Cases-97: Late-Morning Warming And Moistening Of The Convective Boundary Layer Over The Walnut River Watershed

Aircraft, radiosonde, surface-flux, and boundary-layer windprofiler data from the Cooperative Atmosphere Surface Exchange Study's 1997 field project, CASES-97, are combined with synoptic data to study the evolution of the vertically-averaged mixed-layerpotential temperature []and mixing-ratio [Q] onthree nearly-cloudless days from 1000 CST to 1200CST (local noon is approximately 1230 CST). This was achieved through examination of the terms in the time-tendency (`budget')equations for []and [Q]. We estimate three of the terms –local time rate of change, vertical flux divergence, andhorizontal advection. For the [Q]-budget, vertical flux divergence usually dominates, buthorizontal advection is significant on one of the three days. The [Q]-budget balances for two of the three days to within the large experimental error. For the -budget,vertical flux divergence accounts for most of the morningwarming, with horizontal advection of secondary importance.The residual in the -budget has the same sign for all three days, indicating that not all the heating is accounted for. We can balance the []-budgets to within experimental error on two of the three days by correcting the vertical-flux divergence for apparent low biases in the flux measurements of one of the aircraft and in the surface fluxes, and accounting for direct heating of the mixed layer by radiative flux divergence allowing for the effects of carbonaceous aerosols. The [];-budget with these corrections also balances on the third day if horizontal gradients from synoptic maps are used to estimate the horizontal advection. However, the corrected budget for this day does not balance if the horizontal gradient in the advection term is estimated using CASES-97aircraft and radiosondes; we suggest that persistent mesoscale circulations led to an overestimate of the horizontal gradient andhence horizontal advection.     

Wind and wind forces in a plantation spruce forest

Observations have been made of the tubulent structure within and above a dense (LAI=10.2) plantation spruce forest along with measurements of the movement of individual trees. The mean statistics of the turbulence and the turbulence spectra are compared with observations in other crops and complementary wind-tunnel studies using 175 scale plastic trees. The measurements show that momentum transport and the subsequent motion of the trees is dominated by intermittent sweep/ejection events associated with honami waves moving across the forest. The trees themselves act as forced damped harmonic oscillators and appear to short circuit the normal turbulent energy dissipation process by efficiently absorbing energy at their resonant frequencies. It is argued that understanding the nature and formation of honami waves over forests and crops is a crucial problem in agricultural and forest meteorology because of their important role both in turbulent transport and in causing wind damage.     

On Internal Gravity Waves Associated with the Stable Boundary Layer

The stable planetary boundary layer at the baseof the residual layer supports internalwaves that are unambiguously boundary layer incharacter. Some of these wavesare instabilities and some are neutrally stable modes, but they all have critical levelsin the residual layer. These waves exist for a broad range of conditions and should bea major component of any ducted disturbance that propagates within ninety degreesof the wind direction. The wave properties can be computed without the numericaldifficulties usually associated with critical-level systems.     

Shear convection

The paper discusses convection in the presence of wind shear, a condition analysed previously by Zilitinkevich (1971). This region (between the forced and fully developed convective layers) was also considered by Betchov and Yaglom (1971). In the present paper the author endeavors to develop a consistent analysis from the basic hypothesis of a very weak interaction between the vertical convective motions and mechanical turbulence, employing a new similarity model of the turbulent regime. Additional experimental data are introduced. Unlike the notation used in the references quoted above, this regime is termed shear convection rather than free convection. The latter is traditionally regarded as synonymous with the terms pure or fully developed convection.     

