Turbulence decay in stratified and homogeneous marine layers

A spectral approach is applied to shear-induced turbulence in stratified layers. A system of spectral equations for stationary balance of turbulent energy and temperature variances was deduced in the vicinity of the local shear scale L_U = (ε/U_Z³)^1/2. At wavenumbers between the inertial-convective (k^−5/3) and wak turbulence (k⁻³) subranges, additional narrow spectral intervals—‘production’ subranges—may appear (E k⁻¹, E_T k⁻²). The upper boundary of these subranges is determined as L_U, and the lower boundaries as L_R (ε/U_ZN²)^1/2(χ/T_Z²). It is shown that the scale L_U is a unique spectral scale that is uniform up to a constant value for every hydrophysical field. It appears that the spectral scale L_U is equivalent to the Thorpe scale L_Th for the active turbulence model. Therefore, if turbulent patches are generated in a background of permanent mean shear, a linear relation between temperature and mass diffusivities exists. In spectral terms, the fossil turbulence model corresponds to the regime of the Boldgiano-Obukhov buoyancy subrange (E k^−11/5, E_T k^−7/5). During decay the buoyancy subrange is expanded to lower and higher wavenumbers. At lower wavenumbers the buoyancy subrange is bounded by L_** = 3(χ^1/2/N^1/2T_Z), which is equivalent to the Thorpe scale L_Th. In such a transition regime only, when the viscous dissipation rate is removed from the set of main turbulence parameters, the Thorpe scale does not correlate with the buoyancy scale L_N ε^1/2/N^3/2 and fossil turbulence is realized. Oceanic turbulence measurements in the equatorial Pacific near Baker Island confirm the main ideas of the active and fossil turbulence models.     

Inertial ranges in three-dimensional quasi-geostrophic turbulence

A theory is presented both for spectral energy transfer and for the transfer of spectral components of pseudo-potential enstrophy in a homogeneous quasi-geostrophic turbulent field which is rendered anisotropic by the distortion caused by a random collection of vortices superimposed on the principal motions. The fluid is, thus, subjected to an almost irrotational distortion. The random vortices cause straining effects on turbulent velocity and temperature fluctuations and modify the energy spectrum in the spectral ranges of interest. The strain imposed by the distortion is assumed to be homogeneous. For three-dimensional quasi-geostrophic turbulence that conserves pseudo-potential enstrophy as well as energy, this theory predicts –8/3 and –4 power inertial-range energy spectra.The predictions favourably corroborate the observed spectrum of energy in the atmosphere in the region of hemispheric wave-numbers 10–16 with a –8/3 slope and at higher wave-numbers with –4 slope on a log-log energy-wave-number diagram. The transfer rates of pseudo-potential enstrophy in the range 10n16 and of energy in the rangen>16 are identically zero, while the transfer of energy in the first range is from higher to lower wave-numbers and that of the pseudo-potential enstrophy in the second range is from lower to higher wave-numbers.As compared with the earlier two-dimensional turbulence theory of Kraichnan and the quasigeostrophic turbulence theory of Charney, the present theory predicts more realistic shapes of the energy spectra of atmospheric motions at scales shorter than the baroclinic excitation scales.     

Temperature stratification of the atmospheric boundary layer over the Deccan Plateau,India, during the summer monsoon

