An Evaluation of the Flux–Gradient Relationship in the Stable Boundary Layer

Data collected during the SHEBA and CASES-99 field programs are employed to examine the flux–gradient relationship for wind speed and temperature in the stably stratified boundary layer. The gradient-based and flux-based similarity functions are assessed in terms of the Richardson number Ri and the stability parameter z/Λ_*, z being height and Λ_* the local Obukhov length. The resulting functions are expressed in an analytical form, which is essentially unaffected by self-correlation, when thermal stratification is strong. Turbulence within the stably stratified boundary layer is classified into four regimes: “nearly-neutral” (0 < z/Λ_* < 0.02), “weakly-stable” (0.02 < z/Λ_* < 0.6), “very-stable” (0.6 < z/Λ_* < 50), and “extremely-stable” (z/Λ_* > 50). The flux-based similarity functions for gradients are constant in “nearly-neutral” conditions. In the “very-stable” regime, the dimensionless gradients are exponential, and proportional to (z/Λ_*)^3/5. The existence of scaling laws in “extremely-stable” conditions is doubtful. The Prandtl number Pr decreases from 0.9 in nearly-neutral conditions and to about 0.7 in the very-stable regime. The necessary condition for the presence of steady-state turbulence is Ri < 0.7.     

A note on free and forced Rossby wave solutions: The case of a straight coast and a channel

The free Rossby wave (RW) solutions in an ocean with a straight coast when the offshore wavenumber of incident (l₁) and reflected (l₂) wave are equal or complex are discussed. If l₁ = l₂ the energy streams along the coast and a uniformly valid solution cannot be found; if l_1,2 are complex it yields the sum of an exponentially decaying and growing (away from the coast) Rossby wave. The channel does not admit these solutions as free modes.If the wavenumber vectors of the RWs are perpendicular to the coast, the boundary condition of no normal flow is trivially satisfied and the value of the streamfunction does not need to vanish at the coast. A solution that satisfies Kelvin's theorem of time-independent circulation at the coast is proposed.The forced RW solutions when the ocean's forcing is a single Fourier component are studied. If the forcing is resonant, i.e. a free Rossby wave (RW), the linear response will depend critically on whether the wave carries energy perpendicular to the channel or not. In the first case, the amplitude of the response is linear in the direction normal to the channel, y, and in the second it has a parabolic profile in y. Examples of these solutions are shown for channels with parameters resembling the Mozambique Channel, the Tasman Sea, the Denmark Strait and the English Channel. The solutions for the single coast are unbounded, except when the forcing is a RW trapped against the coast. If the forcing is non-resonant, exponentially decaying or trapped RWs could be excited in the coast and both the exponentially “decaying” and exponentially “growing” RW could be excited in the channel.     

Characterization of precipitation δ 18O variation in Nagqu, central Tibetan Plateau and its climatic controls

The stable isotopic composition of precipitation in different regions reflects climatic factors such as temperature, precipitation, moisture sources, and transport process. However, the isotopic variation in the region is usually much complicated due to the combined influences of these factors. A good understanding of climatic controls on the isotopic composition of precipitation can contribute to the study on isotopic tracer for climate and hydrology. To investigate the isotopic variation of precipitation and its climatic controls in the middle of the Tibetan Plateau, a monitoring station for stable isotope in precipitation has been established in Nagqu region, central Tibetan Plateau. We obtained 79 daily samples at Nagqu Meteorological Station in 2000. The observed δ ¹⁸O in precipitation showed a distinctly seasonal pattern with higher values in spring and winter and lower values in summer, despite of individually low values in winter due to extremely low temperature. To further understand this pattern, we evaluated the influence of temperature, precipitation, moisture sources, and moisture transport process on precipitation δ ¹⁸O. A multiple linear regression model represents quantitatively the dependence of precipitation δ ¹⁸O on precipitation and temperature: δ ¹⁸O_ppt?=??0.30P???0.11T???14.8 (R ²?=?0.13, n?=?79, P?=?0.005), which indicates δ ¹⁸O values in precipitation are more dependent on precipitation amount than on temperature. In contrast, when the temperature is low enough (<2°C), δ ¹⁸O values in precipitation are mainly dependent on temperature: δ ¹⁸O_ppt?=?0.53T???10.2 (R ²?=?0.44, n?=?19, P?=?0.002). The variation of δ ¹⁸O in precipitation is also closely related to moisture origins and transport trajectories. A model is set up to trace the trajectories for air masses arriving in the observed region, and the results demonstrated that humid marine air masses from the Indian Ocean generally have significantly lower δ ¹⁸O values than dry continental air masses from the north or local re-evaporation. During monsoon precipitation, the distance and depth of moisture transport as well as convective precipitation all lead to the large variability of δ ¹⁸O in precipitation.     

