Low-level jets (LLJs) are the wind maxima in the lowest 50 to 1000 m of atmospheric boundary layers. Due to their significant influence on the power production of wind farms, it is crucial to understand the interaction between LLJs and wind farms. In the presence of a LLJ, there are positive and negative shear regions in the velocity profile. The positive shear regions of LLJs are continuously turbulent, while the negative shear regions have limited turbulence. We present large eddy simulations of wind farms in which the LLJ is above, below, or in the middle of the turbine rotor swept area. We find that the wakes recover relatively quickly when the LLJ is above the turbines. This is due to the high turbulence below the LLJ and the downward vertical entrainment created by the momentum deficit due to the wind farm power production. This harvests the jet's energy and aids wake recovery. However, when the LLJ is below the turbine rotor swept area, the wake recovery is very slow due to the low atmospheric turbulence above the LLJ. The energy budget analysis reveals that the entrainment fluxes are maximum and minimum when the LLJ is above and in the middle of the turbine rotor swept area, respectively. Surprisingly, we find that the negative shear creates a significant entrainment flux upward when the LLJ is below the turbine rotor swept area. This facilitates energy extraction from the jet, which is beneficial for the performance of downwind turbines.

1.
M.
Abkar
,
A.
Sharifi
, and
F.
Porté-Agel
, “
Wake flow in a wind farm during a diurnal cycle
,”
J. Turbul.
625
,
012031
(
2015
).
2.
N.
Ali
,
G.
Cortina
,
N.
Hamilton
,
M.
Calaf
, and
R. B.
Cal
, “
Turbulence characteristics of a thermally stratified wind turbine array boundary layer via proper orthogonal decomposition
,”
J. Fluid Mech.
828
,
175
195
(
2017
).
3.
N.
Ali
,
N.
Hamilton
,
G.
Cortina
, and
M.
Calaf
, “
Anisotropy stress invariants of thermally stratified wind turbine array boundary layers using large eddy simulations
,”
J. Renewable Sustainable Energy
10
,
013301
(
2018
).
4.
D.
Allaerts
and
J.
Meyers
, “
Large eddy simulation of a large wind-turbine array in a conventionally neutral atmospheric boundary layer
,”
Phys. Fluids
27
,
065108
(
2015
).
5.
D.
Allaerts
and
J.
Meyers
, “
Boundary-layer development and gravity waves in conventionally neutral wind farms
,”
J. Fluid Mech.
814
,
95
130
(
2017
).
6.
D.
Allaerts
and
J.
Meyers
, “
Gravity waves and wind-farm efficiency in neutral and stable conditions
,”
Boundary-Layer Meteorol.
166
,
269
(
2018
).
7.
R. W.
Arritt
,
T. D.
Rink
,
M.
Segal
,
D. P.
Todey
,
C. A.
Clark
,
M. J.
Mitchell
, and
K. M.
Labas
, “
The Great Plains low-level jet during the warm season of 1993
,”
Mon. Weather Rev.
125
,
2176
2192
(
1997
).
8.
P.
Baas
,
F. C.
Bosveld
,
H. K.
Baltink
, and
A. A. M.
Holtslag
, “
A climatology of nocturnal low-level jets at Cabauw
,”
J. Appl. Meteor. Climatol.
48
,
1627
1642
(
2009
).
9.
R. M.
Banta
, “
Stable-boundary-layer regimes from the perspective of the low-level jet
,”
Acta Geophys.
56
,
58
87
(
2008
).
10.
R. M.
Banta
,
R. K.
Newsom
,
J. K.
Lundquist
,
Y. L.
Pichugina
,
R. L.
Coulter
, and
L.
Mahrt
, “
Nocturnal low-level jet characteristics over Kansas during CASES-99
,”
Boundary-Layer Meteorol.
105
,
221
252
(
2002
).
11.
R. J.
Beare
,
M. K.
Macvean
,
A. A. M.
Holtslag
,
J.