The vertical and horizontal temperature structure of the atmospheric boundary layer (ABL) were studied using aircraft observations made in the lowest 2.4 km above ground level during the summer monsoon.The vertical temperature structure of the ABL in the region may be classified into the following four categories.Category The ABL consisted of two layers of thickness 700–900 m separated by a thin transition layer. The lapse rates in the former two layers were dry adiabatic.Category The lowest layer of the ABL of thickness 400–600 m was adiabatically stratified and the overlying layer was stable with gradients of potential temperature 4–5°C km^–1. The stable layer contained a thin adiabatic stratified layer of 200–300 m thickness at a height of 1.5 km.Category The lowest 200–400 m layer of the ABL was adiabatically stratified and the overlying layer was stable with potential temperature gradients of 5–6 °C km¹.Category The ABL was mainly stable with potential temperature gradients of 6 °C km^–1 or greater. Occasionally thin layers with adiabatic stratification were found embedded in the ABL.The temperature distribution of the horizontal temperature at 900 m was mainly normal. The high-frequency portion of the spectra lying between 0.05 and 0.16 Hz (corresponding to wave length 1 km to 300 m) oscillated around the –\2/3 power law line. The spectral curve showed a significant peak at 0.011 Hz having a wave-length of 5 km.Department of Geoscience, North Carolina State University, Raleigh, NC, 27650, U.S.A.     

Seasonal variations of spectra of wind speed and air temperature in the mesoscale frequency range

Seasonal variations of the spectra of wind speed and air temperature in the mesoscale frequency range from 1.3 × 10^-4 to 1.5 × 10^-3 Hz (10 min to 2 h periods) have been studied through observations over land for one year. Spectrographs [time series of isopleths of spectral densities, f · S(f) vs f] of wind speed and air temperature contain occasional peaks that are attributed to short-lived mesoscale atmospheric activity with narrow frequency bands. Significant spectral peaks of wind speed were found in 19% of the total observations in winter, and in 15–16% in the other seasons; for air temperature, they occured in 12% of observations in autumn, and in 16–19% in the other seasons. The peaks most often occurred in the period range from 30 min to 1 h; most had durations less than 24 h. Mesoscale fluctuations of wind speed and air temperature were highly correlated, and in most cases, phase differences were 90–180 ° with air temperature leading wind speed. Significant spectral peaks of wind speed often occurred during northerly seasonal cold winds in winter, and accompanied tropical and/or mid-latitude cyclones in the other seasons. When the peaks occurred, wind speed was usually relatively high and the atmospheric surface layer was unstable.     

Spectra of surface wind speed and air temperature over the ocean in the mesoscale frequency range in JASIN-1978

Based on the data from an array of buoys during the JASIN-1978 field experiment made in an area northwest of Scotland, power spectra of surface wind speed and air temperature over the ocean in the mesoscale frequency range were studied. The averaged composite spectrum of wind speed for the whole period shows the existence of a spectral gap in the frequency range from 10^–4 to 5 × 10^–3 Hz. However, significant peaks in this range are often seen in particular spectra under certain weather conditions. Mesoscale spectral peaks of wind speed occur in 14 segments of the data record, approximately 10% of the total duration of the observations. In 4 of these segments, the mesoscale spectral peaks of both wind speed and air temperature occurred simultaneously. Several wave patterns of mesoscale atmospheric disturbances when mesoscale spectral peaks were seen are derived from phase differences between buoys. Significant mesoscale peaks in spectra appear in relatively strong winds and unstable or near-neutral atmospheric conditions, and none in stable atmospheric conditions. A criterion of wind speed and atmospheric stability is found for the mesoscale spectral peak appearance.     

Model of convective heat exchange due to isolated thermals in the atmospheric boundary layer

A numerical model of convective heat transfer due to isolated thermals in the atmospheric boundary layer is used to describe the temperature profile transformation in undisturbed conditions as a result of intensive dry free convection. Based on some assumptions, the heat transfer Equation (2) is transformed to the form (14) in which the coefficients and the function F are expressed by (d/dz)(ln ) and by parameters of thermals. Equation (14) has been solved numerically with the help of Equation (15) obtained from the statics equation because of Equation (8). The size distribution function f(z, r, t) of the thermals is discrete (Table I), according to Vulf'son (1961). On Figures 1 and 2 are plotted successive temperature profiles for a ground inversion, transformed due to free convection and turbulence (Figures 1a and 2a), and due to turbulence only (Figures 1b and 2b). The profiles are computed from Equation 14 (Figures 1a and 2a) and Equation 16 (Figures 1b and 2b) for k _z= 1 m² s^–1 (Figure 1) and k _z= 10 m² s^–1 (Figure 2). On Figure 3 the real temperature profiles in Sofia for June 22nd 1976 are compared with the profiles computed using the real initial profile for 4.30 h local time. Good qualitative agreement can be seen.     

