Turbulence Reynolds number and the turbulent kinetic energy balance in the atmospheric surface layer

The relation between the turbulence Reynolds numberR and a Reynolds numberz* based on the friction velocity and height from the ground is established using direct measurements of the r.m.s. longitudinal velocity and turbulent energy dissipation in the atmospheric surface layer. Measurements of the relative magnitude of components of the turbulent kinetic energy budget in the stability range 0 >z/L 0.4 indicate that local balance between production and dissipation is maintained. Approximate expressions, in terms of readily measured micrometeorological quantities, are proposed for the Taylor microscale and the Kolmogorov length scale .     

A new theory of the energy spectrum

In a recent paper, the author introduced a new viscous boundary layer, called the mesolayer, in turbulent shear flow. Its importance stems from its location between the inner and outer regions which are controlled by the law of the wall and Reynolds number similarity, respectively. This intrusion prevents the classical overlap assumption which appears to be fundamental in the derivation of the classical logarithmic behavior. The mesolayer has a thickness proportional to Taylor's microscale . This, and the analogy between the energy equation for the spectrum function of isotropic turbulence and the momentum equation for shear flow, suggest the existence of a similar region in wavenumber space with wavenumber k ~ ^-1. This mesoregion separates the inner region k ~ k _s(where k _s^-1 and is the Kolmogorov length) and the outer region k k _e(where k _e ^-1 and l is the energy-containing eddy size) and again invalidates the overlap assumption which appears to be fundamental in the derivation of the classical k ^-5/3-behavior of the inertial subrange.Incorporation of the mesoregion into the argument leads to a new theory with k ^-5/3-behavior in two regions (^-1 k k _s) and (k _e k ^-1) although with two different coefficients of proportionality (Kolmogorov constants). This leads to a wandering of the spectrum curve about the classical k ^-5/3 line similar to a wandering in turbulent shear flow about the logarithmic curve. This is clearly indicated by the data for the variation of the Kolmogorov constant.Other data support the new theory. In particular, the location of the point k _mwhere the curve of the nonlinear energy-transfer function goes through zero shows agreement with the theory, i.e., k _m^-1.     

In-water and remote measurements of ocean color

Spectral measurements of downwelling irradiance, E _d(), above the surface, and of upwelling irradiance just below the surface, E _u(), allow computation of spectral values of the diffuse reflectance R() = E _u()/E _d(); this yields full information about the true color and brightness of the ocean. Typical results are presented and interpreted for waters very different in turbidity and phytoplankton content. Conversely, the possibility of infering the water content from R() data at selected wavelengths is examined in terms of the respective number of equations and unknowns. The necessary use of assumptions and of empirical laws is emphasized.The magnitude of the useful signal emerging from the water, and the magnitude of the additional signals due to specular reflexion at the interface and to atmospheric scattering, are compared on the basis of spectroradiometric measurements performed within and above the sea, from different altitudes. These unwanted signals are dominant, causing a drastic change in the spectral composition of the light received by a remote sensor. The evaluation of the atmospheric effect must be very precise in order to recover the marine signal with a sufficient accuracy for a meaningful application of any kind of algorithm.This work was supported in part by the Centre National d'Exploitation des Océans (under contract CNEXO 77/1695) and in part by the Centre National de la Recherche Scientifique (RCP 247 & ERA 278).     

The Kolmogorov constant for carbon dioxide in the atmospheric surface layer over a paddy field

From measurements in the atmospheric surface layer over a paddy field, the Kolmogorov constants for CO₂ and longitudinal wind velocity were obtained. In this study, the nondimensional dissipation rate _nc = (1–16 _v )^-1/2 for CO₂ variance and = (1–16 _v )^-1/4 – _v for turbulent energy were used, assuming the equality of the local production term and the local dissipation term, and neglecting the divergence flux term in the budget equation. The value of the constant for CO₂ was consistent with recent determinations for temperature and humidity. The constant for longitudinal wind velocity showed good agreement with other recent observations.     

