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

Dissipation rate of turbulent kinetic energy in stably stratified sheared flows

Over the years, the problem of dissipation rate of turbulent kinetic energy (TKE) in stable stratification remained unclear because of the practical impossibility to directly measure the process of dissipation that takes place at the smallest scales of turbulent motion. Poor representation of dissipation causes intolerable uncertainties in turbulence-closure theory and thus in modelling stably stratified turbulent flows. We obtain a theoretical solution to this problem for the whole range of stratifications from neutral to limiting stable; and validate it via (i) direct numerical simulation (DNS) immediately detecting the dissipation rate and (ii) indirect estimates of dissipation rate retrieved via the TKE budget equation from atmospheric measurements of other components of the TKE budget. The proposed formulation of dissipation rate will be of use in any turbulence-closure models employing the TKE budget equation and in problems requiring precise knowledge of the high-frequency part of turbulence spectra in atmospheric chemistry, aerosol science, and microphysics of clouds.</p

Comments on the Numerical Simulation of Homogeneous Stably-Stratified Turbulence

Peer reviewe

Stratified shear flow instabilities at large Richardson numbers

Numerical simulations of stratified shear flow instabilities are performed in two dimensions in the Boussinesq limit. The density variation length scale is chosen to be four times smaller than the velocity variation length scale so that Holmboe or Kelvin-Helmholtz unstable modes are present depending on the choice of the global Richardson number Ri. Three different values of Ri were examined Ri =0.2, 2, 20. The flows for the three examined values are all unstable due to different modes namely: the Kelvin-Helmholtz mode for Ri=0.2, the first Holmboe mode for Ri=2, and the second Holmboe mode for Ri=20 that has been discovered recently and it is the first time that it is examined in the non-linear stage. It is found that the amplitude of the velocity perturbation of the second Holmboe mode at the non-linear stage is smaller but comparable to first Holmboe mode. The increase of the potential energy however due to the second Holmboe modes is greater than that of the first mode. The Kelvin-Helmholtz mode is larger by two orders of magnitude in kinetic energy than the Holmboe modes and about ten times larger in potential energy than the Holmboe modes. The results in this paper suggest that although mixing is suppressed at large Richardson numbers it is not negligible, and turbulent mixing processes in strongly stratified environments can not be excluded.Comment: Submitted to Physics of Fluid

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

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

Large-scale instabilities in a non-rotating turbulent convection

Formation of large-scale coherent structures in a turbulent convection via excitation of large-scale instability is studied. The redistribution of the turbulent heat flux due to non-uniform large-scale motions plays a crucial role in the formation of the coherent large-scale structures in the turbulent convection. The modification of the turbulent heat flux results in strong reduction of the critical Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the excitation of the large-scale instability. The mean-field equations which describe the large-scale instability, are solved numerically. We determine the key parameters that affect formation of the large-scale coherent structures in the turbulent convection. In particular, the degree of thermal anisotropy and the lateral background heat flux strongly modify the growth rates of the large-scale instability, the frequencies of the generated convective-shear waves and change the thresholds required for the excitation of the large-scale instability. This study elucidates the origins of the large-scale circulations and rolls in the atmospheric convective boundary layers and the meso-granular structures in the solar convection.Comment: 13 pages, 13 figures, Physics of Fluids, in pres

Turbulent Diffusion and Turbulent Thermal Diffusion of Aerosols in Stratified Atmospheric Flows

The paper analyzes the phenomenon of turbulent thermal diffusion in the Earth atmosphere, its relation to the turbulent diffusion and its potential impact on aerosol distribution. This phenomenon was predicted theoretically more than 10 years ago and detected recently in the laboratory experiments. This effect causes a non-diffusive flux of aerosols in the direction of the heat flux and results in formation of long-living aerosol layers in the vicinity of temperature inversions. We demonstrated that the theory of turbulent thermal diffusion explains the GOMOS aerosol observations near the tropopause (i.e., the observed shape of aerosol vertical profiles with elevated concentrations located almost symmetrically with respect to temperature profile). In combination with the derived expression for the dependence of the turbulent thermal diffusion ratio on the turbulent diffusion, these measurements yield an independent method for determining the coefficient of turbulent diffusion at the tropopause. We evaluated the impact of turbulent thermal diffusion to the lower-troposphere vertical profiles of aerosol concentration by means of numerical dispersion modelling, and found a regular upward forcing of aerosols with coarse particles affected stronger than fine aerosols.Comment: 19 pages, 10 figure