Comments on the Numerical Simulation of Homogeneous Stably-Stratified Turbulence

Peer reviewe

Similarity theory and calculation of turbulent fluxes at the surface for the stably stratified atmospheric boundary layers

In this paper we revise the similarity theory for the stably stratified atmospheric boundary layer (ABL), formulate analytical approximations for the wind velocity and potential temperature profiles over the entire ABL, validate them against large-eddy simulation and observational data, and develop an improved surface flux calculation technique for use in operational models.Comment: The submission to a special issue of the Boundary-Layer Meteorology devoted to the NATO advanced research workshop Atmospheric Boundary Layers: Modelling and Applications for Environmental Securit

Closure Schemes for Stably Stratified Atmospheric Flows without Turbulence Cutoff

Two recently proposed turbulence closure schemes are compared against the conventional Mellor-Yamada (MY) model for stably stratified atmospheric flows. The Energy and Flux-Budget (EFB) approach solves the budgets of turbulent momentum and heat fluxes and turbulent kinetic and potential energies. The Cospectral Budget (CSB) approach is formulated in wavenumber space and integrated across all turbulent scales to obtain flow variables in physical space. Unlike the MY model, which is subject to a "critical gradient Richardson number," both EFB and CSB models allow turbulence to exist at any gradient Richardson number R-t and predict a saturation of flux Richardson number (R-f -> R-fm) at sufficiently large R-i. The CSB approach further predicts the value of Rim and reveals a unique expression linking the Rotta and von Karman constants. Hence, all constants in the CSB model are nontunable and stability independent. All models agree that the dimensionless sensible heat flux decays with increasing R-i. However, the decay rate and subsequent cutoff in the MY model appear abrupt. The MY model further exhibits an abrupt cutoff in the turbulent stress normalized by vertical velocity variance, while the CSB and EFB models display increasing trends. The EFB model produces a rapid increase in the ratio of turbulent potential energy and vertical velocity variance as Rim is approached, suggesting a strong self-preservation mechanism. Vertical anisotropy in the turbulent kinetic energy is parameterized in different ways in MY and EFB, but this consideration is not required in CSB. Differences between EFB and CSB model predictions originate from how the vertical anisotropy is specified in the EFB model.Peer reviewe

On the Velocity Gradient in Stably Stratified Sheared Flows. Part 2: Observations and Models

Peer reviewe

Phenomenology of Wall Bounded Newtonian Turbulence

We construct a simple analytic model for wall-bounded turbulence, containing only four adjustable parameters. Two of these parameters characterize the viscous dissipation of the components of the Reynolds stress-tensor and other two parameters characterize their nonlinear relaxation. The model offers an analytic description of the profiles of the mean velocity and the correlation functions of velocity fluctuations in the entire boundary region, from the viscous sub-layer, through the buffer layer and further into the log-layer. As a first approximation, we employ the traditional return-to-isotropy hypothesis, which yields a very simple distribution of the turbulent kinetic energy between the velocity components in the log-layer: the streamwise component contains a half of the total energy whereas the wall-normal and the cross-stream components contain a quarter each. In addition, the model predicts a very simple relation between the von-K\'arm\'an slope $\kappa$ and the turbulent velocity in the log-law region $v^+$ (in wall units): $v^+=6 \kappa$. These predictions are in excellent agreement with DNS data and with recent laboratory experiments.Comment: 15 pages, 11 figs, included, PRE, submitte

Formation of Large-Scale Semi-Organized Structures in Turbulent Convection

A new mean-field theory of turbulent convection is developed. This theory predicts the convective wind instability in a shear-free turbulent convection which causes formation of large-scale semi-organized fluid motions in the form of cells or rolls. Spatial characteristics of these motions, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This study predicts also the existence of the convective shear instability in a sheared turbulent convection which results in generation of convective shear waves with a nonzero hydrodynamic helicity. Increase of shear promotes excitation of the convective shear instability. Applications of the obtained results to the atmospheric turbulent convection and the laboratory experiments on turbulent convection are discussed. This theory can be applied also for the describing a mesogranular turbulent convection in astrophysics.Comment: 16 pages, 10 figures, REVTEX4, PHYSICAL REVIEW E, v. 67, in press (2003

