data also agree with MOST scaling arguments. While _q/|q_*| has the same dependence on stability as _t/|t_*|, its magnitude is 28% larger. When we ignore ¯tq/t_*q_* values measured during sunrise and sunset transitions – when MOST is not expected to apply – this statistic has essentially the same magnitude and stability dependence as (_t/t_*)². In a flow that truly obeys MOST, (_t/t_*)², (_q/q_*)², and ¯tq/t_*q_* should all have the same functional form. That (_q/q_*)² differs from the other two suggests that the Sevilleta has an interesting surface not compatible with MOST. The sources of humidity reflect the patchiness while, despite the patchiness, the sources of heat seem uniformly distributed.     

The dynamical range of global circulations — II

The dynamical range of global atmospheric circulations is extended to specialized parameter regions by evaluating the influence of the rotation rate () on axisymmetric, oblique, and diurnally heated moist models. In Part I, we derived the basic range of circulations by altering for moist and dry atmospheres with regular and modified surfaces. Again we find the circulations to be composed of only a few elementary forms. In axisymmetric atmospheres, the circulations consist of a single jet in the rotational midrange (^*=1/2–1) and of double jets in the high range (^*=2–4), together with one or two pairs of Hadley and Ferrel cells; where (^*=/ _E ) is the rotation rate normalized by the terrestrial value. These circulations differ from those predicted by firstorder symmetric-Hadley (SH₁) theory because the moist inviscid atmosphere allows a greater nonlinearity and prefers a higher-order meridional mode. The axisymmetric circulations do, however, resemble the mean flows of the natural system — but only in low latitudes, where they underlie the quasi-Hadley (QH) element of the MOIST flows. In midlatitudes, the axisymmetric jets are stronger than the natural jets but can be reduced to them by barotropic and baroclinic instablities. Oblique atmospheres with moderate to high tilts ( _P =25°–90°) have the equator-straddling Hadley cell and the four basic zonal winds predicted by the geometric theory for the solstitial-symmetric-Hadley (SSH) state: an easterly jet and a westerly tradewind in the summer hemisphere, and a westerly jet and an easterly tradewind in the winter hemisphere. The nonlinear baroclinic instability of the winter westerly produces a Ferrel cell and the same eddy fluxes as the quasi-geostrophic QG element, while the instability of the summer easterly jet produces a QG-Hadley (QGH) element with a unique, vertically bimodal eddy momentum flux. At high _P and low ^*, the oblique atmospheres reach a limiting state having global easterlies, a pole-to-pole Hadley cell, and a warm winter pole. At low tilts _P <10°, the oblique circulations have a mix of solstitial and equinoctial features. Diurnal heating variations exert a fundamental influence on the natural-Hadley (NH) circulations of slowly rotating systems, especially in the singular range where the zonal winds approach extinction. The diurnality just modifies the NH element in the upper singular range (1/45^*1/16), but completely transforms it into a subsolar-antisolar Halley circulation in the lower singular range (0^*<1/45). In the modified NH flows, the diurnality acts through the convection to enhance the generation of the momentum-transferring planetary waves and, thereby, changes the narrow polar jets of the nondiurnal states into broad, super-rotating currents. Circulation theory for these specialized flows remains rudimentary. It does not explain fully how the double jets and the multiple cells arise in the axisymmetric atmospheres, how the QGH element forms in the oblique atmospheres, or how waves propagate in the slowly rotating diurnal atmospheres. But eventually all theories could, in principle, be compared against planetary observation: with Mars testing the QGH elements; Jupiter, the high-range elements; Titan, the equinoctial and solstitital axisymmetric states; and Venus, the diurnally modified NH flows.     

