Measurements of spray at an air-water interface

The spray content in the surface boundary layer above an air—water interface was determined by a series of measurements at various feteches and wind speeds in a laboratory facility. The droplet flux density N(z) can be described in terms of the scaling flux density N_* and von Karman constant K throguh the equation, N(z)/N_* = −(1/K) ln(z/z_0d) where z is height above the mean water level and z_0d is the droplet boundary layer thickness. N_* is given by a unique relationship in terms of the roughness Reynolds number u_*σ/ν where σ is the root-mean-square surface displacement. Spray inception occurred for u_* 0.3. The dominant mode of spray generation in the present and most other laboratory tests, as well as in available field data, appears to be bubble bursting.     

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.     

True gravity in ocean dynamics Part 1 Ekman transport

The direction normal to the Earth spherical (or ellipsoidal) surface is not vertical (called deflected vertical) since the vertical direction is along the true gravity g (= ig_λ+ jg_φ+ kg_z). Here, (λ, φ, z) are (longitude, latitude, depth), and (i, j, k) are the corresponding unit vectors. The spherical (or ellipsoidal) surfaces are not horizontal surfaces (called deflected-horizontal surfaces). The most important body force g (true gravity) has been greatly simplified without justification in oceanography to the standard gravity (-g₀k) with g₀ = 9.81 m/s². Impact of such simplification on ocean dynamics is investigated in this paper using the Ekman layer model. In the classical Ekman layer dynamic equation, the standard gravity (-g₀k) is replaced by the true gravity g(λ, φ, z) with a constant eddy viscosity and a depth-dependent-only density ρ(z) represented by an e-folding near-inertial buoyancy frequency. New Ekman spiral and in turn new formulae for the Ekman transport are obtained for ocean with and without bottom. With the gravity data from the global static gravity model EIGEN-6C4 and the surface wind stress data from the Comprehensive Ocean-Atmosphere Data Set (COADS), large difference is found in the Ekman transport using the true gravity and standard gravity.     

Direct numerical simulation of a vigorously heated low Reynolds number convective boundary layer

Computations of the buoyantly unstable Ekman layer are performed at low Reynolds number. The results are obtained by directly solving the three-dimensional time-dependen Navier-Stokes equations with the Boussinesq buoyancy approximation, resolving all relevant scales of motion (no turbulence closure is needed). The flow is capped by a stable temperature inversion and heated from below at a rate that produces an inversion-height to Obukhov-length ratio −z_i/L_* = 32. Temperature and velocity variance profiles are found to agree well with those from an earlier vigorously heated under-resolved computation at higher Reynolds number, and with experimental data of Deardorff and Willis (Boundary-Layer Meteorol., 32: 205–236, 1985). Significant helicity is found in the layer, and helical convection patterns of the scale of the inversion height are observed.     

Regional roughness of the landes forest and surface shear stress under neutral conditions

Mean wind velocity profiles were measured by means of radio-windsondes over the Landes region in southwestern France, which consists primarily of pine forests with scattered villages and clearings with various crops. Analysis of neutral profiles indicated the existence of a logarithmic layer between approximately z – d ₀ = 67(±18)z ₀ and 128(+-32)z ₀ (z is the height above the ground, z ₀ the surface roughness and d ₀ the displacement height). The upper limit can also be given as z – d ₀ = 0.33 (±0.18)h, where h is the height of the bottom of the inversion. The profiles showed that the surface roughness of this terrain is around 1.2 m and the displacement height 6.0 m. Shear stresses derived from the profiles were in good agreement with those obtained just above the forest canopy at a nearby location with the eddy correlation method by a team from the Institute of Hydrology (Wallingford, England).     

A numerical study of the convective boundary layer

Computations of the buoyantly unstable Ekman layer are performed at low Reynolds number. The turbulent fields are obtained directly by solving the three-dimensional time-dependent Navier-Stokes equations (using the Boussinesq approximation to account for buoyancy effects), and no turbulence model is needed. Two levels of heating are considered, one quite vigorous, the other more moderate. Statistics for the vigorously heated case are found to agree reasonably well with laboratory, field, and large-eddy simulation results, when Deardorff's mixed-layer scaling is used. No indication of large-scale longitudinal roll cells is found in this convection-dominated flow, for which the inversion height to Obukhov length scale ratio –z _i /L _*=26. However, when heating is more moderate (so that –z _i /L _*=2), evidence of coherent rolls is present. About 10% of the total turbulent kinetic energy and turbulent heat flux, and 20% of the Reynolds shear stress, are estimated to be a direct consequence of the observed cells.     

