Stability Correction Functions Research Articles

Modeling snowpack dynamics and surface energy budget in boreal and subarctic peatlands and forests

Abstract. The snowpack has a major influence on the land surface energy budget. Accurate simulation of the snowpack energy and radiation budget is challenging due to, e.g., effects of vegetation and topography, as well as limitations in the theoretical understanding of turbulent transfer in the stable boundary layer. Studies that evaluate snow, hydrology and land surface models against detailed observations of all surface energy balance components at high latitudes are scarce. In this study, we compared different configurations of the SURFEX land surface model against surface energy flux, snow depth and soil temperature observations from four eddy-covariance stations in Finland. The sites cover two different climate and snow conditions, representing the southern and northern subarctic zones, as well as the contrasting forest and peatland ecosystems typical for the boreal landscape. We tested different turbulent flux parameterizations implemented in the Crocus snowpack model. In addition, we examined common alternative approaches to conceptualize soil and vegetation, and we assessed their performance in simulating surface energy fluxes, snow conditions and soil thermal regime. Our results show that a stability correction function that increases the turbulent exchange under stable atmospheric conditions is imperative to simulate sensible heat fluxes over the peatland snowpacks and that realistic peat soil texture (soil organic content) parameterization greatly improves the soil temperature simulations. For accurate simulations of surface energy fluxes, snow and soil conditions in forests, an explicit vegetation representation is necessary. Moreover, we demonstrate the high sensitivity of surface fluxes to a poorly documented parameter involved in snow cover fraction computation. Although we focused on models within the SURFEX platform, the results have broader implications for choosing suitable turbulent flux parameterization and model structures depending on the potential use cases for high-latitude land surface modeling.

Probing eddy size and its effective mixing length in stably stratified roughness sublayer flows

Stably stratified roughness sublayer flows are ubiquitous yet remain difficult to represent in models and to interpret using field experiments. Here, continuous high‐frequency potential temperature profiles from the forest floor up to 6.5 times the canopy height observed with distributed temperature sensing (DTS) are used to link eddy topology to roughness sublayer stability correction functions and coupling between air layers within and above the canopy. The experiments are conducted at two forest stands classified as hydrodynamically sparse and dense. Near‐continuous profiles of eddy sizes (length scales) and effective mixing lengths for heat are derived from the observed profiles using a novel conditional sampling approach. The approach utilizes potential temperature isoline fluctuations from a statically stable background state. The transport of potential temperature by an observed eddy is assumed to be conserved (adiabatic movement) and we assume that irreversible heat exchange between the eddy and the surrounding background occurs along the (vertical) periphery of the eddy. This assumption is analogous to Prandtl's mixing‐length concept, where momentum is transported rapidly vertically and then equilibrated with the local mean velocity gradient. A distinct dependence of the derived length scales on background stratification, height above ground, and canopy characteristics emerges from the observed profiles. Implications of these findings for (1) the failure of Monin–Obukhov similarity in the roughness sublayer and (2) above‐canopy flow coupling to the forest floor are examined. The findings have practical applications in terms of analysing similar DTS data sets with the proposed approach, modelling roughness sublayer flows, and interpreting nocturnal eddy covariance measurements above tall forested canopies.

On the u☆-U Relationship in the Stable Atmospheric Boundary Layer over Arctic Sea Ice

A relationship between the friction velocity u☆ and mean wind speed U in a stable atmospheric boundary layer (ABL) over Arctic sea ice was considered. To that aim, the observations collected during the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment were used. The observations showed the so-called “hockey-stick” shape of the u☆−U relationship, which consists of a slow increase of u☆ with increasing wind speed for U<Utr and a more rapid almost linear increase of u☆ for U>Utr, where Utr is the wind speed of transition between the two regimes. Such a relationship is most pronounced at the highest observational levels, namely at 9 and 14 m, and is also sharper when the air-surface temperature difference exceeds its average values for stable conditions. It is shown that the Monin–Obukhov similarity theory (MOST) reproduces the observed u☆−U relationship rather well. This suggests that at least for the SHEBA dataset, there is no contradiction between MOST and the “hockey-stick” shape of the u☆−U relationship. However, the SHEBA data, as well as the single-column simulations show that for cases with strong stability, u☆ significantly decreases with height due to the shallowness of the ABL. It was shown that when u☆ was assumed independent of height, the value of the normalized drag coefficient, i.e., of the so-called stability correction function for momentum, calculated using observations at a certain level, can be significantly underestimated. To overcome this, the decrease of u☆ with height was taken into account in the framework of MOST using local scaling instead of the scaling with surface fluxes. Using such an extended MOST brought the estimates of the normalized drag coefficient closer to the Businger–Dyer relation.