Turbulence characteristics in a near neutrally stratified urban atmosphere

Turbulence measurements from the city of Uppsala, Sweden, are analysed. Measurements were taken at two sites: one in the central area, ca. 6 m above roof level, the average building height being ca. 15 m; the other at ca. 8 and 50 m above the ground on a tower situated 100 m downwind of a sharp discontinuity between the densely built-up urban area and flat grass-covered land. The average stability was close to neutral, the range being -0.2 < z/L < 0.2. The main emphasis of the study is on the non-dimensional standard deviations of the velocity components _i /u _*t and on the corresponding non-dimensional energy spectra, u _*t being a local velocity scale defined as _i /( _l is the local momentum flux). Comparison with results obtained from surface-layer measurements at ideal sites (with u _*, being the ordinary friction velocity) shows good general agreement. The most complete agreement is found for the tower 50 m measurements, a result which is notable as this measurement point is found to be within a distinctly transitional zone between the urban and post-urban boundary layers. The results from the central city measurement point are also fairly close to the ideal results, the deviations found being small in view of the fact that the site is probably inside the layer in which the roughness elements (the buildings) have direct influence. The measurements at the tower 8 m level show certain distinct deviations from ideal results: all three _i /u _*l , are higher by ca. 10%, the excessive energy being found at the low frequency end of the spectrum. Arguments are presented for this feature to be due to a spectral lag effect.     

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.     

A note on the analogy between momentum transfer across a rough solid surface and the air-sea interface

The aerodynamic classification of the resistance laws above solid surfaces is based on the use of a so-called Reynolds roughness number Re _s =h _s u _*/, whereh _s is the effective roughness height, -viscosity,u _*-friction velocity. The recent experimental studies reported by Toba and Ebuchi (1991), demonstrated that the observed variability of the sea roughness cannot be explained only on the basis of the classification of aerodynamic conditions of the sea surface proposed by Kitaigorodskii and Volkov (1965) and Kitaigorodskii (1968) even though the latter approach gains some support from recent experimental studies (see for example Geernaertet al. 1986). In this paper, an attempt is made to explain some of the recently observed features of the variability of surface roughness (Toba and Ebuchi, 1991; Donelanet al., 1993). The fluctuating regime of the sea surface roughness is also described. It is shown that the contribution from the dissipation subrange to the variability of the sea surface can be very important and by itself can explain Charnock's (1955) regime.     

Boundary-layer parameterizations for applied dispersion modeling over urban areas

Many applied dispersion models require the knowledge of boundary-layer parameters such as sensible heat flux,Q _H , friction velocity,u _*, and turbulent energy components, _w and _v . Formulas are suggested for calculating these parameters over a wide variety of types of ground surfaces, based on simple observations of wind speed near the ground and fractional cloud cover, and specification of constants such as roughness length, albedo, and soil moisture availability. Observations ofu _*,Q _H , _w , and _v during field experiments in St. Louis and Indianapolis are used to test the formulas for urban sites. Relative errors of about ±20% in the predictions are seen to occur whenu _*,Q _H , _w , and _v are large. However, when these quantities are small (e.g.,u _* < 0.2 m/s), the errors in the predictions are as large as the mean value of the quantity itself.In addition, it is concluded from studies of available field data and theories that the magnitude of _w is not well-known at elevations above about 100m during the late afternoon and night. Some simple parameterizations for _w . are suggested that are consistent with the observed steady decrease in ground-level concentration in the afternoon and the sudden increase in concentration that can occur a few hours after sunset due to wind shears associated with a low-level jet, for continuous plumes emitted from moderate to tall stacks.     

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.     

Variability of surface roughness and turbulence intensities at a coastal site in India

