265 research outputs found
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)Â direct numerical simulation (DNS) immediately detecting the dissipation rate and
(ii)Â 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
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 and the turbulent
velocity in the log-law region (in wall units): . These
predictions are in excellent agreement with DNS data and with recent laboratory
experiments.Comment: 15 pages, 11 figs, included, PRE, submitte
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
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
On the parameterisation of the urban atmospheric sublayer in meteorological models
International audienceThe increased resolution of numerical weather prediction models allows nowadays addressing more specifically urban meteorology and air pollution processes and forecasts. This has triggered new interest in modelling and describing experimentally the specific features and processes of urban areas. Recent developments and results performed within the EU-funded project FUMAPEX on integrated systems for forecasting urban meteorology and air pollution are reported here. Issues of optimum resolution, parameterising urban roughness and surface exchange fluxes and the role of the urban soil layers are addressed with advanced meso- or sub-meso meteorological models. Recommendations, especially with respect to advanced urban air quality forecasting and information systems, are given together with an assessment of the needed further research and data
Internal gravity waves in the energy and flux budget turbulence-closure theory for shear-free stably stratified flows
We have advanced the energy and flux budget turbulence closure theory that takes into account a two-way coupling between internal gravity waves (IGWs) and the shear-free stably stratified turbulence. This theory is based on the budget equation for the total (kinetic plus potential) energy of IGWs, the budget equations for the kinetic and potential energies of fluid turbulence, and turbulent fluxes of potential temperature for waves and fluid flow. The waves emitted at a certain level propagate upward, and the losses of wave energy cause the production of turbulence energy. We demonstrate that due to the nonlinear effects more intensive waves produce more strong turbulence, and this, in turn, results in strong damping of IGWs. As a result, the penetration length of more intensive waves is shorter than that of less intensive IGWs. The anisotropy of the turbulence produced by less intensive IGWs is stronger than that caused by more intensive waves. The low-amplitude IGWs produce turbulence consisting up to 90% of turbulent potential energy. This resembles the properties of the observed high-altitude tropospheric strongly anisotropic (nearly two-dimensional) turbulence.Peer reviewe
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