Universal Wind Profile for Conventionally Neutral Atmospheric Boundary Layers.

Conventionally neutral atmospheric boundary layers (CNBLs), which are characterized with zero surface potential temperature flux and capped by an inversion of potential temperature, are frequently encountered in nature. Therefore, predicting the wind speed profiles of CNBLs is relevant for weather forecasting, climate modeling, and wind energy applications. However, previous attempts to predict the velocity profiles in CNBLs have had limited success due to the complicated interplay between buoyancy, shear, and Coriolis effects. Here, we utilize ideas from the classical Monin-Obukhov similarity theory in combination with a local scaling hypothesis to derive an analytic expression for the stability correction function ψ=-c_{ψ}(z/L)^{1/2}, where c_{ψ}=4.2 is an empirical constant, z is the height above ground, and L is the local Obukhov length based on potential temperature flux at that height, for CNBLs. An analytic expression for this flux is also derived using dimensional analysis and a perturbation method approach. We find that the derived profile agrees excellently with the velocity profile in the entire boundary layer obtained from high-fidelity large eddy simulations of typical CNBLs.

The O’KEYPS Equation and 60 Years Beyond

Some 60 years ago, six researchers obtained a semi-empirical equation that describes how the stability correction function for the mean velocity profile ( $$\phi _\mathrm{m}$$ ) in the atmospheric surface layer varies with the stability parameter—the famous O’KEYPS equation. Their derivations are essentially based on interpolation of the turbulent eddy viscosity between neutral and convective conditions. Comparing the O’KEYPS equation with new theoretical developments—such as phenomenological and cospectral budget models—suggests that Heisenberg’s eddy viscosity provides a unifying framework for interpreting the behaviour of $$\phi _\mathrm{m}$$ . The empirical coefficient in the O’KEYPS equation, which is on the order of 10 based on data fitting to observations, is found to be primarily linked to the increase of the size of turbulent eddies as instability increases. The ratio of the sizes of turbulent eddies under convective and neutral conditions is on the order of $$1{/}\kappa $$ , where $$\kappa $$ is the von Karman constant, and is modulated by the turbulent Prandtl number.

Scaling Behavior of a Turbulent Kinetic Energy Closure Scheme for the Stably Stratified Atmosphere: A Steady-State Analysis

Abstract We present a turbulent kinetic energy (TKE) closure scheme for the stably stratified atmosphere in which the mixing lengths for momentum and heat are not parameterized in the same manner. The key difference is that, while the mixing length for heat tends toward the stability independent mixing length for momentum in neutrally stratified conditions, it tends toward one based on the Brunt–Väisälä time scale and square root of the TKE in the limit of large stability. This enables a unique steady-state solution for TKE to be obtained, which we demonstrate would otherwise be impossible if the mixing lengths were the same. Despite the model’s relative simplicity, it is shown to perform reasonably well with observational data from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99) using commonly employed model constants. Analyzing the scaling behavior of the nondimensional velocity and potential temperature gradients, or of the stability (correction) functions, reveals that for large stability the present model scales in the same manner as the first-order operational scheme of Viterbo et al. Alternatively, it appears as a blend of two cases of the TKE closure scheme of Baas et al. Critically, because a unique steady-state TKE can be obtained, the present model avoids the nonphysical behavior identified in one of the cases of Baas et al.

Aerodynamic Resistance Parameterization for Heterogeneous Surfaces Using a Covariance Function Approach in Spectral Space

AbstractSimulating the influence of heterogeneous surfaces on atmospheric flow using mesoscale models (MSM) remains a challenging task, as the resolution of these models usually prohibits resolving important scales of surface heterogeneity. However, surface heterogeneity impacts fluxes of momentum, heat, or moisture, which act as lower boundary conditions for MSM. Even though several approaches for representing subgrid-scale heterogeneities in MSM exist, many of these approaches rely on Monin–Obukhov similarity theory, preventing those models from resolving all scales of surface heterogeneity. To improve upon these residual heterogeneity scales, a novel heterogeneity parameterization is derived by linking the heterogeneous covariance function in spectral space to an associated homogeneous one. This covariance function approach is subsequently used to derive a parameterization of the aerodynamic resistance to heat transfer of the surface layer. Here, the effect of surface heterogeneity enters as a factor applied to the stability correction functions of the bulk similarity approach. To perform a first comparison of the covariance function approach against the conventional bulk similarity and tile approaches, large-eddy simulations (LESs) of distinct surface heterogeneities are conducted. The aerodynamic resistances from these three parameterizations are subsequently tested against the LES reference by resolving the surface heterogeneities with six different test-MSM grids of varying cell dimension. The results of these comparisons show that the covariance function approach proposed here yields the smallest deviations from the LES reference. In addition, the smallest deviation of the covariance function approach to the reference is observed for the LES with the largest surface heterogeneity, which illustrates the advantage of this novel parameterization.