The onset of separation in neutral,turbulent flow over hills

The onset of separation in turbulent, neutrally stratified, boundary-layer flow over hills is considered. Since the flows are fully turbulent, the occurrence of intermittent separation, in the sense of any reversal of near surface flow, will depend strongly on the detailed structure and behaviour of the turbulent eddies. Very little is known about such intermittent separation and the phenomenon cannot be studied with numerical models employing standard turbulence closures; eddy-resolving models are required. Therefore, here, as elsewhere in the literature, the arguably less physically significant process of mean flow separation is studied. Numerical simulations of flow over idealised two- and three-dimensional hills are examined in detail to determine the lowest slope, _crit, for which the mean flow separates.Previous work has identified this critical slope as that required to produce a zero surface stress somewhere over the hill. This criterion, when a mixing-length turbulence closure is applied, reduces to requiring the near-surface vertical velocity shear to vanish at some point on the hill's surface. By applying results from a recent linear analysis for the flow perturbations to this condition, a new expression for _crit is obtained. The expression is approximate but its relative simplicity makes it practically applicable without the need for use of a computer or for detailed mapping of the hill. The approach suggested differs from previous ones in that it applies linear results to a non-linear expression for the surface stress. In the past, a linear expression for the surface stress has been used. The proposed expression for _crit leads to critical angles that are about twice previous predictions. It is shown that the present expression gives good agreement with the numerical results presented here, as well as with other numerical and experimental results. It is also consistent with atmospheric observations.     

The stably stratified internal boundary layer for steady and diurnally varying offshore flow

A two-dimensional numerical mesoscale model is used to investigate the internal structure and growth of the stably stratified internal boundary layer (IBL) beneath warm, continental air flowing over a cooler sea. Two situations are studied — steady-state and diurnally varying offshore flow. In the steady-state case, vertical profiles of mean quantities and eddy diffusion coefficients (K) within the IBL show small, but significant, changes with increasing distance from the coast. The top of the IBL is well defined, with large vertical gradients within the layer and a maximum in the coast-normal wind component near the top. Well away from the coast, turbulence, identified by non-zero K, decreases to insignificant levels near the top of the IBL; the IBL itself is characterised by a critical value of the layer-flux Richardson number equal to 0.18. The overall behaviour of the mean profiles is similar to that found in the horizontally homogeneous stable boundary layer over land.A simple physical model is used to relate the depth of the layer h to several relevant physical parameters viz., x, the distance from the coast and U, the large-scale wind (both normal to the coastline) and g/, being the temperature difference between continental mixed-layer air and sea surface, is the mean potential temperature and g is the acceleration due to gravity. Excellent agreement with the numerical results is found, with h = 0.014x ^1/2 U (g/)^–1/2.In the diurnally varying case, the mean profiles within the IBL show only small differences from the steady-state case, although diurnal variations, particularly in the wind maximum, are evident within a few hundred kilometres of the coast. A mesoscale circulation normal to the coast, and superimposed upon the mean offshore flow, develops seawards of the coastline with maximum vertical velocities about sunset, of depth about 2 km and horizontal scale 500 km. The circulation is related to the advection, and subsequent decay, of daytime convective turbulence over the sea.     

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.     

The influence of anisotropy on stress estimation by the indirect dissipation method

A comparison of observations by different authors reveals that systematic differences exist between momentum fluxes measured directly, and momentum fluxes determined indirectly by the dissipation method. This discrepancy is attributed to systematic errors due to the indirect determination of energy dissipation from the presumed inertial subrange spectrum of the horizontal wind component. The discrepancy increases with increasing degree of anisotropy, indicated by the ratio (vertical wind spectrum): (horizontal wind spectrum) deviating from % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaaiaais% daaeaacaaIZaaaaaaa!33E6!\[\frac{4}{3}\]The results support a value of 0.48 for Kolmogoroff's constant.     

The Askervein Hill Project: Mean wind variations at fixed heights above ground

This is one of a series of papers on the Askervein Hill Project. It presents results on the variations in mean wind speed at fixed heights (z) above the ground from linear arrays of anemometer posts and towers. Most of the data are for z = 10 m but some are for z = 3 m. Selected and directionally grouped data from the 55 Mean Flow runs are presented together with mean flow data from Askervein '83 Turbulence runs. Comparisons are made between the data and guideline estimates of fractional speed-up ratio at hilltop locations and between the data and MS3DJH/3 model predictions along the tower lines. There is good agreement in most cases.     