Particle Size Distribution and Gas-Particle Partition of Polycyclic Aromatic Hydrocarbons in Helsinki Urban Area

Ambient concentrations of polycyclic aromatic hydrocarbons (PAHs) were measured in Helsinki (Finland). Particle mass size distributions were obtained with a cascade impactor (12 stages) with glass fibre filters as substrates. Simultaneously with the impactor measurements, particulate and gaseous PAHs were collected on a quartz filter and XAD-2 adsorbent, respectively, for evaluation of gas-partition coefficients. Samples were analysed for PAHs by on-line coupled supercritical fluid extraction — liquid chromatography — gas chromatography — mass spectrometry. The impactor results showed that most of the PAHs in Helsinki urban area were concentrated in fine particles (<2.5 μm diameter) with unimode peak at about 1 μm. The results were comparable with the number distribution measured with a differential mobility particle sizer. Total amounts of PAHs (gas + particle) varied from 15 (acenaphthylene) to 1990 (fluorene) pg/m³. The PAHs lighter than 202 amu (pyrene and fluoranthene) were exclusively in gas phase, whereas those heavier than 202 amu were mostly associated with particles. A plot of the partition coefficients (logKp) versus the temperature dependent sub-cooled vapour pressures (logp _L ⁰ ) showed a gradient of −0.66, which deviated from equilibrium state (gradient = −1).     

Dynamics of lateral boundary meso-scale jet in the ocean and atmosphere

By using an ageostrophic shallow water model, it is pointed out that a kind of lateral boundary meso-scales jet can be established near the plateau or coast. The characteristic width of this kind of jet is proportional to the scale ofL _c=L₀(C₀/V_g), whereL ₀=C ₀/f is the radius of Rossby deformation,C ₀=(g ^* H)^1/2 the speed of gravity wave and g^* the reduced gravity. In general,L _c is of the order of one hundred kilometes and tens of kilometers in the atmosphere and in the ocean respectively. The large-scale geostrophic current is an important background condition for forming this kind of jet. From this view point it seems that this kind of atmospheric meso-scale jet only occurs in late spring and summer in the eastern part of Asia, because there is a large-scale south monsoon over there. For the ocean, this kind of meso-scale jet seems to be a semi-persistant system and not to show a significant seasonal variation, and it can be established on both sides of the ocean.     

Laboratory studies of the effects of interrupted, sloping topography on intermediate depth boundary currents in linearly stratified fluids

Laboratory experiments are described which provide insight into the interaction of intermediate depth boundary currents (IDBCs) with interrupted sloping topography. Specifically, they contribute to the debate over meddy formation on the Iberian continental slope. The experiments were performed in a rectilinear rotating tank filled initially with a linearly-stratified fluid. A false bottom sloped away from the side-wall along which the current flowed, and was interrupted by a gap of variable length. The effects of varying gap length and rotation rate on the boundary current were observed.In the first of two sets of experiments, the current flowed above the slope, along the vertical sidewall. In the second, the current flowed along the sloping bottom. In the former, current nose speed was consistent with geostrophic predictions, but decreased in the presence of a gap in the topography. Kelvin wave radiation is postulated as a reason for this. The IDBCs exhibited vortical lateral intrusions at values of the Burger number Bu=(N₀/Ω)² at which counterpart flat-bottom studies had been stable, implying that the sloping topography had a de-stabilising effect. Energy measurements and qualitative observations suggest the intrusions were due to mixed barotropic/baroclinic instabilities, the latter dominating at higher rotation rates.In the second configuration, four distinct flows were observed, distinguished by the deformation radius:gap width ratio R_D/G^*. For a range of values of R_D/G^*, attached eddies formed at the upstream end of the gap. They remained at this position, unlike those in similar studies of surface boundary currents (Klinger, 1993). Their persistence and ability to move downstream – salient factors for meddy – formation were greater for a finite gap size than a permanent change from sloping to flat bottom.     