Momentum Absorption in Rough-Wall Boundary Layers with Sparse Roughness Elements in Random and Clustered Distributions

A wind-tunnel experiment has been used to investigate momentum absorption by rough surfaces with sparse random and clustered distributions of roughness elements. An unusual (though longstanding) method was used to measure the boundary-layer depth δ and friction velocity u _* and thence to infer the functional relationship z ₀/h = f(λ) between the normalised roughness length z ₀/ h and the roughness density λ (where z ₀ is the roughness length and h the mean height of the roughness elements). The method for finding u _* is based on fitting the velocity defect in the outer layer to a functional form for the dimensionless velocity-defect profile in a canonical zero-pressure-gradient boundary layer. For the conditions investigated here, involving boundary layers over sparse roughness with strong local heterogeneity, this velocity-defect-law method is found to be more robust than several alternative methods for finding u _* (uw covariance, momentum integral and slope of the logarithmic velocity profile).The experimental results show that, (1) there is general agreement in the relationship z ₀/h = f(λ) between the present experiment with random arrays and other wind-tunnel experiments with regular arrays; (2) the main effect of clustering is to increase the scatter in the z ₀/h = f(λ) relationship, through increased local horizontal heterogeneity; (3) this scatter obscures any trend in the z ₀/h = f(λ) relationship in response to clustering; and (4) the agreement between the body of wind-tunnel data (taken as a whole) and field data is good, though with scatter for which it is likely that a major contribution stems from local horizontal heterogeneity in the field.     

Instabilities of the tidally induced bottom boundary layer in the rotating frame and their mixing effect

To investigate the stability of the bottom boundary layer induced by tidal flow (oscillating flow) in a rotating frame, numerical experiments have been carried out with a two-dimensional non-hydrostatic model. Under homogeneous conditions three types of instability are found depending on the temporal Rossby number Ro_t, the ratio of the inertial and tidal periods. When Ro_t < 0.9 (subinertial range), the Ekman type I instability occurs because the effect of rotation is dominant though the flow becomes more stable than the steady Ekman flow with increasing Ro_t. When Ro_t > 1.1 (superinertial range), the Stokes layer instability is excited as in the absence of rotation. When 0.9 < Ro_t < 1.1 (near-inertial range), the Ekman type I or type II instability appears as in the steady Ekman layer. Being much thickened (100 m), the boundary layer becomes unstable even if tidal flow is weak (5 cm/s). The large vertical scale enhances the contribution of the Coriolis effect to destabilization, so that the type II instability tends to appear when Ro_t > 1.0. However, when Ro_t < 1.0, the type I instability rather than the type II instability appears because the downward phase change of tidal flow acts to suppress the latter. To evaluate the mixing effect of these instabilities, some experiments have been executed under a weak stratification peculiar to polar oceans (the buoyancy frequency N²  10⁻⁶ s⁻²). Strong mixing occurs in the subinertial and near-inertial ranges such that tracer is well mixed in the boundary layer and an apparent diffusivity there is evaluated at 150–300 cm²/s. This suggests that effective mixing due to these instabilities may play an important role in determining the properties of dense shelf water in the polar regions.     

On the instability of a planetary boundary layer with Rossby-number similarity

The formation of longitudinal vortex rolls in the planetary boundary layer (PBL) is investigated by means of perturbation analysis. The method is the same as that used by previous authors who have investigated the instability of a laminar Ekman layer. To study the instability of the turbulent boundary layer of the atmosphere, vertical profiles are needed of the eddy viscosity and of the two components of the basic flow. These profiles have been obtained by a numerical PBL-model; they are universal for zz ₀. (However, the stability equations are not completely universal, i.e., independent of the external parameters). For each thermal stratification, expressed by the internal stratification parameter , one has a set of three consistent profiles.The numerical solution of the stability equations gives the critical values and the perturbation growth rates as functions of thermal stratification and of the surface Rossby number Ro₀. This is in contrast to the case of a laminar Ekman layer, where the instability depends on a Reynolds number only, which makes atmospheric applications difficult. The most unstable perturbations are found for Ro₀ = 1 × 10⁶ approximately, which is in the range of surface Rossby numbers observed in the atmosphere. However, considering vortex rolls oriented in the direction of the surface stress, the instability is found to be universal, i.e., independent of the external parameters combined in the surface Rossby number. With respect to thermal stratification, the results show that the instability of the perturbations increases with increasing static stability.     