Rate constants for the reactions of the NO3 radical with HCOOH/HCOO− and CH3COOH/CH3COO− in aqueous solution between 278 and 328 K

The kinetics of the aqueous phase reactions of NO₃ radicals with HCOOH/HCOO^– and CH₃COOH/CH₃COO^– have been investigated using a laser photolysis/long-path laser absorption technique. NO₃ was produced via excimer laser photolysis of peroxodisulfate anions (S₂O ₈ ^2– ) at 351 nm followed by the reactions of sulfate radicals (SO ₄ ^– ) with excess nitrate. The time-resolved detection of NO₃ was achieved by long-path laser absorption at 632.8 nm. For the reactions of NO₃ with formic acid (1) and formate (2) rate coefficients ofk ₁=(3.3±1.0)×10⁵ l mol^–1 s^–1 andk ₂=(5.0±0.4)×10⁷ l mol^–1 s^–1 were found atT=298 K andI=0.19 mol/l. The following Arrhenius expressions were derived:k ₁(T)=(3.4±0.3)×10¹⁰ exp[–(3400±600)/T] l mol^–1 s^–1 andk ₂(T)=(8.2±0.8)×10¹⁰ exp[–(2200±700)/T] l mol^–1 s^–1. The rate coefficients for the reactions of NO₃ with acetic acid (3) and acetate (4) atT=298 K andI=0.19 mol/l were determined as:k ₃=(1.3±0.3)×10⁴ l mol^–1 s^–1 andk ₄=(2.3±0.4)×10⁶ l mol^–1 s^–1. The temperature dependences for these reactions are described by:k ₃(T)=(4.9±0.5)×10⁹ exp[–(3800±700)/T] l mol^–1 s^–1 andk ₄(T)=(1.0±0.2)×10¹² exp[–(3800±1200)/T] l mol^–1 s^–1. The differences in reactivity of the anions HCOO^– and CH₃COO^– compared to their corresponding acids HCOOH and CH₃COOH are explained by the higher reactivity of NO₃ in charge transfer processes compared to H atom abstraction. From a comparison of NO₃ reactions with various droplets constituents it is concluded that the reaction of NO₃ with HCOO^– may present a dominant loss reaction of NO₃ in atmospheric droplets.     

The perturbed structure of the neutral atmospheric boundary layer over irregular terrain

The first-order (linear) response of the planetary boundary layer is calculated for flow over periodic terrain, for variations in both surface roughness and terrain elevation. Calculations are made for horizontal wavenumbers varying from 10^–4m^–1 to 3 × 10^–3m^–1. A simple second-order closure model of the turbulence is used, and Coriolis and buoyancy forces are neglected. As expected, flow over a periodic terrain produces corresponding periodic structure in all meteorological fields above the surface. The periodic structure consists of two components. The first is very nearly evanescent with height, showing little vertical structure. It corresponds to the motion that would be observed were the atmosphere inviscid. The second component, introduced by turbulent viscosity, exhibits considerable vertical structure, with vertical wavelengths the order of 100 m, and thus could be responsible for the layering often seen on acoustic sounder observations of the atmospheric boundary layer.Wave Propagation Laboratory.Environmental Science Group.     

Calibration and use of a sailplane variometer to measure vertical velocity fluctuations

The calibration of a sailplane variometer to measure vertical velocity fluctuations in the atmospheric boundary layer is described. Its usefulness is demonstrated with typical results from a boundary-layer development study. The atmospheric calibrations gave the ratio of standard deviations of vertical velocity fluctuations measured by a standard tower-mounted turbulence instrument to the values measured by variometer as 2.5 m s^–1 V^–1.     