A Note on Velocity Spectra in the Marine Boundary Layer

Spectra of longitudinal and vertical velocity have been studied at a marine site, östergarnsholm, in the Baltic Sea during a period of six days with near-neutral or slightly unstable conditions, when the wave state gradually changed from pure wind sea to strong swell having approximately the same direction as the wind. During the pure wind sea phase, spectra are shown to adhere closely to general forms for the neutral atmospheric surface layer obtained from a new theory. As soon as the wave age goes slightly beyond that representative of pure wind sea conditions, the spectra deviate in shape from the ideal forms. The spectral modification appears to start at a frequency typical of the swell component. As the wave age increases, it progresses in frequency as a downscale cascade, which is particularly prominent in the spectrum of the vertical component but which is also observed in the longitudinal component. In addition, there is a strong effect in the low-frequency part of the spectra. It is interpreted as an indirect effect of large-scale inactive turbulence, which becomes progressively more important as wave-age increases. It is found that the ratio of the spectrum of the vertical component and the spectrum of the corresponding longitudinal component attains the theoretically predicted value of 4/3 for cases of developing sea (gale force wind) for frequencies above approximately 4 Hz but never much exceeds unity for cases with swell. It is argued that this is an indication of local anisotropy and that the inertial-dissipation method for determination of the momentum flux is inappropriate in the case of mixed seas or swell.     

TURBULENCE STRUCTURE IN A STRATIFIED BOUNDARY LAYER UNDER STABLE CONDITIONS

Turbulence structure in stably stratified boundary layers isexperimentally investigated by using a thermally stratified wind tunnel. Astably stratified flow is created by heating the wind tunnel airflow to atemperature of about 50 °C and by cooling the test-section floor to asurface temperature of about 3 °C. In order to study the effect ofbuoyancy on turbulent boundary layers for a wide range of stability, thevelocity and temperature fluctuations are measured simultaneously at adownwind position of 23.5 m from the tunnel entrance, where the boundarylayer is fully developed. The Reynolds number, Re, ranges from 3.14× 104 to 1.27 × 105, and the bulk Richardson number, Ri,ranges from 0 to 1.33. Stable stratification rapidly suppresses thefluctuations of streamwise velocity and temperature as well as the verticalvelocity fluctuation. Momentum and heat fluxes are also significantlydecreased with increasing stability and become nearly zero in the lowest partof the boundary layer with strong stability. The vertical profiles ofturbulence quantities exhibit different behaviour in three distinct stabilityregimes, the neutral flows, the stratified flows with weak stability(Ri = 0.12, 0.20) and those with strong stability (Ri= 0.39,0.47, 1.33). Of these, the two regimes of stratified flows clearly showdifferent vertical profiles of the local gradient Richardson number Ri,separated by the critical Richardson number Ri cr of about 0.25. Moreover,turbulence quantities in stable conditions are well correlated with Ri.     

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.     

Estimation of the Monin-Obukhov similarity functions from a spectral model

From measured one-dimensional spectra of velocity and temperature variance, the universal functions of the Monin-Obukhov similarity theory are calculated for the range –2 z/L + 2. The calculations show good agreement with observations with the exception of a range –1 z/L 0 in which the function _m , i.e., the nondimensional mean shear, is overestimated. This overestimation is shown to be caused by neglecting the spectral divergence of a vertical transport of turbulent kinetic energy. The integral of the spectral divergence over the entire wave number space is suggested to be negligibly small in comparison with production and dissipation of turbulent kinetic energy.Notation a,b,c contants (see Equations (–4)) - C_i constants i=u, v, w, (see Equation (5) - k_me,k_mT peak wave numbers of 3-d moel spectra of turbulent kinetic energy and of temperature variance, respectively - k_mi peak wave numbers of 1-d spectra of velocity components i=u, v, w and of temperature fluctuations i= - k_sb, k_c characteristics wave numbers of energy-feeding by mechanical effects being modified by mean buoyancy, and of convective energy feeding, respectively - L Monin-Obukhov length - % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gabeivayaaraaaaa!3C5B!\[{\rm{\bar T}}\] difference of mean temperature and mean potential temperature - T* Monin-Obukhov temperature scale - velocity of mean flow in positive x-direction - u* friction velocity - u, v, w components of velocity fluctuations - z height above ground - von Kármanán constant - temperature fluctuation - _m nondimensional mean shear - _H nondimensional mean temperature gradient - nondimensional rate of lolecular dissipation of turbulent kinetic energy - _D nondimensional divergence of vertical transports of turbulent linetic energy     