Dynamics of the Leeuwin Current: Part 2. Impacts of mixing,friction, and advection on a buoyancy-driven eastern boundary current over a shelf

The boundary currents over the Western Australian continental shelf and slope consist of the poleward flowing Leeuwin Current (LC) and the equatorward flowing Leeuwin Undercurrent (LUC). Key properties of the LC are its poleward strengthening, deepening to the south, and shelfbreak intensification. The alongshore flow reverses direction below about 300 m, forming the LUC at greater depths. To investigate the processes that cause these features, we obtain solutions to an idealized, regional ocean model of the South Indian Ocean. Solutions are forced by relaxing surface density to a prescribed, meridionally varying density profile ρ^*(y) with a timescale of δt. In addition, vertical diffusion is intensified near the ocean surface. This diffusion establishes the minimum thickness over which density is well-mixed. We define this thickness as the “upper layer”. Solutions are obtained with and without a continental shelf and slope off Western Australia and for a range of values of δt and mixing parameters. Within this upper layer, there is a meridional density gradient that balances a near-surface, eastward geostrophic flow. The eastward current downwells near the eastern boundary, leading to westward flow at depth. The upper layer's meridional structure and zonal currents crucially depend on coastal processes, including the presence of topography near the eastern boundary. Kelvin waves inhibit the upper layer from deepening at the coast. Rossby waves propagate the coastal density structure offshore, hence modifying the interior currents. A comparison of the solutions with or without a continental shelf and slope demonstrate that topographic trapping of Rossby waves is a necessary process for maintaining realistic eastern boundary current speeds. Significant poleward speeds occur only onshore of where the upper layer intersects the slope, that is, at a grounding line. Its poleward transport increases when surface-enhanced vertical mixing is applied over a greater depth. When the timescale δt is sufficiently short, the poleward current is nearly barotropic. The current's spatial structure over the shelf is controlled by horizontal mixing, having the structure of a Munk layer. Increasing vertical diffusion deepens the upper layer thickness and strengthens the alongshore current speed. Bottom drag leads to an offshore flow along the bottom, reducing the net onshore transport and weakening the current's poleward acceleration. When δt is long, poleward advection of buoyancy forms a density front near the shelf break, intensifying poleward speeds near the surface. With bottom drag, a bottom Ekman flow advects density offshore, shifting the jet core offshore of the shelf break. The resulting cross-shelf density gradient reverses the meridional current's direction at depth, leading to an equatorward undercurrent.     

Surface influence upon vertical profiles in the nocturnal boundary layer

Near-surface wind profiles in the nocturnal boundary layer, depth h, above relatively flat, tree-covered terrain are described in the context of the analysis of Garratt (1980) for the unstable atmospheric boundary layer. The observations at two sites imply a surface-based transition layer, of depth z _*, within which the observed non-dimensional profiles Φ _M ⁰ are a modified form of the inertial sub-layer relation \(\Phi _M \left( {{z \mathord{\left/ {\vphantom {z L}} \right. \kern-0em} L}} \right) = \left( {{{1 + 5_Z } \mathord{\left/ {\vphantom {{1 + 5_Z } L}} \right. \kern-0em} L}} \right)\) according to $$\Phi _M^{\text{0}} \simeq \left( {{{1 + 5z} \mathord{\left/ {\vphantom {{1 + 5z} L}} \right. \kern-\nulldelimiterspace} L}} \right)\exp \left[ { - 0.7\left( {{{1 - z} \mathord{\left/ {\vphantom {{1 - z} z}} \right. \kern-\nulldelimiterspace} z}_ * } \right)} \right]$$ , where z is height above the zero-plane displacement and L is the Monin-Obukhov length. At both sites the depth z _* is significantly smaller than the appropriate neutral value (z _*N ) found from the previous analysis, as might be expected in the presence of a buoyant sink for turbulent kinetic energy.     