One-Equation Turbulence Modelling for Atmospheric and Engineering Applications

A new algebraic turbulent length scale model is developed, based on previous one-equation turbulence modelling experience in atmospheric flow and dispersion calculations. The model is applied to the neutral Ekman layer, as well as to fully-developed pipe and channel flows. For the pipe and channel flows examined the present model results can be considered as nearly equivalent to the results obtained using the standard k– model. For the neutral Ekman layer, the model predicts satisfactorily the near-neutral Cabauw friction velocities and a dependence of the drag coefficient versus Rossby number very close to that derived from published (G. N. Coleman) direct numerical simulations. The model underestimates the Cabauw cross-isobaric angles, but to a less degree than the cross-isobar angle versus Rossby dependence derived from the Coleman simulation. Finally, for the Cabauw data, with a geostrophic wind magnitude of 10 ms^–1, the model predicts an eddy diffusivity distribution in good agreement with semi-empirical distributions used in current operational practice.     

Further studies of the temperature dependence of the rate coefficients for the reactions of OH with a series of ethers under simulated atmospheric conditions

The following temperature-dependent rate coefficients (k/cm³ molecule^–1 s^–1) of the reactions of hydroxyl radicals with aliphatic ethers have been determined over the temperature range 247–373 K by a competitive flow technique: diethyl ether,k _OH=5.2×10^–12 exp[(262±150)/T]; methyln-butyl ether,k _OH=5.4×10^–12 exp[(309±150)/T]; ethyln-butyl ether,k _OH=7.3×10^–12 exp[(335±150)/T]; di-n-butyl ether,k _OH=5.5×10^–12 exp[(502±150)/T] and di-n-pentyl ether,k _OH=8.5×10^–12 exp[(417±150)/T]. The data have been measured relative to the rate coefficientk(OH + 2,3-dimethylbutane)=6.2×10^–12 cm³ molecule^–1 s^–1 independent of temperature.Previous discrepancies in the room-temperature rate coefficients for the OH reactions with ethyln-butyl ether and di-n-butyl ether, obtained in the flow and static experiments of Bennett and Kerr (J. Atmos. Chem. 8, 87–94, 1989;10, 29–38, 1990) compared with those of Wallingtonet al. (Int. J. Chem. Kinet. 20, 541–547, 1988;21, 993–1001, 1989) and of Nelsonet al. (Int. J. Chem. Kinet. 22, 1111–1126, 1990) have been resolved. The results are considered in relation to the available literature data and evaluated rate expressions are deduced where possible. The data are also discussed in terms of structure-activity relationships.     

Prediction of the abiotic degradability of organic compounds in the troposphere

A statistically relevant correlation between the reaction rate coefficient, k _OH, for the OH radical reaction with 161 organic compounds in the gas phase at 300 K, and the corresponding vertical ionisation energies E _i,v, reveals two classes of compounds: aromatics where –log(k _OH/cm³s^-1)3/2E _i,v(eV)–2 and aliphatics where –log(k _OH/cm³s^-1)4/5E _i,v(eV)+3. The prediction of the rate coefficient, k _OH, for the reaction of OH with organic molecules from the above equations has a probability of about 90%. Assuming a global diurnal mean of the OH radical concentration of 5×10⁵ cm³, the upper limit of the tropospheric half-life of organic compounds and their persistence can be estimated.     

Mechanistic and Kinetic Study of the Gas-Phase Reaction of Atomic Chlorine with Cyclohexanone using an Absolute and a Relative Technique; Influence of Temperature