Numerical integration errors in calculated tropospheric photodissociation rate coefficients

Tropospheric photodissociation rate coefficients (J values) were calculated for NO₂, O₃, HNO₂, CH₂O, and CH₃CHO using high spectral resolution (0.1 mm wavelength increments), and compared to the J values obtained with numerically degraded resolution (=1, 2, 4, 6, 8, and 10 nm, and several commonly used nonuniform grids). Depending on the molecule, substantial errors can be introduced by the larger increments. Thus for =10 nm, errors are less than 1% for NO₂, less than 2% for HNO₂, +6.5% to -16% for CH₂O, -6.9% to +24% for CH₃CHO, and -24% to +110% for O₃. The errors for CH₂O arise from the fine structure of its absorption spectrum, and are prevalently negative (underestimate of J). The errors for O₃, and to a lesser extent for CH₃CHO, arise mainly from under-resolving the overlap of the molecular action spectrum and the tropospheric actinic flux in the wavelength region of stratospheric ozone attenuation. The sign of those errors depends on whether the actinic flux is averaged onto the grid before or after the radiative transfer calculation. In all cases studied, grids with 2 nm produced errors no larger than 5%.     

Modelling radiation quantities and photolysis frequencies in the troposphere

STAR (System for Transfer of Atmospheric Radiation) was developed to calculate accurately and efficiently the irradiance, the actinic flux, and the radiance in the troposphere. Additionally a very efficient calculation scheme to computer photolysis frequencies for 21 different gases was evolved. STAR includes representative data bases for atmospheric constituents, especially aerosol particles. With this model package a sensitivity study of the influence of different parameter on photolysis frequencies in particular of O₃ to Singlet D oxygen atoms, of NO₂, and of HCHO was performed. The results show the quantitative effects of the influence of the solar zenith angle, the ozone concentration and vertical profile, the aerosol particles, the surface albedo, the temperature, the pressure, the concentration of NO₂, and different types of clouds on the photolysis frequencies.Notation I _A(, ) actinic flux - I _H(, ) irradiance - L(, , , ) radiance - wavelength - azimuth angle - cosine of zenith angle - _s cosine of solar zenith angle - optical depth - _s scattering coefficient - _c extinction coefficient - _o single scattering albedo - p _mix mixed phase function - g _mix mixed asymmetry factor - J _gas photolysis frequency     

Synchronous Scan and Excitation-Emission Matrix Fluorescence Spectroscopy of Water-Soluble Organic Compounds in Atmospheric Aerosols

Three-dimensional excitation–emission matrix (EEM) fluorescence spectra of water-soluble organic compounds (WSOC) from aerosol samples were measured and compared with those reported in the literature for natural dissolved organic matter. The EEM profiles of the WSOC presented three characteristic excitation/emission (_Exc/_Em) peaks: 240/405 nm, 310/405 nm and 280/340 nm. The fluorescence intensities at _Exc/_Em240/405 nm and _Exc/_Em310/405 nm are located at wavelengths shorter than those reported for aquatic humic substances, indicating a smaller content of both aromatic structures and condensed unsaturated bond systems in the WSOC fraction. The EEM profiles of fractions obtained by the isolation procedure of the WSOC by the XAD resins showed that a fractionation has occurred and the XAD-8 eluate is highly representative of the total WSOC of collected aerosol. Synchronous scan spectra were more detailed than conventional fluorescence emission spectra, appearing more suitable for studying multicomponent samples such as the WSOC from atmospheric aerosols.     

Energy Fluxes of an Open Water Area in a mid-Latitude Prairie Wetland

Concurrent measurements of the surface energy balance components (net radiation, heat storage, and sensible and latent heat fluxes) were made in three communities (open water, Phragmites australis, Scirpus acutus) in a wetland in north-central Nebraska, U.S.A., during May-October, 1994. The Bowen ratio – energy balance method was used to calculate latent and sensible heat fluxes. This paper presents results from the open water area. The heat stored in water (G) was found to play a major role in the energy exchange over the water surface. During daytime, G consumed 45–60% of R _n , the net radiation (seasonally averaged daytime G was about 127 W m^–2). At night, G was a significant source of energy (seasonally averaged nighttime G was about -135 Wm^–). The diurnal pattern of latent heat flux ( E) did not follow that of R _n . On some days, E was near zero during midday periods with large R _n . The diurnal variability in E seemed to be significantly affected by temperature inversions formed over the cool water surface. The daily evaporation rate (E) ranged from 2 to 8 mm during the measurement period, and was generally between 70 and 135% of the equilibrium rate.     