A Study in Search of Interconnection between Surface Parameters and Surrounding Synoptic And Subsynoptic Features

The paper reveals that the variations in parameters like u*, the scaling velocity and θ*. The scaling tempera-ture during the various phases of monsoon might be linked with subsynoptic features. The rise in u* is mainly connected with the presence of lower tropospheric cyclonic vorticity over a subsynoptic scale of the site. However the variations in θ* is mainly linked with the various phases of monsoon and θ* shows a sharp rise in presence of low level convective cloud.Besides the correlation studies of u and u*, θv and θv* , θv-θv0 and θv* are undertaken. The correlation be?tween θv and θv* is poor. In other two cases correlations are good. Besides u/u* , has shown good coefficient of variation values within the ζ range.     

Numerical study on the bulk heat transfer coefficient for a variety of vegetation types and densities

The relationship between the geometrical structure of a canopy layer and the bulk transfer coefficient was investigated using a numerical canopy model. The following results were obtained:

1. The bulk transfer coefficients for momentum and heat, C _M and C _H , change with non-dimensional canopy density C _* each has a maximum.
2. The value of C _M is always larger than the value of C _H for a canopy with c _m > c _h , c _m and c _h being the drag coefficient and the heat transfer coefficient of an individual canopy element, respectively.
3. The value of C _* at which C _H has its maximum value is larger than the value of C _* at which C _M has its maximum. Therefore, the reciprocal of the sublayer Stanton number b _h ^?1 ranges between 50 and 65 for C _* around 0.1 while it ranges between 0 and 30 for C _* < 10^?2 and C _* > 2 (when c _m = 0.5).
4. The value of B _H ^?1 in the present study is consistent with most available observations, except for canopies of medium density (when C _* is around 0.1) for which no observational value has been obtained.

     

Variability of energy fluxes in relation to the net-radiation of urban and suburban areas: a case study

This paper addresses the relation between the net-radiation (Q ^*) and the ground heat flux (Q _G), the energy stored in the soil ( $\Updelta Q_{\rm S}$ ), and the residual of the energy partition (R = Q ^* ? Q _H  ? Q _E ) of urban and suburban areas of Oklahoma City, USA. These three forms of energy were observed or estimated from observations taken during Joint Urban 2003 Campaign. The database includes net-radiation, soil temperature, ground heat flux, and turbulent fluxes. In most cases the estimates of the energy stored in the soil were obtained by assuming roughly a certain type of soil and an effective soil depth. From the residuals it seems to be possible to distinguish the urban boundary layer from the suburban boundary layer when plotted as a function of net-radiation. Hysteresis coefficients were computed for fits of net-radiation against R, $\Updelta Q_{\rm S}$ and Q _G. In particular, the hysteresis patterns show that Q ^* vs. R represents clearer urban areas or suburban areas under the influence of an urban “plume”. On the other hand, hysteresis curves obtained from $\Updelta Q_{\rm S}$ or Q _G account for better the ground composition. A possible consequence is that the land use of urban areas could be roughly inferred from curve shapes such as Q ^* vs. R, or Q ^* versus another input variable representing the storage term. The objective is to show the variability of the subsurface-related energy fluxes across an urban area using these three different quantities and also to show that $\Updelta Q_{\rm S}, \,Q_{\rm G}$ , or R (and their corresponding hysteresis curves) are likely to be quantitatively different, which have not been clearly stated in the literature.     

Spatiotemporal distributions of δD in atmospheric water vapor based on TES Data during 2004–2009

The spatial and temporal distributions of the stable isotopes such as HD¹⁶O (or ¹H²H¹⁶O, or HDO) and H₂ ¹⁸O in atmospheric water vapor are related to evaporation in source places, vapor condensation during transport, and vapor convergence and divergence, and thus provide useful information for investigation and understanding of the global water cycle. This paper analyzes spatiotemporal variations of the content of isotope HDO (i.e., δ _D), in atmospheric water vapor, namely, δ _{D v}, and the relationship of δ _{D v} with atmospheric humidity and temperature at different levels in the troposphere, using the HDO and H₂O data retrieved from the Tropospheric Emission Spectrometer (TES) at seven pressure levels from 825 to 100 hPa. The results indicate that δ _{D v} has a clear zonal distribution in the troposphere and a good correspondence with atmospheric precipitable water. The results also show that δ _{D v} decreases logarithmically with atmospheric pressure and presents a decreasing trend from the equator to high latitudes and from lands to oceans. Seasonal changes of δ _{D v} exhibit regional differences. The spatial distribution and seasonal variation of δ _{D v} in the low troposphere are consistent with those in the middle troposphere, but opposite situations occur from the upper troposphere to the lower stratosphere. The correlation between δ _{D v} and temperature has a similar distribution pattern to the correlation between δ _{D v} and precipitable water in the troposphere. The stable isotope HDO in water vapor (δ _{D v}), compared with that in precipitation (δ _{D p}), is of some differences in spatial distribution and seasonal variation, and in its relationship with temperature and humidity, indicating that the impacts of stable isotopic fractionation and atmospheric circulation on the two types of stable isotopes are different.     