Analytical solutions for the Ekman layer

The PBL equation that governs the transition from the constant-stress surface layer to the geostrophic wind in a neutrally stratified atmosphere for which the eddy viscosityK(z) is assumed to vary smoothly from the surface-layer value U _*z (0.4,U _*=friction velocity,z=elevation) to the geostrophic asymptoteK _GU _*d forzd is solved through an expansion in fd/U _*1 (f=Coriolis parameter). The resulting solution is separated into Ekman's constant-K solution an inner component that reduces to the classical logarithmic form forzd and isO() relative to the Ekman component forzd. The approximationKU _*d is supported by the solution of Nee and Kovasznay's phenomenological transport equation forK(z), which yieldsK–U _*d exp(–z/d), where is an empirical constant for which observation implies, 1. The parametersA andB in Kazanskii and Monin's similarity relation forG/U _* (G=geostrophic velocity) are determined as functions of . The predicted values ofG/U _* and the turning angle are in agreement with the observed values for the Leipzig wind profile. The predicted value ofB based on the assumption of asymptotically constantK is 4.5, while that based on the Nee-Kovasznay model is 5.1; these compare with the observed value of 4.7 for the Leipzig profile. A thermal wind correction, an asymptotic solution for arbitraryK(z) and 1, and an exact (unrestricted ) solution forK(z)=U _*d[1–exp(–z/d)] are developed in appendices.     

An approximate analytical solution to the diffusion equation for short-range dispersion from a continuous ground-level source

An easily-evaluated expression for the dimensionless concentration profile (z/z ₀,/z ₀, z ₀/L) = = cu _*/kQ (or z ₀cu_*/kQ) downwind of a continuous ground-level area (or line) source in the stable surface layer is obtained by integrating the diffusion equation using the Shwetz approximation method (c = concentration, Q = source strength, k = von Kárman's constant). The analytical solution compares closely with concentration profiles obtained using a trajectory-simulation model over a useful range of heights, the important discrepancies occurring at the upper edge of the plume. The analytical solution is used to generate predictions of ground-level concentration for the Project Prairie Grass experiments; good agreement with the observations is obtained at all downwind distances (50 to 800 m).     

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.     

Statistics of Scalar Fields in the Atmospheric Boundary Layer Based on Large-eddy Simulations. Part 1: Free Convection

Convection in a quasi-steady, cloud-free, shear-free atmospheric boundary layer is investigated based on a large-eddy simulation model. The performed tests indicate that the characteristic (peak) values of statistical moments at the top of the mixed layer are proportional to the interfacial scales (from gradients of scalars in the interfacial layer). Based on this finding a parameterization is proposed for profiles of scalar variances. The parameterization employs two, semi-empirical similarity functions F_m(z/z_i) andF_i(z/z_i), multiplied by a combination of the mixed-layer scales and the interfacial scales.     

The effect of ekman suction on a flow over a shallow topography in the beta plane

The effect of bottom Ekman layer suction on a homogeneous, constant depth, eastwards, low Rossby number flow over a shallow bottom topography in the beta plane is studied. The governing vorticity equation is obtained by expanding the velocities in the continuity and momentum equations in powers of the Rossby number, ?, and matching the vertical velocity with the vertical velocity at the outer edge of the bottom Ekman layer obtained from the Ekman layer solution. The suction effect is then linearized using an Oseen approxiamation and the resulting linear model is solved using Fourier transforms with the requirement that the solution behave like a vortex near the origin which is equivalent to the effect of an isolated bump, i.e., a Green's function solution is obtained. An analytical solution is thus, obtained in integral form and then numerically integrated. The effect of Ekman suction is found to be a damping of the downstream Rossby waves in a distance of order $\text{2√2U/f}{}_0\text{E}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, an increased upstream influence, and a counterclockwise rotation of the closed streamline region about the origin. It is pointed out that the vortex solutions can be superimposed in order to obtain the solution for flow over topographies of finite horizontal text. This technique was used to compute the flow over a right circular cylinder. The results agree favorably with the experimental results of McCartney (1975).     

An atmospheric dispersion model with continuous vertical variation of dispersion parameters

Summary A dispersion model is proposed to predict the continuous vertical variation of the dispersion parameters _y and _z in case of hot pollutant release to the atmosphere. In such a case, the plume rises far above the ground and is subject to varying levels of turbulence. The framework in this paper can be divided into three approaches: (1) determination of the eddy diffusivitiesK _y (z, _y ) andK _z (z, _z ) as functions of height above ground and plume dimensions, (2) determination of both the plume rise and its vertical velocity using a modified version of Brigg's formula, and (3) numerical solution of actual problems with buoyant plumes at each time step. The model results have been applied to a case of pollutant release from fire destruction of a chemical storehouse roof.With 15 Figures     

Henry's law coefficients for aqueous solutions of acetone,acetaldehyde and acetonitrile,and equilibrium constants for the addition compounds of acetone and acetaldehyde with bisulfite