Uncoupled multi-layer model for the transfer of sensible and latent heat flux densities from vegetation

The sensible heat flux density C and the latent heat flux density E are coupled in the case of a multi-layer model of vegetation. Therefore two linearly independent combinations of C and E, the enthalpy flux density H and the saturation heat flux density J, are introduced. Two electrical analogues, for H and J, are designed. They are equivalent to the resistance scheme for C and E, but uncoupled. Penman's formulas for C and E, which are applicable only to single-layer models, can be expressed equivalently in terms of H and J. This version of Penman's formulas can be extended easily to multi-layer canopies.     

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     

Drag and drag partition on rough surfaces

An analytic treatment of drag and drag partition on rough surfaces is given. The aims are to provide simple predictive expressions for practical applications, and to rationalize existing laboratory and atmospheric data into a single framework. Using dimensional analysis and two physical hypotheses, theoretical predictions are developed for total stress (described by the square root of the canopy drag coefficient), stress partition (described by the ratio _S/ of the stress _s on the underlying ground surface to total stress ), zero-plane displacement and roughness length. The stress partition prediction is the simple equation _S/= 1/(1+), where = C_RC_S the ratio of element and surface drag coefficients. This prediction agrees very well with data and is free of adjustable constants. Other predictions also agree well with a range of laboratory and atmospheric data.     

Aktinometrische Kurzstrahlung und Trübungskoeffizient

Zusammefassung Um Trübungsbestimmungen nach Aktinometermessungen gegenüber demSchüeppschen Verfahren (und ähnlichen) wesentlich zu erleichtern, wird an Hand derSchüeppschen Unterlagen ein Diagramm zur Bestimmung des dekadischen TrübungskoeffizientenB ₅₀₀ aus Messungen der Kurzstrahlung (J _K , <625 nm) berechnet. Die so erhaltenen Werte vonJ _K sind praktisch unabhängig vom -Exponenten der Dunstextinktion.J _K -Werte fürB=0 verschiedener Autoren werden verglichen, und Trübungsgrößen verschiedener Diagramme (,T _K ,B nachSchüepp) werden in Beziehung gesetzt. Es wird darauf hingewiesen, daß dieSchüepp-sche Methode bei kleinen Trübungen wahrscheinlich etwas zu hohe Werte ergibt.

---

Summary To simplify the determination of atmospheric turbidity by actinometric measurements with respect to theSchüepp method, a diagram has been computed from the data ofSchüepp to derive the decadic turbidity coefficientB ₅₀₀ from measurements of short wave radiation (J _K , <625 nm). Values ofJ _K are practically independent of the -exponent of haze attenuation.J _K -values forB=0 of different authors and turbidity values of different diagrams (,T _K ,B _Schüepp) are compared. It is pointed out that theSchüepp method yields probably slightly too high values with small turbidity.

---

Résumé Le calcul du trouble atmosphérique d'après les mesures actinométriques est assez compliqué selon la méthode deSchüepp ou d'autres méthodes semblables. Afin d'en faciliter notablement la détermination, l'auteur a calculé une abaque en se basant sur les données deSchüepp. Ce diagramme permet d'évaluer le coefficient de trouble atmosphérique décadaireB ₅₀₀ en partant de la mesure du rayonnement à ondes courtes (J _K , <625 m). Les valeurs deJ _K obtenues alors sont pratiquement indépendantes de l'exposant de l'extinction due à la brume. Les valeurs deJ _K pourB=0 et provenant de divers auteurs sont comparées entre elles. On a en outre établi le rapport existant entre le trouble atmosphérique calculé d'après divers diagrammes (,T _K ,B _Schüepp). On rend le lecteur attentif au fait que les valeurs calculées selonSchüepp sont probablement trop élevées lorsque le trouble atmosphérique est peu important.

---

---

Mit 2 Textabbildungen     

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.     

Simultaneous measurements of turbulence over land and water

Turbulence and mean flow variables under unstable conditions are examined with special emphasis on the consequences of roughness and surface elevation change. An interpolation formula for _w ², between neutral and free convection, is shown to bring order to the data. The spectral distribution of vertical wind variance is found to be in good agreement with results over horizontal homogeneous terrain, both with respect to form and position. In particular, the length scale _m corresponding to the maximum of nS _w(n) is unchanged. Another turbulent length scale, (k/)z, is found to be substantially reduced in the disturbed zone of the internal boundary layer. To a first approximation, the flow-acceleration effect on the non-dimensional wind shear can be separated from the diabatic effect.     