Buoyancy in tropical cyclones and other rapidly rotating atmospheric vortices

Motivated primarily by its application to understanding tropical-cyclone intensification and maintenance, we re-examine the concept of buoyancy in rapidly rotating vortices, distinguishing between the buoyancy of the symmetric balanced vortex or system buoyancy, and the local buoyancy associated with cloud dynamics. The conventional definition of buoyancy is contrasted with a generalized form applicable to a vortex, which has a radial as well as a vertical component. If, for the special case of axisymmetric motions, the balanced density and pressure distribution of a rapidly rotating vortex are used as the reference state, the buoyancy field then characterizes the unbalanced density perturbations, i.e. the local buoyancy. We show how to determine such a reference state without approximation.The generation of the toroidal circulation of a vortex, which is necessary for vortex amplification, is characterized in the vorticity equation by the baroclinicity vector. This vector depends, inter-alia, on the horizontal (or radial) gradient of buoyancy evaluated along isobaric surfaces. We show that for a tropical-cyclone-scale vortex, the buoyancy so calculated is significantly different from that calculated at constant height or on surfaces of constant σ (σ = (p − p^*)/(p_s − p^*), where p is the actual pressure, p^* some reference pressure and p_s is the surface pressure). Since many tropical-cyclone models are formulated using σ-coordinates, we examine the calculation of buoyancy on σ-surfaces and derive an expression for the baroclinicity vector in σ-coordinates. The baroclinic forcing term in the azimuthal vorticity equation for an axisymmetric vortex is shown to be approximately equal to the azimuthal component of the curl of the generalized buoyancy. A scale analysis indicates that the vertical gradient of the radial component of generalized buoyancy makes a comparatively small contribution to the generation of toroidal vorticity in a tropical cyclone, but may be important in tornadoes and possibly also in dust devils.We derive also a form of the Sawyer–Eliassen equation from which the toroidal (or secondary) circulation of a balanced vortex may be determined. The equation is shown to be the time derivative of the toroidal vorticity equation in which the time rate-of-change of the material derivative of potential toroidal vorticity is set to zero. In analogy with the general case, the diabatic forcing term in the Sawyer–Eliassen equation is shown to be approximately equal to the time rate-of-change of the azimuthal component of the curl of generalized buoyancy.Finally, we discuss the generation of buoyancy in tropical cyclones and contrast the definitions of buoyancy that have been used in recent studies of tropical cyclones. We emphasize the non-uniqueness of the buoyancy force, which depends on the choice of a reference density and pressure, and note that different, but equivalent interpretations of the flow dynamics may be expected to arise if different reference quantities are chosen.     

Bulk characteristics of heat transfer in the unstable,baroclinic atmospheric boundary layer

Field data for the unstable, baroclinic, atmospheric boundary layer over land and over the sea are considered in the context of a general similarity theory of vertical heat transfer. The dependence of δθ/θ_* upon logarithmic functions of h _c z _T and stability (through the similarity function C) is clearly demonstrated in the data. The combined data support the conventional formulation for the heat transfer coefficient δθ/θ_* when,

1. the surface scaling length is z _T (« z ₀), the height at which the surface temperature over land is obtained by extrapolation of the temperature profile
2. the height scale is taken as the depth of convective mixing h _c
3. the temperature profile equivalent of the von Karman constant is taken as 0.41
4. areal average, rather than single point, values of δθ are employed in strongly baroclinic conditions. No significant effect of baroclinity or the height scale ratio as proposed in the general theory is found. Variations in C about a linear regression relation against stability are most probably due to uncertainties in the areal surface temperature and to experimental errors in general temperature measurements.