Analysis of Dual Nature of Heat Flux Predicted by Monin‐Obukhov Similarity Theory: An Impact of Empirical Forms of Stability Correction Functions

AbstractThe behavior of sensible heat flux H with stability parameter ζ in the stable atmospheric surface layer is analyzed within the framework of Monin‐Obukhov similarity theory (MOST). Using MOST equations, H is expressed as a function of ζ and wind shear ∂U/∂z. A systematic mathematical analysis is carried out to analyze the behavior of H with ζ utilizing the linear as well as various nonlinear empirical functional forms of the similarity functions. In case of linear form, for a given value of H, two different values of ζ along with the “downward heat flux maximum” with a unique critical point are found to occur. However, for the other selected empirical similarity functions, more than two values of ζ having the same magnitude of H may occur suggesting the existence of multiple critical points. Further, the observational variation of H with ζ is analyzed using data from three different sites. Data suggest the existence of two different stability regimes for the same magnitude of heat flux. However, the data do not support the existence of multiple values of ζ for the same magnitude of H, as predicted by MOST with the other selected empirical forms of similarity functions. This suggests that the phenomenon of existence of downward heat flux maximum, as predicted by MOST equations, depends on the functional form of the similarity functions, and it appears to break down for some selected empirical forms of similarity functions under very stable conditions.

Sediment Suspension by Straining‐Induced Convection at the Head of Salinity Intrusion

AbstractThe tidal straining can generate convective motions and exert a periodic modification of turbulence and sediment transport in estuarine and coastal bottom boundary layers. However, the evidence and physics of convection and sediment suspension induced by tidal straining have not been straightforward. To examine these questions, mooring and transect surveys have been conducted in September 2015 in the region of the Yangtze River plume influence. Field observations and scaling analyses indicate an occurrence of convective motions at the head of saline wedge. Theoretical analyses of stratification evolution in the saline wedge show that unstable stratification and resultant convection are induced by tidal straining. Vertical turbulent velocity and eddy viscosity at the head of saline wedge are both larger than their neutral counterparts in the main body, largely enhancing sediment suspension at the head of saline wedge. Moreover, sediment suspension in both neutral and convection‐affected flows is supported by the variance of vertical turbulent velocity, rather than the shearing stress. Finally, the stability correction functions in the Monin‐Obukhov similarity theory can be simply derived from the local turbulent kinetic energy balance to successfully describe the effects of tidal straining on turbulent length scale, eddy viscosity, and sediment diffusivity in the convection‐affected flow. These recognitions may provide novel understanding of estuarine turbidity maxima, and the dynamical structure and processes for coastal hypoxia.

Role of large eddies in the breakdown of the Reynolds analogy in an idealized mildly unstable atmospheric surface layer

While the breakdown in similarity between turbulent transport of heat and momentum (or Reynolds analogy) is not disputed in the atmospheric surface layer (ASL) under unstably stratified conditions, the causes of this breakdown are still debated. One reason for the breakdown is differences between how coherent structures transport heat and momentum, and their differing responses to increasing instability. Monin—Obukhov Similarity Theory (MOST), which hypothesizes that only local length‐scales play a role in ASL turbulent transport, implicitly assumes that large‐scale structures are inactive, despite their large energy content. Widely adopted mixing‐length models also rest on this assumption in the ASL. The difficulty of characterizing low‐wavenumber turbulent motions with field measurements motivates the use of high‐resolution Direct Numerical Simulation (DNS), which is free from subgrid‐scale parametrizations and adhoc assumptions near the boundary. Despite the low Reynolds number and idealized geometry of the DNS, DNS‐estimated MOST functions are consistent with ASL field experiments, as are low‐frequency features of the spectra. Parsimonious spectral models for MO stability correction functions for momentum (φm) and heat (φh) are derived, based on idealized vertical velocity variance and buoyancy variance spectra fit to the corresponding DNS spectra. For φm, a spectral model, based only on local length‐scales, matches DNS and field measurements well. In contrast, for φh, the model is substantially biased unless contributions from larger length‐scales are also included. These results are supported by sensitivity analyses based on field measurements that are independent of the DNS. They show that ASL heat transport is not MO‐similar, even under mild stratification, and in the absence of entrainment, non‐stationarity and canopy effects. It further suggests that the breakdown of the Reynolds analogy is at least partially caused by the influence of large eddies on turbulent heat transport.