Cuxart
,
I.
Esau
,
J.-C.
Golaz
,
M. A.
Jimenez
,
M.
Khairoutdinov
,
B.
Kosovic
,
D.
Lewellen
,
T. S.
Lund
,
J. K.
Lundquist
,
A.
Mccabe
,
A. F.
Moene
,
Y.
Noh
,
S.
Raasch
, and
P.
Sullivan
, “
An intercomparison of large eddy simulations of the stable boundary layer
,”
Boundary-Layer Meteorol.
118
,
247
272
(
2006
).
12.
K.
Bhaganagar
and
M.
Debnath
, “
The effects of mean atmospheric forcings of the stable atmospheric boundary layer on wind turbine wake
,”
J. Renewable Sustainable Energy
7
,
013124
(
2015
).
13.
A. K.
Blackadar
, “
Boundary layer wind maxima and their significance for the growth of nocturnal inversions
,”
Bull. Am. Meteorol. Soc.
38
,
283
290
(
1957
).
14.
E.
Bou-Zeid
,
C.
Meneveau
, and
M. B.
Parlange
, “
A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows
,”
Phys. Fluids
17
,
025105
(
2005
).
15.
W.
Brutsaert
,
Evaporation into the Atmosphere: Theory, History and Applications
(
Springer Science & Business Media.
,
1982
), Vol. 1.
16.
R. B.
Cal
,
J.
Lebrón
,
L.
Castillo
,
H. S.
Kang
, and
C.
Meneveau
, “
Experimental study of the horizontally averaged flow structure in a model wind-turbine array boundary layer
,”
J. Renewable Sustainable Energy
2
,
013106
(
2010
).
17.
M.
Calaf
,
C.
Meneveau
, and
J.
Meyers
, “
Large eddy simulations of fully developed wind-turbine array boundary layers
,”
Phys. Fluids
22
,
015110
(
2010
).
18.
M.
Calaf
,
M. B.
Parlange
, and
C.
Meneveau
, “
Large eddy simulation study of scalar transport in fully developed wind-turbine array boundary layers
,”
Phys. Fluids
23
,
126603
(
2011
).
19.
C.
Canuto
,
M. Y.
Hussaini
,
A.
Quarteroni
, and
T. A.
Zang
,
Spectral Methods in Fluid Dynamics
(
Springer
,
Berlin
,
1988
).
20.
A.
Doosttalab
,
D.
Siguenza-Alvarado
,
V.
Pulletikurthi
,
Y.
Jin
,
H. B.
Evans
,
L. P.
Chamorro
, and
L.
Castillo
, “
Interaction of low-level jets with wind turbines: On the basic mechanisms for enhanced performance
,”
J. Renewable Sustainable Energy
12
,
053301
(
2020
).
21.
M.
Dörenkämper
,
B.
Witha
,
G.
Steinfeld
,
D.
Heinemann
, and
M.
Kühn
, “
The impact of stable atmospheric boundary layers on wind-turbine wakes within offshore wind farms
,”
J. Wind Eng. Ind. Aerodyn.
144
,
146
153
(
2015
).
22.
J. B.
Duncan
,
Observational Analyses of the North Sea Low-Level Jet
(
TNO
,
Petten
,
2018
).
23.
J. H.
Ferziger
and
M.
Perić
,
Computational Methods for Fluid Dynamics
(
Springer
,
2002
).
24.
A. C.
Fitch
,
J. B.
Olson
, and
J. K.
Lundquist
, “
Parameterization of wind farms in climate models
,”
J. Wind Eng. Ind. Aerodyn.
26
,
6439
6458
(
2013
).
25.
S. N.
Gadde
and
R. J. A. M.
Stevens
, “
Effect of Coriolis force on a wind farm wake
,”
J. Phys. Conf. Ser.
1256
,
012026
(
2019
).
26.
S. N.
Gadde
and
R. J. A. M.
Stevens
, “Interaction between low-level jets and wind farms in a stable atmospheric boundary layer,”
Phys. Rev. Fluids.