     

Equations for the Drag Force and Aerodynamic Roughness Length of Urban Areas with Random Building Heights

We use a conceptual model to investigate how randomly varying building heights within a city affect the atmospheric drag forces and the aerodynamic roughness length of the city. The model is based on the assumptions regarding wake spreading and mutual sheltering effects proposed by Raupach (Boundary-Layer Meteorol 60:375?C395, 1992). It is applied both to canopies having uniform building heights and to those having the same building density and mean height, but with variability about the mean. For each simulated urban area, a correction is determined, due to height variability, to the shear stress predicted for the uniform building height case. It is found that u _*/u _*R , where u _* is the friction velocity and u _*R is the friction velocity from the uniform building height case, is expressed well as an algebraic function of ?? and ?? _h /h _m , where ?? is the frontal area index, ?? _h is the standard deviation of the building height, and h _m is the mean building height. The simulations also resulted in a simple algebraic relation for z ₀/z _0R as a function of ?? and ?? _h /h _m , where z ₀ is the aerodynamic roughness length and z _0R is z ₀ found from the original Raupach formulation for a uniform canopy. Model results are in keeping with those of several previous studies.     

On the symmetrization rate of an intense geophysical vortex

Numerical models demonstrate that a broad class of geophysical vortices freely evolve toward vertically aligned, axisymmetric states. In principle, this intrinsic drive toward symmetry opposes destructive shearing by the environmental flow.This article examines the case in which a discrete vortex-Rossby-wave dominates a perturbation from symmetry, and symmetrization occurs by decay of the wave. The wave is damped by a resonance with the fluid rotation frequency at a critical radius, r_*. The damping rate is proportional to the radial derivative of potential vorticity at r_*. Until now, the theory of resonantly damped vortex-Rossby-waves (technically quasi-modes) was formally restricted to slowly rotating vortices, which obey quasigeostrophic (QG) dynamics. This article extends the theory to rapidly rotating vortices.The analysis makes use of the asymmetric balance (AB) approximation. Even at a modest Rossby number (unity), AB theory can predict damping rates that exceed extrapolated QG results by orders of magnitude. This finding is verified upon comparison of AB theory to numerical experiments, based on the primitive equations. The experiments focus on the decay of low azimuthal wave-number asymmetries.A discrete vortex-Rossby-wave can also resonate with an outward propagating inertia-buoyancy wave (Lighthill radiation), inducing both to grow. At large Rossby numbers, this growth mechanism can be dynamically relevant. All balance models, including AB theory, neglect inertia-buoyancy waves, and therefore ignore the possibility of a Rossby-inertia-buoyancy (RIB) instability. This article shows that a large potential vorticity gradient (of the proper sign) at the critical radius r_* can suppress the RIB instability, and thereby preserve balanced flow, even at large Rossby numbers.     

Estimation of atmospheric surface layer parameters and numerical simulation using MM5 at Mangalore, West Coast of India

Atmospheric surface layer meteorological observations obtained from 20-m-high meteorological tower at Mangalore, situated along the west coast of India are used to estimate the surface layer scaling parameters of roughness length (z _o) and drag coefficient (C _D), surface layer fluxes of sensible heat and momentum. These parameters are computed using the simple flux–profile relationships under the framework of Monin–Obukhov (M–O) similarity theory. The estimated values of z _o are higher (1.35–1.54 m) than the values reported in the literature (>0.4–0.9 m) probably due to the undulating topography surrounding the location. The magnitude of C _D is high for low wind speed (<1.5 m s^?1) and found to be in the range 0.005–0.03. The variations of sensible heat fluxes (SHF) and momentum fluxes are also discussed. Relatively high fluxes of heat and momentum are observed during typical days on 26–27 February 2004 and 10–11 April 2004 due to the daytime unstable atmospheric conditions. Stable or near neutral conditions prevail after 1700 h IST with negative SHF. A mesoscale model PSU/NCAR MM5 is run using a high-resolution (1 km) grid over the study region to examine the influence of complex topography on the surface layer parameters and the simulated fluxes are compared with estimated values. Spatial variations of the frictional velocity (u _*), C _D, surface fluxes, planetary boundary layer (PBL) height and surface winds are noticed according to the topographic variations in the simulation.     