How do Stability Corrections Perform in the Stable Boundary Layer Over Snow?

We assess sensible heat-flux parametrizations in stable conditions over snow surfaces by testing and developing stability correction functions for two alpine and two polar test sites. Five turbulence datasets are analyzed with respect to, (a) the validity of the Monin–Obukhov similarity theory, (b) the model performance of well-established stability corrections, and (c) the development of new univariate and multivariate stability corrections. Using a wide range of stability corrections reveals an overestimation of the turbulent sensible heat flux for high wind speeds and a generally poor performance of all investigated functions for large temperature differences between snow and the atmosphere above (>10 K). Applying the Monin–Obukhov bulk formulation introduces a mean absolute error in the sensible heat flux of $$6\,\hbox {W m}^{-2}$$ (compared with heat fluxes calculated directly from eddy covariance). The stability corrections produce an additional error between 1 and $$5\,\hbox {W m}^{-2}$$ , with the smallest error for published stability corrections found for the Holtslag scheme. We confirm from previous studies that stability corrections need improvements for large temperature differences and wind speeds, where sensible heat fluxes are distinctly overestimated. Under these atmospheric conditions our newly developed stability corrections slightly improve the model performance. However, the differences between stability corrections are typically small when compared to the residual error, which stems from the Monin–Obukhov bulk formulation.

Assessment of surface layer parameterizations in ARW using micro‐meteorological observations from a tropical station

ABSTRACTThe performance of two surface layer parameterizations (MM5‐similarity/Eta‐similarity schemes) in an Advanced Research Weather Research and Forecasting (ARW) mesoscale model is assessed over the tropical site Kalpakkam in southeast India. The ARW is run with four‐nested domains and at a high resolution (1 km) for four 2 day periods covering eight days in each season, 9–17 January, 4–12 April, 4–12 August and 13–21 October 2014 representing winter, summer, the southwest monsoon and the northeast monsoon, respectively. Turbulence observations on winds collected using a fast‐response ultrasonic anemometer are used to estimate the surface layer parameters of friction velocity (u*), and Monin–Obukhov length (L), and surface fluxes of heat and moisture using the eddy correlation method. Results of simulations indicate seasonal variation in friction velocity, drag co‐efficient, turbulent fluxes of heat and moisture, air temperature, humidity and winds at the study site. Relatively higher u*, drag co‐efficients, turbulent fluxes of heat and moisture are found during summer and the southwest monsoon, followed by the northeast monsoon and winter due to the prevalence of more unstable conditions in these seasons. Although the diurnal cycle of various parameters is well produced by both the schemes, the Eta‐similarity scheme produced higher values of surface layer variables relative to the MM5‐similarity scheme. Although both schemes depict a systematic bias in various surface layer parameters, the predicted values with MM5‐similarity scheme are in better agreement with observational estimates as indicated by the qualitative and quantitative comparisons of results. The differences in the results of the two schemes are attributed to the variation in the empirical stability correction functions and the stability regimes used in the two schemes.

A Spectral Budget Model for the Longitudinal Turbulent Velocity in the Stable Atmospheric Surface Layer

Abstract A spectral budget model is developed to describe the scaling behavior of the longitudinal turbulent velocity variance with the stability parameter and the normalized height in an idealized stably stratified atmospheric surface layer (ASL), where z is the height from the surface, L is the Obukhov length, and δ is the boundary layer height. The proposed framework employs Kolmogorov’s hypothesis for describing the shape of the longitudinal velocity spectra in the inertial subrange, Heisenberg’s eddy viscosity as a closure for the pressure redistribution and turbulent transfer terms, and the Monin–Obukhov similarity theory (MOST) scaling for linking the mean longitudinal velocity and temperature profiles to ζ. At a given friction velocity , reduces with increasing ζ as expected. The model is consistent with the disputed z-less stratification when the stability correction function for momentum increases with increasing ζ linearly or as a power law with the exponent exceeding unity. For the Businger–Dyer stability correction function for momentum, which varies linearly with ζ, the limit of the z-less onset is . The proposed framework explains why does not follow MOST scaling even when the mean velocity and temperature profiles may follow MOST in the ASL. It also explains how δ ceases to be a scaling variable in more strongly stable (although well-developed turbulent) ranges.