Numerical modelling of the turbulent flow developing within and over a 3-d building array,part ii: a mathematical foundation for a distributed drag force approach

In this paper, we lay the foundations of a systematic mathematical formulation for the governing equations for flow through an urban canopy (e.g., coarse-scaled building array) where the effects of the unresolved obstacles on the flow are represented through a distributed mean-momentum sink. This, in turn, implies additional corresponding terms in the transport equations for the turbulence quantities. More specifically, a modified k-- model is derived for the simulation of the mean wind speed and turbulence for a neutrally stratified flow through and over a building array, where groups of buildings in the array are aggregated and treated as a porous medium. This model is based on time averaging the spatially averaged Navier--Stokes equations, in which the effects of the obstacle--atmosphere interaction are included through the introduction of a volumetric momentum sink (representing drag on the unresolved buildings in the array).The k-- turbulence closure model requires two additional prognostic equations, namely one for the time-averaged resolved-scale kinetic energy of turbulence,, and another for the dissipation rate, , of . The transport equation for is derived directly from the transport equation for the spatially averaged velocity, and explicitly includes additional sources and sinks that arise from time averaging the product of the spatially averaged velocity fluctuations and the distributed drag force fluctuations. We show how these additional source/sink terms in the transport equation for can be obtained in a self-consistent manner from a parameterization of the sink term in the spatially averaged momentum equation. Towards this objective, the time-averaged product of the spatially averaged velocity fluctuations and the distributed drag force fluctuations can be approximated systematically using a Taylor series expansion. A high-order approximation is derived to represent this source/sink term in the transport equation for . The dissipation rate () equation is simply obtained as a dimensionally consistent analogue of the equation. The relationship between the proposed mathematical formulation of the equations for turbulent flow within an urban canopy (where the latter is treated as a porous medium) and an earlier heuristic two-band spectral decomposition for parameterizing turbulence in a plant canopy is explored in detail.     

Methods of measuring wind stress over a water surface — Discussions of displacement height and von Karman constant

Experiments were conducted in a wind-wave tank to study the long-standing discrepancy between wind stresses over a water surface determined with the profile and eddy-correlation methods. Inasmuch as the eddy-correlation method measures the turbulence flux directly, such a discrepancy is considered as an error in the way the profile data are analyzed. Uncertainties in selections of the zero reference plane for the logarithmic velocity profile and of the value for the von Karman constant are suggested to be major sources of the error. To match the results obtained with two methods, the displacement height needs to vary with wave conditions, and the value of the von Karman constant is also discussed.     

Flux Footprints Within and Over Forest Canopies

The characteristics of turbulence within a forest arespatially heterogeneous and distinct from thoseassociated with the surface boundary layer. Consequently, the size and probability distribution offlux footprints emanating from sources below aforest canopy have the potential to differ from thoseobserved above forests.A Lagrangian random walk model was used toinvestigate this problem since no analytical solutionof the diffusion equation exists. Model calculations suggest that spatialcharacteristics of flux footprint probabilitydistributions under forest canopies are muchcontracted, compared to those evaluated in the surfaceboundary layer. The key factors affecting thestatistical spread of the flux footprint, and theposition of the peak of its probability distribution,are horizontal wind velocity and the standarddeviations of vertical and horizontal velocityfluctuations. Consequently, canopies, which attenuatemean horizontal wind speed, or atmospheric conditions,which enhance vertical velocity fluctuations, willcontract flux footprint distributions mostly near thefloor of a forest. It was also found that theprobability distributions of the flux footprint arenarrower when horizontal wind velocity fluctuationsare considered, instead of the simpler case that considers only vertical velocity fluctuations and meanhorizontal wind velocity.     