Vapor phase concentrations of acetone, acetaldehyde and acetonitrile over their aqueous solutions were measured to determine Henry's law partition coefficients for these compounds in the temperature range 5–40 °C. The results are for acetone: ln(H ₁/atm)=–(5286±100)T+(18.4±0.3); acetaldehyde: ln(H ₁/atm)=–(5671±22)/T+(20.4±0.1); and acetonitrile: ln(H ₁/atm)=–(4106±101)/T+(13.8±0.3). Artificial seawater of 3.5% salinity in place of deiionized water raisesH ₁ by about 15%. A similar technique has been used to measure the equilibrium constants for the addition compounds of acetone and acetaldehyde with bisulfite in aqueous solution. The results are ln(K ₁/M ^–1)=(4972±318)/T–(11.2±1.1) and ln(K ₁/M ^–1)=(6240±427)/T–(8.1±1.3), respectively. The results are compared and partly combined with other data in the literature to provide an average representation.     

Formation of horizontal convective rolls in urban areas

The formation of horizontal convective rolls (HCRs) in urban areas is investigated in this paper using observations and fine-scale numerical simulations. Cloud streets organized parallel to the mean boundary-layer wind (a manifestation of HCRs) are seen in the Fengyun-2C satellite imagery around local noon in Beijing. Observed vertical velocity and horizontal wind fields from an urban wind profiler suggest that the time scale for alternating updraft and downdraft in the boundary layer is about 30 min, and the length of the updraft/downdraft is about 9 km. Numerical simulations show that most HCRs occur in the urban areas with − z_i / L < 25 (z_i: the boundary-layer depth, L: the Monin–Obukhov length). Sensitivity tests reveal that HCRs are common in urban boundary layers, while rural areas are more conducive to forming cellular convection; the aspect ratio of HCRs in urban areas is smaller than the typical value over natural landscapes.     

The impact of turbulence closure schemes on predictions of the Mixed Spectral Finite-Difference model for flow over topography

Impacts of different closure schemes in the Mixed Spectral Finite-Difference model (Beljaarset al., 1987) for neutrally stratified atmospheric surface-layer flow over complex terrain are studied. Six different closure schemes, (Z+z ₀), Mixing Length,E–(Z+z ₀),E–,E–– andq ² l are compared. Model results for flow over an infinite series of sinusoidal ridges are examined in the context of the inner and outer layers defined by Jackson and Hunt (1975). Results are compared with rapid distortion estimates of the changes in normal stresses. The effects of streamline curvature are also examined in a qualitative sense.     

Performance of various similarity functions for nondimensional wind and temperature profiles in the surface layer in stable conditions

The linear functions for non-dimensional wind and temperature profiles are commonly used to describe the surface layer fluxes in atmospheric models. However, their applicability is limited to smaller values of the stability parameter z/L (where z is the height above ground and L is the Obukhov length) i.e. z/L < 1.0. These linear functions have been modified (Webb 1970, Quart. J. Roy. Meteor. Soc. 96, 67–90; Clarke 1970, Quart. J. Roy. Meteor. Soc. 96, 91–114; Hicks 1976, Quart. J. Roy. Meteor. Soc. 102, 535–551; Beljaars and Holtslag 1991, J. Appl. Meteorol. 30, 327–341; Cheng and Brutsaert 2005, Boundary-Layer Meteorol. 114, 519–538) over the years for calculating fluxes when z/L > 1.0 under strongly stable conditions. In view of this, the objective of the present study is to analyze the performance of these similarity functions to compute surface fluxes in stable conditions.The meteorological observations from the Cooperative Atmosphere-Surface Exchange Study (CASES-99) experiment are utilized for computing the surface fluxes in stable conditions. The computed fluxes are found to be reasonably close to those observed. The ratio of observed to computed fluxes reveals that the computed fluxes are close to the observations for all the similarity functions for z/L < 1.0 whereas the computed values show relatively a large scatter from observations for z/L > 1.0. The computed values of u and heat flux do not show significant differences from those observed at 99% confidence limit. The performance of all the similarity functions considered here is found to be comparable to each other in strongly stable conditions.     

Formulation of the thermal internal boundary layer in a mesoscale model

Mesoscale models using a non-local K-scheme for parameterization of boundary-layer processes require an estimate of the planetary boundary layer (PBL) height z _i at all times. In this paper, two-dimensional sea-breeze experiments are carried out to evaluate three different formulations for the advective contribution in the z _i prognostic equation of Deardorff (1974).Poor representation of the thermal internal boundary layer in the sea breeze is obtained when z _i is advected by the wind at level z _i . However, significantly better results are produced if the mean PBL wind is used for the advecting velocity, or if z _i is determined simply by checking for the first sufficiently stable layer above the ground.A Lagrangian particle model is used to demonstrate the effect of each formulation on plume dispersion by the sea breeze.