Overview: Recent advances in the understanding of the northern Eurasian environments and of the urban air quality in China – a Pan-Eurasian Experiment (PEEX) programme perspective

The Pan-Eurasian Experiment (PEEX) Science Plan, released in 2015, addressed a need for a holistic system understanding and outlined the most urgent research needs for the rapidly changing Arctic-boreal region. Air quality in China, together with the long-range transport of atmospheric pollutants, was also indicated as one of the most crucial topics of the research agenda. These two geographical regions, the northern Eurasian Arctic-boreal region and China, especially the megacities in China, were identified as a "PEEX region". It is also important to recognize that the PEEX geographical region is an area where science-based policy actions would have significant impacts on the global climate. This paper summarizes results obtained during the last 5 years in the northern Eurasian region, together with recent observations of the air quality in the urban environments in China, in the context of the PEEX programme. The main regions of interest are the Russian Arctic, northern Eurasian boreal forests (Siberia) and peatlands, and the megacities in China. We frame our analysis against research themes introduced in the PEEX Science Plan in 2015. We summarize recent progress towards an enhanced holistic understanding of the land-atmosphere-ocean systems feedbacks. We conclude that although the scientific knowledge in these regions has increased, the new results are in many cases insufficient, and there are still gaps in our understanding of large-scale climate-Earth surface interactions and feedbacks. This arises from limitations in research infrastructures, especially the lack of coordinated, continuous and comprehensive in situ observations of the study region as well as integrative data analyses, hindering a comprehensive system analysis. The fast-changing environment and ecosystem changes driven by climate change, socio-economic activities like the China Silk Road Initiative, and the global trends like urbanization further complicate such analyses. We recognize new topics with an increasing importance in the near future, especially "the enhancing biological sequestration capacity of greenhouse gases into forests and soils to mitigate climate change" and the "socio-economic development to tackle air quality issues".Peer reviewe

Universal Dependences between Turbulent and Mean Flow Parameters in Stably and Neutrally Stratified Planetary Boundary Layers

We consider the resistance law for the planetary boundary layer (PBL) from the point of view of the similarity theory. In other words, we select the set of the PBL governing parameters and search for an optimal way to express through these parameters the geostrophic drag coefficient Cg=u*/Ug and the cross isobaric angle α(where u* is the friction velocity and Ug is the geostrophic wind speed). By this example, we demonstrate how to determine the “parameter space” in the most convenient way, so that make independent the dimensionless numbers representing co-ordinates in the parameter space, and to avoid (or at least minimise) artificial self- correlations caused by the appearance of the same factors (such as u*) in the examined dimensionless combinations (e.g. in Cg=u*/Ug) and in dimensionless numbers composed of the governing parameters. We also discuss the “completeness” of the parameter space from the point of view of large-eddy simulation (LES) modeller creating a database for a specific physical problem. As recognised recently, very large scatter of data in prior empirical dependencies of Cg and α on the surface Rossby number Ro=Ug|fZ0|-1 (where z0 is the roughness length) and the stratification characterised by μ was to a large extent caused by incompactness of the set of the governing parameters. The most important parameter overlooked in the traditional approach is the typical value of the Brunt-Väisälä frequency N in the free atmosphere (immediately above the PBL), which involves, besides Ro and μ, one more dimensionless number: μN=N/|f|. Accordingly, we consider Cg and α as dependent on the three (rather then two) basic dimensionless numbers (including μN) using LES database DATABASE64. By these means we determine the form of the dependencies under consideration in the part of the parameter space representing typical atmospheric PBLs, and provide analytical expressions for Cg and α