This paper presents a numerical method for predicting the atmospheric boundary layer under stable, neutral, or unstable thermal stratifications. The flow field is described by the Reynolds’ averaged Navier-Stokes equations complemented by the $k‐ϵ$ turbulence model. Density variations are introduced into the momentum equation using the Boussinesq approximation, and appropriate buoyancy terms are included in the $k$ and $ϵ$ equations. An original expression for the closure coefficient related to the buoyancy production term is proposed in order to improve the accuracy of the simulations. The resulting mathematical model has been implemented in FLUENT. The results presented in this paper include comparisons with respect to the Monin-Obukhov similarity theory, measurements, and earlier numerical solutions based on $k‐ϵ$ turbulence models available in the literature. It is shown that the proposed version of the $k‐ϵ$ model significantly improves the accuracy of the simulations for the stable atmospheric boundary layer. In neutral and unstable thermal stratifications, it is shown that the version of the $k‐ϵ$ models available in the literature also produce accurate simulations.

1.
Högström
,
U.
,
Asimakopoulos
,
D. N.
,
Kambezidis
,
H.
,
Helmis
,
C. G.
, and
Smedman
,
A.
, 1988, “
A Field Study of the Wake behind a 2 MW Wind Turbine
,”
Atmos. Environ.
0004-6981,
22
(
4
), pp.
803
820
.
2.
Vermeer
,
L. J.
,
Sorensen
,
J. N.
, and
Crespo
,
A.
, 2003, “
Wind Turbine Wake Aerodynamics
,”
Prog. Aerosp. Sci.
0376-0421,
39
, pp.
467
510
.
3.
Gibson
,
M. M.
, and
Launder
,
B. E.
, 1976, “
On the Calculation of Horizontal, Turbulent, Free Shear Flows Under Gravitational Influence
,”
ASME J. Heat Transfer
0022-1481,
98
(
1
), pp.
81
87
.
4.
Panofsky
,
H.
,
Dutton
, and
J.
, 1984,
Atmospheric Turbulence
,
Wiley
, New York.
5.
Crespo
,
A.
,
Manuel
,
F.
,
Moreno
,
D.
,
Fraga
,
E.
, and
Hernandez
,
J.
, 1985, “
Numerical Analysis of Wind Turbine Wakes
,”
Workshop on Wind Energy Applications, Delphi, Greece
.
6.
Riddle
,
A.
,
Carruthers
,
D.
,
Sharpe
,
A.
,
McHugh
,
C.
, and
Stocker
,
J.
, 2004, “
Comparison between FLUENT and ADMS for Atmospheric Dispersion modeling
,”
Atmos. Environ.
1352-2310,
38
, pp.
1029
1038
.
7.
Thanh
,
C. V.
,
Yasunobu
,
A.
, and
Takashi
,
A.
, 2002, “
A k‐ϵ Turbulence Closure Model for the Atmospheric Boundary Layer Including Urban Canopy
,”
Boundary-Layer Meteorol.
0006-8314,
102
, pp.
459
490
.
8.
Apsley
,
D. D.
, and
Castro
,
I. P.
, 1997, “
A Limited-Length-Scale k‐ϵ Model for Neutral and Stably-Stratified Atmospheric Boundary Layer
,”
Boundary-Layer Meteorol.
0006-8314,
83
, pp.
75
98
.
9.
Mellor
,
G. L.
, and
,
T.
, 1982, “
Development of a Turbulence Closure Model for Geophysical Fluid Problems
,”
Rev. Geophys. Space Phys.
0034-6853,
20
, pp.
851
875
.
10.
Jones
,
W. P.
, and
Launder
,
B. E.
, 1972, “
The Prediction of Laminarization with a Two-Equation Model of Turbulence
,”
Int. J. Heat Mass Transfer
0017-9310,
15
, pp.
301
314
.
11.
Rodi
,
W.
, 1982,
Turbulent Buoyant Jets and Plumes
,
Pergamon Press
, New York, p.
184
.
12.
,
T.
, 1987, “
Turbulence Structure of Sea Breeze Front and its Implication in Air Pollution Transport-Application of k‐ϵ Turbulence Model
,”
Boundary-Layer Meteorol.
0006-8314,
41
, pp.
217
239
.
13.
Betts
,
P. L.
, and
Haroutunian
,
V.
, 1983, “
A k‐ϵ Finite Element Simulation of Buoyancy Effects in the Atmospheric Surface Layer
,” ASME paper 83-WA∕HT-32.
14.
FLUENT 6 User’s Guide
, 2001, Volume
1-4
,
Fluent Inc.
, Lebanon.
15.
Vandoormaal
,
J. P.
, and
Raithby
,
G. D.
, 1984, “
Enhancements of the SIMPLE Method for Predicting Incompressible Fluid Flows
,”
Numer. Heat Transfer
0149-5720,
7
, pp.
147
163
.
16.
Barth
,
T. J.
, and
Jespersen
,
D.
, 1989, “
The Design and Application of Upwind Schemes on Unstructured meshes
, AIAA paper AIAA-89-0366,
AIAA 27th Aerospace Sciences Meeting, Reno, NV
.
17.
Patankar
,
S. V.
, 1980,
Numerical Heat Transfer and Fluid Flow
,
McGraw-Hill
, New York.
18.
Magnusson
,
M.
, and
Smedman
,
A.-S.
, 1994, “
Influence of Atmospheric Stability on Wind Turbine Wakes
,”
Wind Eng.
0309-524X,
18
(
3
), pp.
139
152
.
19.
Magnusson
,
M.
, and
Smedman
,
A.-S.
, 1999, “
Air Flow behind Wind Turbines
,”
J. Wind. Eng. Ind. Aerodyn.
0167-6105,
80
(
1-2
), pp.
169
189
.