Estimating atmospheric stability from observations and correcting wind shear models accordingly

Atmospheric stability strongly influences wind shear and thus has to be considered when performing load calculations for wind turbine design. Numerous methods exist however for obtaining stability in terms of the Obukhov length L as well as for correcting the logarithmic wind profile. It is therefore questioned to what extend the choice of adopted methods influences results when performing load analyses. Four methods found in literature for obtaining L, and five methods to correct the logarithmic wind profile for stability are included in the analyses (two for unstable, three for stable conditions). The four methods used to estimate stability from observations result in different PDF's of L, which in turn results in differences in estimated lifetime fatigue loads up to 81%. For unstable conditions hardly any differences are found when using either of the proposed stability correction functions, neither in wind shear nor in fatigue loads. For stable conditions however the proposed stability correction functions differ significantly, and the standard correction for stable conditions might strongly overestimate fatigue loads caused by wind shear (up to 15% differences). Due to the large differences found, it is recommended to carefully choose how to obtain stability and correct wind shear models accordingly.

Global Intermittency and Collapsing Turbulence in the Stratified Planetary Boundary Layer

Direct numerical simulation of the turbulent Ekman layer over a smooth wall is used to investigate bulk properties of a planetary boundary layer under stable stratification. Our simplified configuration depends on two non-dimensional parameters: a Richardson number characterizing the stratification and a Reynolds number characterizing the turbulence scale separation. This simplified configuration is sufficient to reproduce global intermittency, a turbulence collapse, and the decoupling of the surface from the outer region of the boundary layer. Global intermittency appears even in the absence of local perturbations at the surface; the only requirement is that large-scale structures several times wider than the boundary-layer height have enough space to develop. Analysis of the mean velocity, turbulence kinetic energy, and external intermittency is used to investigate the large-scale structures and corresponding differences between stably stratified Ekman flow and channel flow. Both configurations show a similar transition to the turbulence collapse, overshoot of turbulence kinetic energy, and spectral properties. Differences in the outer region resulting from the rotation of the system lead, however, to the generation of enstrophy in the non-turbulent patches of the Ekman flow. The coefficient of the stability correction function from Monin–Obukhov similarity theory is estimated as $$\beta \approx 5.7$$ in agreement with atmospheric observations, theoretical considerations, and results from stably stratified channel flows. Our results demonstrate the applicability of this set-up to atmospheric problems despite the intermediate Reynolds number achieved in our simulations.

Buoyancy effects on the integral lengthscales and mean velocity profile in atmospheric surface layer flows

Within the diabatic atmospheric surface layer (ASL) under quasi-stationary and horizontal homogeneous conditions, the mean velocity profile deviates from its conventional logarithmic shape by a height-dependent universal stability correction function ϕm(ζ) that varies with the stability parameter ζ. The ζ parameter measures the relative importance of mechanical to buoyant production or destruction of turbulent kinetic energy (TKE) within the ASL. A link between ϕm(ζ) and the spectrum of turbulence in the ASL was recently proposed by Katul et al. [“Mean velocity profile in a sheared and thermally stratified atmospheric boundary layer,” Phys. Rev. Lett. 107, 268502 (2011)]. By accounting for the stability-dependence of TKE production, Katul et al. were able to recover scalings for ϕm with the anticipated power-law exponents for free convective, slightly unstable, and stable conditions. To obtain coefficients for the ϕm(ζ) curve in good agreement with empirical formulas, they introduced a correction for the variation of the integral lengthscale of vertical velocity with ζ estimated from the Kansas experiment. In the current work, the link between the coefficients in empirical curves for ϕm(ζ) and stability-dependent properties of turbulence in the ASL, including the variation with ζ of the integral lengthscale and the anisotropy of momentum transporting eddies is investigated using data from the Advection Horizontal Array Turbulence Study. The theoretical framework presented by Katul et al. is revised to account explicitly for these effects. It is found that the coefficients in the ϕm(ζ) curve for unstable and near-neutral conditions can be explained by accounting for the stability-dependence of the integral lengthscale and anisotropy of momentum-transporting eddies; however, an explanation for the observed ϕm(ζ) curve for stable conditions remains elusive. The effect of buoyancy on the horizontal and vertical integral lengthscales is also analyzed in detail.