Surface-layer features with different prevailing wind directions for two distinct seasons (Southwest Monsoon and Northeast Monsoon) on the west coast of India are studied using data obtained from tower-based sensors at a site located about 500 m from the coast. Only daytime runs have been used for the present analysis. The surface boundary-layer fluxes have been estimated using the eddy correlation method. The surface roughnessz ₀ obtained using the stability-corrected wind profiles (Paulson, 1970) has been found to be low for the Southwest monsson season. For the other season,z ₀ is relatively high. The drag coefficientC _D varies with height in the NE monsoon season but not in the season with lowz ₀. This aspect is reflected in the wind profiles for the two seasons and is discussed in detail. The scaling behaviour of friction velocityu _* and the turbulence intensity of longitudinal, lateral and vertical winds _u, _v and _w, respectively) are further examined to study their dependence on fetch. Our study shows that for the non-dimensional case, _u/u_* and _v/u_* do not show any surface roughness dependence in either season. On the other hand, for _w/u_* for the season with lowz ₀, the values are seen to agree well with that of Panofskyet al. (1977) for homogeneous terrain whereas for the other season with highz ₀, the results seem to conform more to the values observed by Smedman and Högström (1983) for coastal terrain. The results are discussed in the light of observations by other investigators.     

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.     

A Richardson Number criterion for the air-sea interface

It is shown that the observationally determined roughness relation z ₀ = u _* ²/g in which g is the acceleration of gravity, u _*, is the friction velocity in air, and = 0.0185 (Wu, 1982) for the wind profile over the sea surface relative to the surface current, is consistent with the existence of a Richardson Number criterion at the air-sea interface in which the critical Richardson Number, Ri_c = 1, such that all the shear energy is converted into potential energy.     

Local Similarity Relationships In The Urban Boundary Layer

To investigate turbulent structures in an urban boundary layer (UBL) with many tallbuildings, a number of non-dimensional variable groups based on turbulent observationsfrom a 325-m meteorological tower in the urban area of Beijing, China, are analyzedin the framework of local similarity. The extension of surface-layer similarity to localsimilarity in the stable and unstable boundary layer is also discussed. According to localsimilarity, dimensionless quantities of variables: e.g., velocity and temperature standarddeviations _i/u_*l (i=u,v,w) and_T/T_*l,correlation coefficients of uw and wT covariance, gradients of wind and temperature_m and _h, and dissipation rates of turbulent kinetic energy (TKE) andtemperature variance and _N can be represented as a functiononly of a local stability parameter z/, where is the local Obukhovlength and z is the height above ground. The average dissipation rates of TKE andtemperature variance are computed by using the u spectrum, and the uw and wTcospectra in the inertial subrange. The functions above were found to be in a goodagreement with observational behaviour of turbulence under unstable conditions, butthere were obvious differences in the stable air.     

Similarity of atmospheric Reynolds shear stress and heat flux fluctuations over a rough surface

Horizontal u and vertical w velocity fluctuations have been measured together with temperature fluctuations in the atmospheric surface layer, at a small height above a wheat crop canopy. Marginal probability density functions are presented for both individual fluctuations u, w, and for the instantaneous Reynolds stress uw, and heat fluxes w and u. Probability density functions of the velocity fluctuations deviate less significantly from the Gaussian form than the probability density of temperature. There appears to be closer similarity between statistics of the instantaneous heat fluxes than between the momentum flux and either of the heat fluxes investigated. The mean momentum flux receives equal contributions from the events referred to as ejections and sweeps in laboratory boundary layers. Sweeps provide the largest contribution to the heat fluxes.     

Near-field dispersion from instantaneous sources in the surface layer

This paper considers the near-field dispersion of an ensemble of tracer particles released instantaneously from an elevated source into an adiabatic surface layer. By modelling the Lagrangian vertical velocity as a Markov process which obeys the Langevin equation, we show analytically that the mean vertical drift velocity w(t) is w()=bu _*(1–e ^–(1+)), where is time since release (nondimensionalized with the Lagrangian time scale at the source), b Batchelor's constant, and u _*, the friction velocity. Hence, the mean height and mean depth of the ensemble are calculated. Although the derivation is formally valid only when 1, the predictions for w, mean height and mean depth are consistent in the downstream limit ( 1) with surface-layer Lagrangian similarity theory and with the diffusion equation. By comparing the analytical predictions with numerical, randomflight solutions of the Langevin equation, the analytical predictions are shown to be good approximations at all times, both near-field and far-field.     