Atmospheric effects in the remote sensing of phytoplankton pigments

We investigate the accuracy with which relevant atmospheric parameters must be estimated to derive phytoplankton pigment concentrations (chlorophyll a plus phaeophytin a ) of a given accuracy from measurements of the ocean's apparent spectral radiance at satellite altitudes. The analysis is limited to an instrument having the characteristics of the Coastal Zone Color Scanner scheduled to orbit the Earth on NIMBUS-G. A phytoplankton pigment algorithm is developed which relates the pigment concentration (C) to the three ratios of upwelling radiance just beneath the sea surface which can be formed from the wavelengths () 440, 520 and 550 nm. The pigment algorithm explains from 94 to 98% of the variance in log₁₀ C over three orders of magnitude in pigment concentration. This is combined with solutions to the radiative transfer equation to simulate the ocean's apparent spectral radiance at satellite altitudes as a function of C and the optical properties of the aerosol, the optical depth of which is assumed to be proportioned to ^-n . A specific atmospheric correction algorithm, based on the assumption that the ocean is totally absorbing at 670 nm, is then applied to the simulated spectral radiance, from which the pigment concentration is derived. Comparison between the true and derived values of C show that: (1) n is considerably more important than the actual aerosol optical thickness; (2) for C 0299-1 0.2 g l^-1 acceptable concentrations can be determined as long as n is not overestimated; (3) as C increases, the accuracy with which n must be estimated, for a given relative accuracy in C, also increases; and (4) for C greater than about 0.5 g 1^-1, the radiance at 440 nm becomes essentially useless in determining C. The computations also suggest that if separate pigment algorithms are used for C 1gl^-1 and C 1 gl^-1, accuracies considerably better than ±± in log C can be obtained for C 1 g l^-1 with only a coarse estimate of n, while for C 10 gl^-1, this accuracy can be achieved only with very good estimates of n.Contribution No. 387 from the NOAA/ERL Pacific Environmental Laboratory.On leave from Department of Physics, University of Miami, Coral Gables, Florida.     

Three-dimensional modeling of synthetic cold fronts interacting with northern Alpine foehn

Summary The effect of the Alpine orography on prototype cold fronts approaching from the west is investigated by three-dimensional numerical model simulations. The numerical experiments cover a range of parameter constellations which govern the prefrontal environment of the front. Especially, the appearance and intensity of prefrontal northern Alpine foehn varies from case to case.The behaviour of a cold front north of the Alps depends much on the prefrontal condition it encounters. It is found that prefrontal foehn can either accelerate or retard the approaching front.An important feature is the pressure depression along the northern Alpine rim that results from the southerly foehn flow. In cases where this depression compensates the eastward directed pressure gradient associated with the largescale flow, the front tends to accelerate and the foehn breaks down as soon as the front passes. In contrast, the foehn prevents the front from a rapid eastward propagation if it is connected with a strong southerly wind component.No-foehn experiments are performed for comparison, where either the mountains are removed, or the static stability is set to neutral. Also shown are effects of different crossfrontal temperature contrasts.List of Symbols c _F propagation speed of a front - x, y horizontal grid spacing (cartesian system) - , horizontal grid spacing (geographic system) - t time step - z vertical grid spacing (cartesian system) - cross-frontal potential temperature difference - _i potential temperature step at an inversion - E turbulent kinetic energy - f Coriolis parameter - FGP frontogenesis parameter (see section 2.2) - g gravity acceleration (g=9.81 m s^–2) - vertical gradient of potential temperature - h terrain elevation (above MSL) - h _i height of an inversion (h _i =1000 m MSL) - H height of model lid (H=9000 m MSL) - K _M exchange coefficient of momentum - K _H exchange coefficient of heat and moisture - longitude - N Brunt-Väisäla-frequency - p pressure - Exner function (=T/) - latitude - q _v specific humidity - R _d gas constant of dry air (R _d =287.06 J kg^–1 K^–1) - density of dry air - t time - T temperature - potential temperature - TFP thermal front parameter (see section 2.2) - u, v, w cartesian wind components - u _g ,v _g geostrophic wind components - horizontal wind vector - x, y, z cartesian coordinates Abbreviations GND (above) ground level - MSL (above) mean sea level - UTC universal time coordinated With 20 Figures     