Turbulence and Vertical Fluxes in the Stable Atmospheric Boundary Layer. Part II: A Novel Mixing-Length Model

Abstract This is the second part of a study about turbulence and vertical fluxes in the stable atmospheric boundary layer. Based on a suite of large-eddy simulations in Part I where the effects of stability on the turbulent structures and kinetic energy are investigated, first-order parameterization schemes are assessed and tested in the Geophysical Fluid Dynamics Laboratory (GFDL)’s single-column model. The applicability of the gradient-flux hypothesis is first examined and it is found that stable conditions are favorable for that hypothesis. However, the concept of introducing a stability correction function fm as a multiplicative factor into the mixing length used under neutral conditions lN is shown to be problematic because fm computed a priori from large-eddy simulations tends not to be a universal function of stability. With this observation, a novel mixing-length model is proposed, which conforms to large-eddy simulation results much better under stable conditions and converges to the classic model under neutral conditions. Test cases imposing steady as well as unsteady forcings are developed to evaluate the performance of the new model. It is found that the new model exhibits robust performance as the stability strength is changed, while other models are sensitive to changes in stability. For cases with unsteady forcings, which are very rarely simulated or tested, the results of the single-column model and large-eddy simulations are also closer when the new model is used, compared to the other models. However, unsteady cases are much more challenging for the turbulence closure formulations than cases with steady surface forcing.

Mean scalar concentration profile in a sheared and thermally stratified atmospheric surface layer

Using only dimensional considerations, Monin and Obukhov proposed a "universal" stability correction function φ(c)(ζ) that accounts for distortions caused by thermal stratification to the mean scalar concentration profile in the atmospheric surface layer when the flow is stationary, planar homogeneous, fully turbulent, and lacking any subsidence. For nearly 6 decades, their analysis provided the basic framework for almost all operational models and data interpretation in the lower atmosphere. However, the canonical shape of φ(c)(ζ) and the departure from the Reynold's analogy continue to defy theoretical explanation. Here, the basic processes governing the scalar-velocity cospectrum, including buoyancy and the scaling laws describing the velocity and temperature spectra, are considered via a simplified cospectral budget. The solution to this cospectral budget is then used to derive φ(c)(ζ), thereby establishing a link between the energetics of turbulent velocity and scalar concentration fluctuations and the bulk flow describing the mean scalar concentration profile. The resulting theory explains all the canonical features of φ(c)(ζ), including the onset of power laws for various stability regimes and their concomitant exponents, as well as the causes of departure from Reynold's analogy.

Mean velocity and temperature profiles in a sheared diabatic turbulent boundary layer

In the atmospheric surface layer, modifications to the logarithmic mean velocity and air temperature profiles induced by thermal stratification or convection are accounted for via stability correction functions ϕm and ϕh, respectively, that vary with the stability parameter ς. These two stability correction functions are presumed to be universal in shape and independent of the surface characteristics. To date, there is no phenomenological theory that explains all the scaling laws in ϕh with ς, how ϕh relates to ϕm, and why ϕh ⩽ ϕm is consistently reported. To develop such a theory, the recently proposed links between the mean velocity profile and the Kolmogorov spectrum of turbulence, which were previously modified to account for the effects of buoyancy, are generalized here to include the mean air temperature profile. The resulting theory explains the observed scaling laws in ϕm and ϕh reported in many field and numerical experiments, predicts their behaviors across a wide range of atmospheric stability conditions, and elucidates why heat is transported more efficiently than momentum in certain stability regimes. In particular, it is shown that the enhancement in heat transport under unstable conditions is linked to a “scale-resonance” between turnover eddies and excursions in the instantaneous air temperature profiles. Excluding this scale-resonance results in the conventional Reynolds analogy with ϕm = ϕh across all stability conditions.

Mean Velocity Profile in a Sheared and Thermally Stratified Atmospheric Boundary Layer

A stability correction function φ(m)(ζ) that accounts for distortions to the logarithmic mean velocity profile (MVP) in the lower atmosphere caused by thermal stratification was proposed by Monin and Obukhov in the 1950s using dimensional analysis. Its universal character was established from many field experiments. However, theories that describe the canonical shape of φ(m)(ζ) are still lacking. A previous link between the spectrum of turbulence and the MVP is expanded here to include the effects of thermal stratification on the turbulent kinetic energy dissipation rate and eddy-size anisotropy. The resulting theory provides a novel explanation for the power-law exponents and coefficients already reported for φ(m)(ζ) from numerous field experiments.