6
(
1
),
014603
(
2021
).
27.
S. N.
Gadde
,
A.
Stieren
, and
R. J. A. M.
Stevens
, “
Large-eddy simulations of stratified atmospheric boundary layers: Comparison of different subgrid models
,”
Boundary-Layer Meteorol.
2020
,
1
20
.
28.
S.
Greene
,
K.
McNabb
,
R.
Zwilling
,
M.
Morrissey
, and
S.
Stadler
, “
Analysis of vertical wind shear in the southern great plains and potential impacts on estimation of wind energy production
,”
Int. J. Global Energy
32
,
191
211
(
2009
).
29.
W.
Gutierrez
,
G.
Araya
,
P.
Kiliyanpilakkil
,
A.
Ruiz-Columbie
,
M.
Tutkun
, and
L.
Castillo
, “
Structural impact assessment of low level jets over wind turbines
,”
J. Renewable Sustainable Energy
8
,
023308
(
2016
).
30.
W.
Gutierrez
,
A.
Ruiz-Columbie
,
M.
Tutkun
, and
L.
Castillo
, “
Impacts of the low-level jet's negative wind shear on the wind turbine
,”
Wind Energy Sci.
2
,
533
545
(
2017
).
31.
A. A. M.
Holtslag
and
F. T. M.
Nieuwstadt
, “
Scaling the atmospheric boundary layer
,”
Boundary-Layer Meteorol.
36
,
201
209
(
1986
).
32.
A.
Jimenez
,
A.
Crespo
,
E.
Migoya
, and
J.
Garcia
, “
Advances in large-eddy simulation of a wind turbine wake
,”
J. Phys. Conf. Ser.
75
,
012041
(
2007
).
33.
A.
Jimenez
,
A.
Crespo
,
E.
Migoya
, and
J.
Garcia
, “
Large-eddy simulation of spectral coherence in a wind turbine wake
,”
Environ. Res. Lett.
3
,
015004
(
2008
).
34.
P. C.
Kalverla
,
J. B.
Duncan
, Jr.
,
G.-J.
Steeneveld
, and
A. A. M.
Holtslag
, “
Low-level jets over the North Sea based on ERA5 and observations: Together they do better
,”
Wind Energy Sci.
4
,
193
209
(
2019
).
35.
P. C.
Kalverla
,
G.-J.
Steeneveld
,
R. J.
Ronda
, and
A. A. M.
Holtslag
, “
An observational climatology of anomalous wind events at offshore meteomast IJmuiden (North Sea)
,”
J. Wind Eng. Ind. Aerodyn.
165
,
86
99
(
2017
).
36.
R. E.
Keck
,
M.
de Maré
,
M. J.
Churchfield
,
S.
Lee
,
G.
Larsen
, and
H. A.
Madsen
, “
On atmospheric stability in the dynamic wake meandering model
,”
Wind Energy
17
,
1689
1710
(
2014
).
37.
N.
Kelley
,
M.
Shirazi
,
D.
Jager
,
S.
Wilde
,
J.
Adams
,
M.
Buhl
,
P.
Sullivan
, and
E.
Patton
, “
Lamar low-level jet project interim report
,” National Renewable Energy Laboratory, National Wind Technology Center, Golden, CO, Technical Paper No. NREL/TP-500–34593,
2004
.
38.
J. B.
Klemp
and
D. K.
Lilly
, “
Numerical simulation of hydrostatic mountain waves
,”
J. Atmos. Sci.
68
,
46
50
(
1978
).
39.
G. A. M.
van Kuik
,
J.
Peinke
,
R.
Nijssen
,
D.
Lekou
,
J.
Mann
,
J. N.
Sørensen
,
C.
Ferreira
,
J. W.
van Wingerden
,
D.
Schlipf
,
P.
Gebraad
,
H.
Polinder
,
A.