The reaction of Cl with cyclohexanone (1) was investigated, for the first time, as a function of temperature (273–333 K) and at a low total pressure (1 Torr) with helium as a carrier gas using a discharge flow-mass spectrometry technique (DF-MS). The resulting Arrhenius expression is proposed, k ₁= (7.7 ± 4.1) × 10^–10 exp[–(540 ± 169)/T]. We also report a mechanistic study with the quantitative determination of the products of the reaction of Cl with cyclohexanone. The absolute rate constant derived from this study at 1 Torr of total pressure and room temperature is (1.3 ± 0.2) × 10^–10 cm³ molecule^–1 s^–1. A yield of 0.94 ± 0.10 was found for the H-abstraction channel giving HCl. In relative studies, using a newly constructed relative rate system, the decay of cyclohexanone was followed by gas chromatography coupled with flame-ionisation detection. These relative measurements were performed at atmospheric pressure with synthetic air and room temperature. Rate constant measured using the relative method for reaction (1) is: (1.7 ± 0.3) × 10^–10 cm³ molecule^–1 s^–1. Finally, results and atmospheric implications are discussed and compared with the reactivity with OH radicals.     

A comparison of turbulence statistics in the surface layer over plant canopies with those over several other surfaces

Turbulence statistics, including higher order moments, in the surface layer over plant canopies were compared with those observed over several different surfaces, using a nondimensional height (z – d)/z ₀: The values of (z – d)/z ₀extend over a very wide range from 10 over plant canopies to 10⁷ over the ocean. Several properties such as intensities of turbulence and skewness factors show a remarkable height-dependency in the air layer below (z – d)/z ₀ = 10², which is supposed to be much influenced by the underlying surface. In that layer, some peculiar phenomena, such as a downward energy transport and positive flux of shear stress, are frequently observed.     

On the Kinetic Energy Budget of the Unstable Atmospheric Surface Layer

We present a new account of the kinetic energy budget within an unstable atmospheric surface layer (ASL) beneath a convective outer layer. It is based on the structural model of turbulence introduced by McNaughton (Boundary-Layer Meteorology, 112: 199–221, 2004). In this model the turbulence is described as a self-organizing system with a highly organized structure that resists change by instability. This system is driven from above, with both the mean motion and the large-scale convective motions of the outer layer creating shear across the surface layer. The outer convective motions thus modulate the turbulence processes in the surface layer, causing variable downwards fluxes of momentum and kinetic energy. The variable components of the momentum flux sum to zero, but the associated energy divergence is cumulative, increasing both the average kinetic energy of the turbulence in the surface layer and the rate at which that energy is dissipated. The tendency of buoyancy to preferentially enhance the vertical motions is opposed by pressure reaction forces, so pressure production, which is the work done against these reaction forces, exactly equals buoyant production of kinetic energy. The pressure potential energy that is produced is then redistributed throughout the layer through many conversions, back and forth, between pressure potential and kinetic energy with zero sums. These exchanges generally increase the kinetic energy of the turbulence, the rate at which turbulence transfers momentum and the rate at which it dissipates energy, but does not alter its overall structure. In this model the velocity scale for turbulent transport processes in the surface layer is (kzɛ)^1/3 rather than the friction velocity, u_*. Here k is the von Kármán constant, z is observation height, ɛ is the dissipation rate. The model agrees very well with published experimental results, and provides the foundation for the new similarity model of the unstable ASL, replacing the older Monin–Obukhov similarity theory, whose assumptions are no longer tenable.     