Effect of the Entrainment Flux Ratio on the Relationship between Entrainment Rate and Convective Richardson Number

The parameterization of the dimensionless entrainment rate (w _e /w _*) versus the convective Richardson number (Ri _δθ ) is discussed in the framework of a first-order jump model (FOM). A theoretical estimation for the proportionality coefficient in this parameterization, namely, the total entrainment flux ratio, is derived. This states that the total entrainment flux ratio in FOM can be estimated as the ratio of the entrainment zone thickness to the mixed-layer depth, a relationship that is supported by earlier tank experiments, and suggesting that the total entrainment flux ratio should be treated as a variable. Analyses show that the variability of the total entrainment flux ratio is actually the effect of stratification in the free atmosphere on the entrainment process, which should be taken into account in the parameterization. Further examination of data from tank experiments and large-eddy simulations demonstrate that the different power laws for w _e /w _* versus Ri _δθ can be interpreted as the variability of the total entrainment flux ratio. These results indicate that the dimensionless entrainment rate depends not only on the convective Richardson number but also upon the total entrainment flux ratio.     

Effects Of Changing Surface Heat Flux On Atmospheric Boundary-Layer Flow Over Flat Terrain

We examine the unsteady response of a neutral atmospheric boundary layer (ABL) of depth h and friction velocity u _* when a uniform surface heat flux is applied abruptly or decreased rapidly over a time scale t<inf>θ</inf> less than about h /(10u _*). Standard Monin–Obukhov (MO) relationships are used for the perturbed eddy viscosity profile in terms of the changes to the heat flux and mean shear. Analytical solutions for changes in temperature, mean wind and shear stress profile are obtained for the surface layer, when there are small changes in h /|L_MO| over the time scale t_MO~|L _MO|/(10u_*) (where L _MO and t _MO are the length and time scales, respectively). They show that a maximum in the wind speed profile occurs at the top of the thermal boundary layer for weak surface cooling, i.e. a wind jet, whereas there is a flattening of the profile and no marked maximum for weak surface heating. The modelled profiles are approximately the same as those obtained from the U.K. Met Office Unified Model when operating as a mesoscale model at 12-km horizontal resolution. The theoretical model is modified when strong surface heating is suddenly applied, resulting in a large change in h /|L _MO| (>>1), over the time scale t _MO. The eddy structure is predicted to change significantly and the addition of convective turbulence increases the shear turbulence at the ground. A low-level wind jet can form, with convective turbulence adding to the mean momentum of the flow. This was verified by our laboratory experiment and direct numerical simulations. Additionally, it is shown that the effects of Coriolis acceleration diminish (rather than as suggested in the literature, amplify) the formation of the wind jets in the situations considered here. Hence, only when the surface heat flux changes over time scales greater than 1/f (where f is the Coriolis parameter) does the ABL adjust monotonically between its equilibrium states. These results are also applicable to the ABL passing over spatially varying surface heat fluxes.     

Heat and Mass Transfer to and from Surfaces with Dense Vegetation or Similar Permeable Roughness

A differential equation is obtained to describe the concentration of passive admixtures (water vapor, sensible heat, pollutants, CO₂, etc.) of turbulent flow inside a dense and uniform vegetational canopy. The profiles of eddy diffusivity, wind speed and shear stress are assumed to be exponential decay functions of depth below the top of the canopy. This equation is solved for the case of a vegetation with constant concentration of the admixture at the foliage surfaces. The solution is used to formulate bulk mass or heat transfer coefficients, which can be applied to practical problems involving surfaces covered with a vegetation or with similar porous or fibrous roughness elements. The results are shown to be consistent with experimental data presented by Chamberlain (1966), Garratt and Hicks (1973) and Garratt (1978). Calculations with the model illustrate that, as compared to its behavior over surfaces with bluff roughness elements, ln(z ₀/ z _oc ) (where z ₀ is the momentum roughness and Z _oc the scalar roughness) for permeable roughness elements is relatively insensitive to u _* and practically independent of z ₀.