Turbulent flows over mountainous terrain modelled by the Reynolds equations

A numerical model based upon fundamental principles, a standard (k, ) turbulence closure and a finite element integration technique, is applied to separated flows over hills. Predictions are compared to experimental data from a wind tunnel. Although few-equation turbulence closures have been shown to have obvious deficiencies with respect to comparable flows, the model predicts remarkably accurately, without coefficient adjustments of any kind. Even the turbulent intensity is predicted quite realistically.     

Interactions between internal gravity waves and their traumatic effect on a continuous stratification

An investigation is made of the detailed kinematic conditions which characterize breaking of internal waves in a continuous density field. It has been observed that breaking is associated with localized, abruptly appearing intensifications of the density gradient. Turbulence subsequently develops from these intensifications or traumata.Interactions between two or more disparate waves produce distortions more extreme than would be deduced from linear combination. This is exploited experimentally by crossing two weak internal wave beams from separate sources.Lagrangian integration of the motion field defined by the beams gives extrema of isopycnic slope, Richardson number defined by shear across isopycnics and dynamic vertical density gradient, and dynamic density gradient, under conditions for the appearance of traumata.     

The wind regime in coastal areas with special reference to results obtained from the Swedish wind energy program

The paper describes various aspects of the wind regime in coastal areas as obtained from several experimental programs along the Baltic coast of Sweden. The studies include the change with distance inland of mean wind structure as well as the turbulence structure in various conditions. It is found that wind spectra are usually well described by local similarity in its high frequency part, even in complex terrain. The low frequency parts of the spectra show clear spectral lag effects. The effects of a small slope, ca 5 m height change over 300 m travel distance, is clearly seen in some spectra, and it is shown that current flow over a hill theory can be used to account for it. The change of mean wind speed throughout the entire boundary layer as the wind passes a low but wooded island (Gotland), ca 30 km wide, has been studied in a series of relatively strong wind, near neutral cases. Some unexpected features are found; in particular the wind speed decreases more rapidly with distance inland than predicted by current numerical models. Two cases with a low level jet are discussed in some detail. Arguments are presented for the phenomenon to be caused by frictional decoupling at the Latvian coast, about 200 km upwind — the jet being thus an analogy in space to the classical Blackadar nocturnal jet frequently observed in continental areas.     

The Effect of Atmospheric Stability on the Surface-Layer Characteristics in a Low-Wind Area of Tropical West Africa

This study details the observed effects ofatmospheric stability on characteristics of thesurface layer in a low wind speed (U = 1.5 m s-1)regime of tropical West Africa. Theaerodynamic roughness length, z0, anddisplacement height, d, obtained from profilewind-speed data at our bush land site (height 2 m)have values of 0.24 ± 0.10 m and 1.54 ± 0.04 mrespectively. In the unstable range (-2.5 < Ri < -0.1; Riis gradient Richardson number), thestandard deviation in wind speed fluctuations, u, increased from 0.57 ± 0.19 m s-1 toa maximum of 0.7 ± 0.2 m s-1 in near-neutralconditions, and in the stable range, the parameterdecreased rapidly to 0.41 ± 0.15 m s-1 at Ri 0.2.In the same stability range, the horizontal winddispersion, , decreased withincreasing stability from 19 ± 8 deg. to 13 ± 5 deg.The surface-layer integral quantity, u/u*, when plottedas a function of stability, is in agreement with theempirical results. The ratio ofsensible heat flux (estimated) to the net radiationranged between 0.1 and 0.2 at nighttime,increasing to about 0.5 during the daytime, and showeda strong dependency on season.