Atmospheric Loss Processes of Dimethyl and Diethyl Carbonate

A combined study of the OH gas phase reaction and uptake on aqueous surfacesof two carbonates, dimethyl and diethyl carbonate has been carried out todetermine the atmospheric lifetimes of these compounds. Rate coefficients havebeen measured for gas phase reactions of OH radicals with dimethyl and diethylcarbonate. The experiments were carried out using pulsed laser photolysis– laser induced fluorescence over the temperature range 263–372K and the kinetic data were used to derive the following Arrhenius expressions(in units of cm³ molecule^–1 s^–1):for dimethyl carbonate, k₁ = (0.83±0.27)×10^–12 exp [–(247± 98)/T] and fordiethyl carbonate, k₂ = (0.46±0.15)×10^–12 exp [(503± 203)/T]. At 298 K, therate coefficients obtained (in units of 10^–12 cm³molecule^–1 s^–1) are: k₁ =(0.35± 0.04) and k₂ = (2.31± 0.29). The results arediscussed in terms of structure-activity relationships.The uptake coefficients of both carbonates on aqueous surfaces were measuredas a function of temperature and composition of the liquid phase, using thedroplet train technique coupled to a mass spectrometric detection. Dimethyland diethyl carbonate show very similar results. For both carbonates, themeasured uptake kinetics were found to be independent of the aqueous phasecomposition (pure water, NaOH solutions) but dependent on gas-liquid contacttime which characterises a surface saturation effect. The uptake coefficientvalues show a slight negative temperature dependence for both carbonates.These values vary from 1.4×10^–2 to0.6×10^–2 in the temperature range of 265–279 Kfor dimethyl carbonate, from 2.4×10^–2 to0.9×10^–2 in the temperature range of 270–279 Kfor diethyl carbonate. From the kinetic data, the following Henry's lawconstants were derived between 279 and 265 K: dimethyl carbonate,H₁ = 20–106 M atm^–1; and diethyl carbonate,H₂ = 30–98 M atm^–1. The reported data showthat the OH reaction is the major atmospheric loss process of these twocarbonates with lifetimes of 33 and 5 days, respectively, while the wetdeposition is a negligible process.     

Two-Dimensional Scalar Spectra in the Deeper Layers of a Dense and Uniform Model Canopy

The turbulent flow inside dense canopies is characterized by wake production and short-circuiting of the energy cascade. How these processes affect passive scalar concentration variability in general and their spectral properties in particular remains a vexing problem. Progress on this problem is frustrated by the shortage of high resolution spatial concentration measurements, and by the lack of simplified analytical models that connect spectral modulations in the turbulent kinetic energy (TKE) cascade to scalar spectra. Here, we report the first planar two-dimensional scalar concentration spectra (ϕ _cc ) inside tall canopies derived from flow visualization experiments. These experiments were conducted within the deeper layers of a model canopy composed of densely arrayed cylinders welded to the bottom of a large recirculating water channel. We found that in the spectral region experiencing wake production, the ϕ _cc exhibits directional scaling power laws. In the longitudinal direction (x), or the direction experiencing the largest drag force, the ϕ _cc (k _x ) was steeper than and followed an approximate at wavenumbers larger than the injection scale of wake energy, where k _x is the longitudinal wavenumber. In the lateral direction (y), the spectra scaled as up to the injection scale, and then decayed at an approximate power law. This departure from the classical inertial subrange scaling (i.e., k ^−5/3) was reproduced using a newly proposed analytical solution to a simplified scalar spectral budget equation. Near the velocity viscous dissipation range, the scalar spectra appear to approach an approximate k ⁻³, a tantalizing result consistent with dimensional analysis used in the inertial-diffusive range. Implications to subgrid modelling for large-eddy simulations (LES) inside canopies are briefly discussed.     

Kinetics of the Gas-Phase Reactions of OH Radicals, NO3 Radicals and O3 with Three C7-Carbonyls Formed From The Atmospheric Reactions of Myrcene, Ocimene and Terpinolene