Abrahamsen
,
G. J. W.
van Bussel
,
J. D.
Sørensen
,
P.
Tavner
,
C. L.
Bottasso
,
M.
Muskulus
,
D.
Matha
,
H. J.
Lindeboom
,
S.
Degraer
,
O.
Kramer
,
S.
Lehnhoff
,
M.
Sonnenschein
,
P. E.
Sørensen
,
R. W.
Künneke
,
P. E.
Morthorst
, and
K.
Skytte
, “
Long-term research challenges in wind energy—A research agenda by the European Academy of wind energy
,”
Wind Energy Sci.
1
,
1
39
(
2016
).
40.
V.
Kumar
,
G.
Svensson
,
A. A. M.
Holtslag
,
C.
Meneveau
, and
M. B.
Parlange
, “
Impact of surface flux formulations and geostrophic forcing on large-eddy simulations of diurnal atmospheric boundary layer flow
,”
J. Appl. Meteorol. Climatol.
49
,
1496
1516
(
2010
).
41.
G. C.
Larsen
,
H. A.
Madsen
,
K.
Thomsen
, and
T. J.
Larsen
, “
Wake meandering: A pragmatic approach
,”
Wind Energy
11
,
377
395
(
2008
).
42.
H.
Liu
,
M.
He
,
B.
Wang
, and
Q.
Zhang
, “
Advances in low-level jet research and future prospects
,”
J. Meteorol. Res.
28
,
57
75
(
2014
).
43.
H.
Lu
and
F.
Porté-Agel
, “
Large-eddy simulation of a very large wind farm in a stable atmospheric boundary layer
,”
Phys. Fluids
23
,
065101
(
2011
).
44.
X.
Mao
and
J. N.
Sørensen
, “
Far-wake meandering induced by atmospheric eddies in flow past a wind turbine
,”
J. Fluid Mech.
846
,
190
209
(
2018
).
45.
J.
Meyers
and
C.
Meneveau
, “
Flow visualization using momentum and energy transport tubes and applications to turbulent flow in wind farms
,”
J. Fluid Mech.
715
,
335
358
(
2013
).
46.
C.-H.
Moeng
, “
A large-eddy simulation model for the study of planetary boundary-layer turbulence
,”
J. Atmos. Sci.
41
,
2052
2062
(
1984
).
47.
J. S.
Na
,
E.
Koo
,
E. K.
Jin
,
R.
Linn
,
S. C.
Ko
,
D.
Muñoz-Esparza
, and
J. S.
Lee
, “
Large-eddy simulations of wind-farm wake characteristics associated with a low-level jet
,”
Wind Energy
21
,
163
173
(
2018
).
48.
F.
Porté-Agel
,
M.
Bastankhah
, and
S.
Shamsoddin
, “
Wind-turbine and wind-farm flows: A review
,”
Boundary-Layer Meteorol.
174
,
1
59
(
2020
).
49.
T. V.
Prabha
,
B. N.
Goswami
,
B. S.
Murthy
, and
J. R.
Kulkarni
, “
Nocturnal low-level jet and ‘atmospheric streams' over the rain shadow region of Indian Western Ghats
,”
Q. J. R. Meteorol. Soc.
137
,
1273
1287
(
2011
).
50.
P.
Sagaut
,
Large Eddy Simulation for Incompressible Flows: An Introduction
(
Springer Science & Business Media
,
2006
).
51.
V.
Sharma
,
M. B.
Parlange
, and
M.
Calaf
, “
Perturbations to the spatial and temporal characteristics of the diurnally-varying atmospheric boundary layer due to an extensive wind farm
,”
Boundary-Layer Meteorol.
162
,
255
282
(
2017
).
52.
D. L.
Sisterson
and
P.
Frenzen
, “
Nocturnal boundary-layer wind maxima and the problem of wind power assessment
,”
Environ. Sci. Technol.
12
,
218
221
(
1978
).
53.
A.
Smedman
,
U.