Models of eddy viscosity for numerical simulation of horizontally inhomogeneous,neutral surface-layer flow

Modification of a turbulent flow due to a change from a smooth to a rough surface has been studied by means of a stream function-vorticity model. Results of four models of eddy viscosity (or turbulent exchange coefficient) K _mhave been compared. The models are: (1) K _m = l²S, where l is the mixing length and S is the deformation of mean flow; (2) K _m E/S, which is based on the assumption that turbulent momentum flux is proportional to turbulent kinetic energy E; (3) K _m lE^1/2, the so called Prandtl-Kolmogoroff approach; and (4) K _m E²/, the E — closure, where is the dissipation of turbulent kinetic energy.It is found that net-production, i.e., the difference of production and dissipation of turbulent kinetic energy counteracts the influence of mean shear on turbulent shear stress and diminishes turbulent shear stress. The reduction of mixing-length, being predicted by Model 4 only, adds to this attenuation. As a consequence, in Models 2 and 4, loss of horizontal mean momentum is concentrated close to the ground, which results in an inflexion point in the logarithmic, vertical profile of horizontal mean velocity. By contrast, in Models 1 and 3, modification of turbulent shear stress reaches larger heights causing deeper internal boundary layers. Concerning the existence of an inflexion point in U(lnz), the depth of the internal boundary layer for mean velocity, and the modification of bottom shear stress, Model 4 comes closest to experimental data.A remarkable difference of Models 1, 2, 3 and Model 4 is that only Model 4 predicts a very slow relaxation of eddy viscosity which can be attributed to the reduction of mixing-length.     

The atmospheric tide as a continuous spectrum: Lunar semidiurnal tide in surface pressure

Summary The standard equations for the theory of atmospheric tides are solved here by an integral representation on the continuous spectrum of free oscillations. The model profile of back-ground temperature is that of the U.S. Standard Atmosphere in the lower and middle atmosphere, and in the lower thermosphere, above which an isothermal top extends to arbitrarily great heights. The top is warm enough to bring both the Lamb and the Pekeris modes into the continuous spectrum.Computations are made for semidiurnal lunar tidal pressure at sea level at the equator, and the contributions are partitioned according to vertical as well as horizontal structure. Almost all the response is taken up by the Lamb and Pekeris modes of the slowest westward-propagating gravity wave. At sea level, the Lamb-mode response is direct and is relatively insensitive to details of the temperature profile. The Pekeris mode at sea level has an indirect response-in competition with the Lamb mode-and, as has been known since the time of its discovery, it is quite sensitive to the temperature profile, in particular to stratopause temperature. In the standard atmosphere the Lamb mode contributes about +0.078 mb to tidal surface pressure at the equator and the Pekeris mode about –0.048 mb.The aim of this investigation is to illustrate some consequences of representing the tide in terms of the structures of free oscillations. To simplify that task as much as possible, all modifying influences were omitted, such as background wind and ocean or earth tide. Perhaps the main defect of this paper's implementation of the free-oscillation spectrum is that, in contrast to the conventional expansion in the structures of forced oscillations, it does not include dissipation, either implicity or explicity, and thus does not satisfy causality. Dissipation could be added implicity by means of an impedance condition, for example, which would cause up-going energy flux to exceed downgoing flux at the base of the isothermal top layer. To achieve complete causality, however, the dissipation must be modeled explicity. Nevertheless, since the Lamb and Pekeris modes are strongly trapped in the lower and middle atmosphere, where dissipation is rather weak (except possibly in the surface boundary layer), more realistic modeling is not likely to change the broad features of the present results.Symbols a earth's mean radius; expansion coefficient in (5.3) - b recursion variable in (7.4); proximity to resonance in (9.2) - c sound speed in (2.2); specific heatc _p in (2.2) - f Coriolis parameter 2sin in (2.2) - g standard surface gravity - h equivalent depth - i ; discretization index in (7.3) - j index for horizontal structure - k index for horizontal structure; upward unit vectork in (2.2) - m wave number in longitude - n spherical-harmonic degree; number of grid layers in a model layer - p tidal pressure perturbation; background pressurep ₀ - q heating function (energy per mass per time) - r tidal state vector in (2.1) - s tidal entropy perturbation; background entropys ₀ - t time - u tidal horizontal velocityu - w tidal vertical component of velocity - x excitation vector defined in (2.3); vertical coordinate lnp _*/p ₀ [except in (3.8), where it is lnp /p ₀] - y vertical-structure function in (7.1) - z geopotential height - A constant defined in (6.2) - C spherical-harmonic expansion coefficient in (3.6) - D vertical cross section defined in (5.6) and (5.9) - E eigenstate vector - F vertical-structure function for eigenstate pressure in (3.2) [re-defined with WKB scaling in (7.2)] - G vertical-structure function for eigenstate vertical velocity in (3.2) [re-defined with WKB scaling in (7.2)] - H pressure-scale height - I mode intensity defined in (8.1) - K quadratic form defined in (4.4) - L quadratic form defined in (4.4); horizontal-structure magnification factor defined in (5.11) - M vertical-structure magnification factor defined in (4.6) - P eigenstate pressure in (3.2); tidal pressure in (6.2) - R tidal state vector in (5.1) - S eigenstate entropy in (3.2); spherical surface area, in differential dS - T background molecular-scale (NOAA, 1976) absolute temperatureT ₀ - U eigenstate horizontal velocityU in (3.2); coefficient in (7.3) - V horizontal-structure functionV for eigenstate horizontal velocity in (3.2); recursion variable in (7.3) - W eigenstate vertical velocity in (3.2) - X excitation vector in (5.1) - Y surface spherical harmonic in (3.7) - Z Hough function defined in (3.6) - +dH/dz - (1––)/2 - Kronecker delta; Dirac delta; correction operator in (7.6) - equilibrium tide elevation - (square-root of Hough-function eigenvalue) - ratio of specific gas constant to specific heat for air=2/7 - longitude - - - background density ₀ - eigenstate frequency in (3.1) - proxy for heating functionq =c _P/t - latitude - tide frequency - operator for the limitz - horizontal-structure function for eigenstate pressure in (3.2) - Hough function defined in (6.2) - earth's rotation speed - horizontal gradient operator - ()₀ background variable - ()_* surface value of background variable - () value at base of isothermal top layer - Õ state vector with zerow-component - , energy product defined in (2.4) - | | energy norm - ()^* complex conjugate With 10 Figures     

