Nondimensionalization of the Atmospheric Boundary-Layer System: Obukhov Length and Monin–Obukhov Similarity Theory

The Obukhov length, although often adopted as a characteristic scale of the atmospheric boundary layer, has been introduced purely based on a dimensional argument without a deductive derivation from the governing equations. Here, its derivation is pursued by the nondimensionalization method in the same manner as for the Rossby deformation radius and the Ekman-layer depth. Physical implications of the Obukhov length are inferred by nondimensionalizing the turbulence-kinetic-energy equation for the horizontally homogeneous boundary layer. A nondimensionalization length scale for a full set of equations for boundary-layer flow formally reduces to the Obukhov length by dividing this scale by a rescaling factor. This rescaling factor increases with increasing stable stratification of the boundary layer, in which flows tend to be more horizontal and gentler; thus the Obukhov length increasingly loses its relevance. A heuristic, but deductive, derivation of Monin–Obukhov similarity theory is also outlined based on the obtained nondimensionalization results.

Wind-Tunnel Simulation of Approximately Horizontally Homogeneous Stable Atmospheric Boundary Layers

Two cases of an overlying inversion imposed on a stable boundary layer are investigated, extending the work of Hancock and Hayden (Boundary-Layer Meteorol 168:29–57, 2018; 175:93–112, 2020). Vertical profiles of Reynolds stresses and heat flux show closely horizontally homogeneous behaviour over a streamwise fetch of more than eight boundary-layer heights. However, profiles of mean temperature and velocity show closely horizontally homogeneous behaviour only in the top two-thirds of the boundary layer. In the lower one-third the temperature decreases with fetch, directly as a consequence of heat transfer to the surface. A weaker effect is seen in the mean velocity profiles, curiously, such that the gradient Richardson number is invariant with fetch, while various other quantities are not. Stability leads to a ‘blocking’ of vertical influence. Inferred aerodynamic and thermal roughness lengths increase with fetch, while the former is constant in the neutral case, as expected. Favourable validation comparisons are made against two sets of local-scaling systems over the full depth of the boundary layer. Close concurrence is seen for all stable cases for z/L < 0.2, where z and L are the vertical height and local Obukhov length, respectively, and over most of the layer for some quantities.

Lettau’s Contribution to the Obukhov Length Scale: A Scientific Historical Study

It has been repeatedly assumed that Heinz Lettau found the Obukhov length in 1949 independently of Obukhov in 1946. However, it was not the characteristic length scale, the Obukhov length L, but the ratio of height and the Obukhov length (z/L), the Obukhov stability parameter, that he analyzed. Whether Lettau described the parameter z/L independently of Obukhov is investigated herein. Regardless of speculation about this, the significant contributions made by Lettau in the application of z/L merit this term being called the Obukhov–Lettau stability parameter in the future.

A k–ε Turbulence Model for the Convective Atmosphere

A k–ε turbulence model for the stable atmosphere is extended for the convective atmosphere. The new model represents the buoyancy-induced increase in the kinetic energy and scale of eddies, and is consistent with the Monin–Obukhov similarity theory for convective atmospheric boundary layers (ABLs). After being incorporated into an ABL model with the Coriolis force, the model is tested by comparing the ABL model results with the Businger–Dyer (BD) relationship. ABL model simulations are carried out to reveal the sensitivity of the vertical wind profile to model parameters (e.g., the Obukhov length, friction velocity, and geostrophic wind). When the friction velocity is consistent with geostrophic wind speed (or the turbulence in the inner regime is in equilibrium with that in the outer regime), the modeled wind profile is close to the BD relationship near the ground surface. Otherwise, the modeled wind profile deviates from the BD relationship, resembling the hockey stick transition model.

The impact of the atmospheric turbulence-development tendency on new particle formation: a common finding on three continents

A new mechanism of new particle formation (NPF) is investigated using comprehensive measurements of aerosol physicochemical quantities and meteorological variables made in three continents, including Beijing, China; the Southern Great Plains site in the USA; and SMEAR II Station in Hyytiälä, Finland. Despite the considerably different emissions of chemical species among the sites, a common relationship was found between the characteristics of NPF and the stability intensity. The stability parameter (ζ = Z/L, where Z is the height above ground and L is the Monin–Obukhov length) is found to play an important role; it drops significantly before NPF as the atmosphere becomes more unstable, which may serve as an indicator of nucleation bursts. As the atmosphere becomes unstable, the NPF duration is closely related to the tendency for turbulence development, which influences the evolution of the condensation sink. Presumably, the unstable atmosphere may dilute pre-existing particles, effectively reducing the condensation sink, especially at coarse mode to foster nucleation. This new mechanism is confirmed by model simulations using a molecular dynamic model that mimics the impact of turbulence development on nucleation by inducing and intensifying homogeneous nucleation events.