Högström
, and
H.
Bergström
, “
Low level jets
A decisive factor for off-shore wind energy siting in the Baltic sea
,”
Wind Eng.
20
,
137
147
(
1996
); available at www.jstor.org/stable/43749611.
54.
A.-S.
Smedman
,
M.
Tjernström
, and
U.
Högström
, “
Analysis of the turbulence structure of a marine low-level jet
,”
Boundary-Layer Meteorol.
66
,
105
126
(
1993
).
55.
J. N.
Sørensen
, “
Aerodynamic aspects of wind energy conversion
,”
Annu. Rev. Fluid Mech.
43
,
427
448
(
2011
).
56.
R. J. A. M.
Stevens
,
D. F.
Gayme
, and
C.
Meneveau
, “
Generalized coupled wake boundary layer model: Applications and comparisons with field and LES data for two real wind farms
,”
Wind Energy
19
,
2023
2040
(
2016
).
57.
R. J. A. M.
Stevens
,
J.
Graham
, and
C.
Meneveau
, “
A concurrent precursor inflow method for large eddy simulations and applications to finite length wind farms
,”
Renewable Energy
68
,
46
50
(
2014
).
58.
R. J. A. M.
Stevens
,
L. A.
Martínez-Tossas
, and
C.
Meneveau
, “
Comparison of wind farm large eddy simulations using actuator disk and actuator line models with wind tunnel experiments
,”
Renewable Energy
116
,
470
478
(
2018
).
59.
R. J. A. M.
Stevens
and
C.
Meneveau
, “
Flow structure and turbulence in wind farms
,”
Annu. Rev. Fluid Mech.
49
,
311
339
(
2017
).
60.
R.
Stoll
and
F.
Porté-Agel
, “
Effects of roughness on surface boundary conditions for large-eddy simulation
,”
Boundary-Layer Meteorol.
118
,
169
187
(
2006
).
61.
R.
Stoll
and
F.
Porté-Agel
, “
Large-eddy simulation of the stable atmospheric boundary layer using dynamic models with different averaging schemes
,”
Boundary-Layer Meteorol.
126
,
1
28
(
2007
).
62.
H.
Tennekes
and
J. L.
Lumley
,
A First Course in Turbulence
(
MIT Press
,
1972
).
63.
N.
Troldborg
,
J. N.
Sørensen
, and
R.
Mikkelsen
, “
Numerical simulations of wake characteristics of a wind turbine in uniform inflow
,”
Wind Energy
13
,
86
99
(
2010
).
64.
D.
Wagner
,
G.
Steinfeld
,
B.
Witha
,
H.
Wurps
, and
J.
Reuder
, “
Low level jets over the Southern North Sea
,”
Meteorol. Z.
28
,
389
415
(
2019
).
65.
J.
Wilczak
,
C.
Finley
,
J.
Freedman
,
J.
Cline
,
L.
Bianco
,
J.
Olson
,
I.
Djalalova
,
L.
Sheridan
,
M.
Ahlstrom
,
J.
Manobianco
,
J.
Zack
,
J. R.
Carley
,
S.
Benjamin
,
R.
Coulter
,
L. K.
Berg
,
J.
Mirocha
,
K.
Clawson
,
E.
Natenberg
, and
M.
Marquis
, “
The wind forecast improvement project (WFIP): A public–private partnership addressing wind energy forecast needs
,”
Bull. Am. Meteorol. Soc.
96
,
1699
1718
(
2015
).
66.
Y.-T.
Wu
and
F.
Porté-Agel
, “
Large-eddy simulation of wind-turbine wakes: Evaluation of turbine parametrisations
,”
Boundary-Layer Meteorol.
138
,
345
366
(
2011
).
67.
M.
Zhang
,
M. G.
Arendshorst
, and
R. J. A. M.
Stevens
, “
Large eddy simulations of the effect of vertical staggering in extended wind farms
,”
Wind Energy
22
,
189
204
(
2019
).
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