Experiments On Buoyant Plume Dispersion In A Laboratory Convection Tank

Plume dispersion in the convective boundary layer (CBL) is investigated experimentally in a laboratory convection tank. The focusis on highly-buoyant plumes that loft near or become trapped in the CBL capping inversion and resistdownward mixing. Such plumes are defined by dimensionless buoyancy fluxes F_* 0.1, where F_* = F_b/(U w_* ² z_i), F_b is the stack buoyancy flux,U is the mean wind speed, w_* is the convective velocity scale, and z_i is the CBL depth. The aim is to obtain statistically-reliable mean (C) and root-mean-square (rms, _c) concentration fields as a function of F_* and the dimensionless distance X = w_*x/(U z_i), where x is the distance downstream of the source.The experiments reveal the following mainresults: (1) For 3 X 4and F_* 0.1, the crosswind-integrated concentration (CWIC) fields exhibit distinctly uniform profiles below z_i with a CWIC maximum aloft, in contrast to the nonuniform profiles obtained earlier by Willis and Deardorff. (2) The lateral dispersion (_y) variation with X is consistent with Taylor's theory for _* 0.1 and a buoyancy-enhanced dispersion, _y/z_i F_* ^1/3X^2/3, forF_* = 0.2 and 0.4. (3) The entrapment, the plume fraction above z_i, has a mean (E) that follows a systematic variationwith X and F_*, and a variability (_e/E) that is broad ( 0.3 to 2) near the source but subsides to 0.25 far downstream. (4) Vertical profiles of the concentration fluctuation intensity (c/C) are uniform for z < z_i and X > 1.5, but exhibit significant increases: (a) at the surface and close to the source (X 1.5), and(b) in the entrainment zone. (5) The cumulative distribution functions (CDFs) of the scaled concentration fluctuations (c/_c) separate into mixed-layer and entrainment-layer CDFs for X 2, with the mixed-layer group collapsing to a single distribution independent of z.These are the first experiments to obtain all components of the lateral and vertical dispersion parameters (rms meander, relative dispersion, total dispersion) for continuous buoyant releases in a convection tank. They also are the first tank experiments to demonstrate agreement with field observations of: (1) the scaled ground-level concentration along the plume centreline, and (2) the dimensionless lateral dispersion _y/z_i of buoyant plumes.     

The use of σ T as a temperature scale in the atmospheric surface layer

The standard deviation of temperature _T is proposed as a temperature scale and as a velocity scale to describe the behaviour of turbulent flows in the Atmospheric Surface Layer (ASL), instead of _* andu _* of the Monin—Obukhov similarity theory, and ofT _f andU _f used for free convection stability conditions. On the basis of experimental evidence reported in the literature, it is shown that _T T _f andv _* U _f in the free convection region, and _{T *} andv _* U _* in nearneutral and stable conditions. This implies that the proposed scales can be applied for all stabilities. Furthermore, a new length scale is proposed and its relation with Obukhov length is given. Also, a simple semi-empirical expression is presented with which _T andv _* can be evaluated in a rather simple way. Some examples of practical applications are given, e.g., a stability classification for unstable conditions.     

Third- and fourth-order mixed moments of turbulent velocity and temperature fluctuations in the atmospheric surface layer

Fourth-order mixed moments of velocity and temperature fluctuations, measured within the atmospheric surface layer, are compared with results obtained by assuming the quasi-Gaussian approximation. Standard deviations of the products uw, u and w(u and w are the longitudinal and vertical velocity fluctuations; is the temperature fluctuation) are in good agreement with those obtained using the quasi-Gaussian assumption. Good agreement is also obtained between measured and Gaussian estimates of fourth-order moments including all three fluctuations u, w, Schwarz inequalities, commonly used in the clipping approximation in turbulence modelling, are found to provide bounds for third-order moments of w, that are too conservative. More reasonable, tighter, bounds for these moments are given by inequalities obtained by Lumley.