Rate constants for the gas-phase reactions of OH radicals, NO₃ radicals and O₃ with the C₇-carbonyl compounds 4-methylenehex-5-enal [CH₂=CHC(=CH₂)CH₂CH₂CHO], (3Z)- and (3E)-4-methylhexa-3,5-dienal [CH₂=CHC(CH₃)=CHCH₂CHO] and 4-methylcyclohex-3-en-1-one, which are products of the atmospheric degradations of myrcene, Z- and E-ocimene and terpinolene, respectively, have been measured at 296 ± 2 K and atmospheric pressure of air using relative rate methods. The rate constants obtained (in cm³ molecule^–1 s^–1 units) were: for 4-methylenehex-5-enal, (1.55 ± 0.15) × 10^–10, (4.75 ± 0.35) × 10^–13 and (1.46 ± 0.12) × 10^–17 for the OH radical, NO₃ radical and O₃ reactions, respectively; for (3Z)-4-methylhexa-3,5-dienal: (1.61 ± 0.35) × 10^–10, (2.17 ± 0.30) × 10^–12, and (4.13 ± 0.81) × 10^–17 for the OH radical, NO₃ radical and O₃ reactions, respectively; for (3E)-4-methylhexa-3,5-dienal: (2.52 ± 0.65) × 10^–10, (1.75 ± 0.27) × 10^–12, and (5.36 ± 0.28) × 10^–17 for the OH radical, NO₃ radical and O₃ reactions, respectively; and for 4-methylcyclohex-3-en-1-one: (1.10 ± 0.19) × 10^–10, (1.81 ± 0.35) × 10^–12, and (6.98 ± 0.40) × 10^–17 for the OH radical, NO₃ radical and O₃ reactions, respectively. These carbonyl compounds are all reactive in the troposphere, with daytime reaction with the OH radical and nighttime reaction with the NO₃ radical being predicted to dominate as loss processes and with estimated lifetimes of about an hour or less.     

Turbulence Structure of the Unstable Atmospheric Surface Layer and Transition to the Outer Layer

We present a new model of the structure of turbulence in the unstable atmospheric surface layer, and of the structural transition between this and the outer layer. The archetypal element of wall-bounded shear turbulence is the Theodorsen ejection amplifier (TEA) structure, in which an initial ejection of air from near the ground into an ideal laminar and logarithmic flow induces vortical motion about a hairpin-shaped core, which then creates a second ejection that is similar to, but larger than, the first. A series of TEA structures form a TEA cascade. In real turbulent flows TEA structures occur in distorted forms as TEA-like (TEAL) structures. Distortion terminates many TEAL cascades and only the best-formed TEAL structures initiate new cycles. In an extended log layer the resulting shear turbulence is a complex, self-organizing, dissipative system exhibiting self-similar behaviour under inner scaling. Spectral results show that this structure is insensitive to instability. This is contrary to the fundamental hypothesis of Monin--Obukhov similarity theory. All TEAL cascades terminate at the top of the surface layer where they encounter, and are severely distorted by, powerful eddies of similar size from the outer layer. These eddies are products of the breakdown of the large eddies produced by buoyancy in the outer layer. When the outer layer is much deeper than the surface layer the interacting eddies are from the inertial subrange of the outer Richardson cascade. The scale height of the surface layer, z _s, is then found by matching the powers delivered to the creation of emerging TEAL structures to the power passing down the Richardson cascade in the outer layer. It is z _s = u _* ³ /k_s, where u _* is friction velocity, k is the von Kármán constant and _s is the rate of dissipation of turbulence kinetic energy in the outer layer immediately above the surface layer. This height is comparable to the Obukhov length in the fully convective boundary layer. Aircraft and tower observations confirm a strong qualitative change in the structure of the turbulence at about that height. The tallest eddies within the surface layer have height z _s, so z _s is a new basis parameter for similarity models of the surface layer.     

New Approaches in Two-equation Turbulence Modelling for Atmospheric Applications

The turbulence closure in atmospheric boundary-layer modelling utilizing Reynolds Averaged Navier–Stokes (RANS) equations at mesoscale as well as at local scale is lacking today a common approach. The standard kɛ model, although it has been successful for local scale problems especially in neutral conditions, is deficient for mesoscale flows without modifications. The k–ɛ model is re-examined and a new general approach in developing two-equation turbulence models is proposed with the aim of improving their reliability and consequently their range of applicability. This exercise has led to the replacement of the ɛ-transport equation by the transport equation for the turbulence inverse length scale (wavenumber). The present version of the model is restricted to neutrally stratified flows but applicable to both local scale and mesoscale flows. The model capabilities are demonstrated by application to a series of one-dimensional planetary boundary-layer problems and a two-dimensional flow over a square obstacle. For those applications, the present model gave considerably better results than the standard k–ɛ model.