Estimations of the Mexicali Valley (Mexico) Mixing Height

We report estimations of the Mexicali Valley (Mexico) mixing height for three seasons. Surface and upper air meteorological measurements were carried out nearby Cerro Prieto geothermal power plant during July 2010 (summer), January 2012 (winter), and October 2016 (autumn). Four different methods were applied to estimate the convective boundary layer (CBL) height from radiosonde (RS) profiles: the parcel method, the gradients method, the least-squares variational approach based on the slab model of the CBL structure, and a covariance method. For nocturnal conditions, we used diagnostic models based on friction velocity and Monin–Obukhov length. Under unstable conditions, we obtained (on average) mixing heights of 497 m at 06:00 LST, 1242 m at 12:00 LST, 1404 m at 15:00 LST, and 482 at 18:00 LST during summer; 754 m at 12:00 LST during winter; and 1195 m at 12:00 LST and 13:00 m between the 14:00 and 15:00 LST during the autumn. The results allowed adjusting a semiempirical model to evaluate mixing height from turbulent sensible heat flux and friction velocity data. Our results provide practical tools that could facilitate the application of regulatory dispersion models to assess air quality in the region.

Wind-Tunnel Simulation of Stable Atmospheric Boundary Layers with an Overlying Inversion

Four cases of an overlying inversion imposed on a stable boundary layer are investigated, extending the earlier work of Hancock and Hayden (Boundary-Layer Meteorol 168:29–57, 2018), where no inversion was imposed. The inversion is imposed to one or other of two depths within the layer: midway or deep. Four cases of changed surface condition are also investigated, and it is seen that the surface and imposed conditions behave independently. A change of imposed inversion condition leaves the bottom 1/3 of the layer almost completely unaffected; a change of the surface condition leaves the top 2/3 unaffected. Comparisons are made against two sets of local-scaling systems over the full height of the boundary layer. Both show some influence of the inversion condition. The surface heat flux and the reduction in surface shear stress, and hence the ratio of the boundary-layer height to surface Obukhov length, are determined by the temperature difference across the surface layer (not the whole layer), bringing all cases together in single correlations as functions of a surface-layer bulk Richardson number.

Comparison of Length Scale Parameterization Methodologies

Atmospheric stability has been studied for decades. There are several methodologies that evolved over the years. In this study, a special experimental meteorological mast that has been erected to a complex site has been used to calculate dimensionless Obukhov length ( ζ = z L ) , dimensionless momentum ( φ m ), and heat coefficients ( φ h ). The results are compared with the ones from average value approaches: Richardson number, flux-profile (F-P) relations, and wind shear exponent methods. The results show that the estimated ζ values, using the bulk Richardson number, get along well with the reference ζ within the neutral and stable regimes. F-P relations and wind shear exponent methods result in the best agreement for stable and neutral regimes. Nevertheless, average oriented methods are not reliable for the other regimes.

Micro-scale modelling of the urban wind speed for air pollution applications

Modelling wind speeds in urban areas have many applications e.g. in relation to assessment of wind energy, modelling air pollution, and building design and engineering. Models for extrapolating the urban wind speed exist, but little attention has been paid to the influence of the upwind terrain and the foundations for the extrapolation schemes. To analyse the influence of the upwind terrain and the foundations for the extrapolation of the urban wind speed, measurements from six urban and non-urban stations were explored, and a model for the urban wind speed with and without upwind influence was developed and validated. The agreement between the wind directions at the stations is found to be good, and the influence of atmospheric stability, horizontal temperature gradients, land-sea breeze, temperature, global radiation and Monin-Obukhov Length is found to be small, although future work should explore if this is valid for other urban areas. Moreover, the model is found to perform reasonably well, but the upwind influence is overestimated. Areas of model improvement are thus identified. The upwind terrain thus influences the modelling of the urban wind speed to a large extent, and the fundamental assumptions for the extrapolation scheme are fulfilled for this specific case.

Stratification Effects in the Turbulent Boundary Layer beneath a Melting Ice Shelf: Insights from Resolved Large-Eddy Simulations

Ocean turbulence contributes to the basal melting and dissolution of ice shelves by transporting heat and salt toward the ice. The meltwater causes a stable salinity stratification to form beneath the ice that suppresses turbulence. Here we use large-eddy simulations motivated by the ice shelf–ocean boundary layer (ISOBL) to examine the inherently linked processes of turbulence and stratification, and their influence on the melt rate. Our rectangular domain is bounded from above by the ice base where a dynamic melt condition is imposed. By varying the speed of the flow and the ambient temperature, we identify a fully turbulent, well-mixed regime and an intermittently turbulent, strongly stratified regime. The transition between regimes can be characterized by comparing the Obukhov length, which provides a measure of the distance away from the ice base where stratification begins to dominate the flow, to the viscous length scale of the interfacial sublayer. Upper limits on simulated turbulent transfer coefficients are used to predict the transition from fully to intermittently turbulent flow. The predicted melt rate is sensitive to the choice of the heat and salt transfer coefficients and the drag coefficient. For example, when coefficients characteristic of fully developed turbulence are applied to intermittent flow, the parameterized three-equation model overestimates the basal melt rate by almost a factor of 10. These insights may help to guide when existing parameterizations of ice melt are appropriate for use in regional or large-scale ocean models, and may also have implications for other ice–ocean interactions such as fast ice or drifting ice.