Numerical simulation of particle trajectories in inhomogeneous turbulence,II: Systems with variable turbulent velocity scale

It is shown that for the purpose of trajectory simulation, the vertical velocityw _L (t) of a fluid element, which is moving in a system (such as a forest canopy, or the unstably stratified atmospheric surface layer) whose turbulent velocity scale _w is height-dependent, must be chosen from a frequency-distribution which is asymmetric aboutw _L = 0. If the gradient _w /z varies only slowly with height, correct trajectories may be obtained by adding a bias (where _L is the length scale) to a fluctuating velocity chosen from a symmetric distribution with variance _w ²(z).     

The response of a propeller anemometer to turbulent flow with the mean wind vector perpendicular to the axis of rotation

The system transfer function ¦H(v)¦² at frequencyv (units of Hz) for a vertical velocity propeller anemometer in a statistically stationary and horizontally homogeneous turbulent flow is determined from: (1) experimental estimates of propeller velocity spectra; and (2) estimates of Eulerian vertical velocity spectra based on the hypothesis that degradation of the input vertical velocity Fourier components occurs in the inertial subrange. The experimental estimates of ¦H(v)¦² were adequately summarized with the mathematical expression for the system transfer function of a first-order system with parameterT which has units of time and is analogous to the time constant of a horizontal velocity propeller anemometer. Dimensional analysis techniques and the Monin-Obukhov similarity hypothesis were used to construct a model for the system parameterT which yielded the result that _w /D ₁ ( _w /)^1/3, where _w , andD ₁ denote the standard deviation of the input vertical velocity fluctuations, the horizontal mean wind speed, and the diameter of the propeller, respectively. The system parameterT is interpreted in terms of the time required for the propeller velocity statistics to become asymptotically independent of time upon being released from rest in a statistically stationary turbulent flow.Currently on leave of absence from the Indian Institute of Technology, New Delhi, India.