Large-Eddy Simulation of Turbulent Flow Above and Within a Plant Canopy

145 Pages·2012·0.92 MB·English

Large-Eddy Simulation of Turbulent Flow
Above and Within a Plant Canopy
by
Edward Garrett Patton
B.S. (University of California at Davis) 1991
DISSERTATION
Submitted in partial satisfaction of the requirements for the degree of
DOCTOR OF PHILOSOPHY
in
Atmospheric Science
in the
OFFICE OF GRADUATE STUDIES
of the
UNIVERSITY OF CALIFORNIA
DAVIS
Approved:
Committee in Charge
1997
- i -
ii
Large-Eddy Simulation of Turbulent Flow
Above and Within a Plant Canopy
Copyright 1997
by
Edward Garrett Patton
Abstract
Large-Eddy Simulation of Turbulent Flow
Above and Within a Plant Canopy
by
Edward Garrett Patton
DOCTOR OF PHILOSOPHY in Atmospheric Science
University of California at Davis
Dr. Roger H. Shaw, Chair
The large-eddy simulation of Moeng (1984) and Moeng and Wyngaard (1988) is modi(cid:12)ed
to include the aerodynamic and thermodynamic e(cid:11)ects of porous drag elements such as a
plant canopy or a windbreak and is used to investigate the interaction of the atmospheric
surface layer with these obstacles.
Thecodeistestedundervariousatmosphericconditionsandcanopyspeci(cid:12)cations,
and is compared against an earlier LES pilot study and previously published observations.
Pro(cid:12)les of mean statistics are in general agreement with experimental results. Above the
canopy, imposed boundary conditions force di(cid:11)erences in simulated pro(cid:12)les of higher-order
statistics. However, most within-canopy statistics show good agreement with expected pro-
(cid:12)les. Instantaneous(cid:12)eldsfromtheLESshowspatially andtemporallyvaryingfeaturesvery
similar to what has previously been observed in measurements. Generally, the important
features of the (cid:13)ow are reproduced, paving the way for future investigations.
LES(cid:13)ow (cid:12)elds are utilized to investigate the transport of turbulent kinetic energy
by the pressure (cid:12)eld to regions deep within the canopy. The LES results show the pressure
transport term to serve as the major source of turbulent kinetic energy deep within a plant
canopy, and to become even more important under unstable atmospheric conditions.
Testing the ability of the LES code to perform under adverse conditions, a two-
dimensional porous barrier (a windbreak) is set lengthwise, across the mean wind, within
a spatially homogeneous canopy. A detailed comparison is performed with a similar ex-
periment in a wind tunnel. Numerically derived mean (cid:12)elds agree with the wind tunnel
iii
simulation results. Although the turbulent statistics reveal a lag in the redevelopment of
the turbulence behind the windbreak by the LES, the general features are in qualitative
agreement. Spatial pictures of mean turbulent kinetic energy, mean pressure, and pressure
variance are presented and are discussed in relation to the forcings. Scalar and vector (cid:12)elds
reveal the region of protection downstream from the break. Budgets of momentum and
scalars provideinsight into the dominant mechanisms that drive the resultant (cid:13)ow (cid:12)eld and
scalar distributions.
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This dissertation is dedicated to the advancement of science. May someone
or something at sometime use the work contained in this manuscript to better their
existence or improve their life.
I would also like to dedicate this work to the many trout and steelhead that
I have tortured throughout the years. May they forgive me for using them for the
betterment of my person. Without their assistance, I would most de(cid:12)nitely not have
made it this far in life, this happy, this full of adventure. I hope that someday I can
return to them what I have taken away.
v
vi
Contents
List of Figures viii
List of Tables xii
1 Introduction 1
References 5
2 Evaluation of a Large-Eddy Simulation as a Tool for the Investigation of
Turbulent Flows Interacting with a Plant Canopy 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 The Large-Eddy Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 The Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Subgrid-Scale Closure . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.4 Canopy Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Comparison of LES Output with Field Measurements . . . . . . . . . . . . 15
2.4 Sensitivity of the LES to Canopy Structure . . . . . . . . . . . . . . . . . . 39
2.4.1 Canopy Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.2 Canopy Subgrid-Scale Parameterization . . . . . . . . . . . . . . . . 44
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
References 52
3 TurbulentKineticEnergyBudgetsFrom aLarge-EddySimulationof Flow
Above and Within a Forest Canopy 57
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.2.1 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.2.2 Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.2.3 The TKE Budget Equation . . . . . . . . . . . . . . . . . . . . . . . 69
3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.5 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
References 83
4 Large-Eddy Simulation of Windbreak Flow 86
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.2 The Large-Eddy Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2.1 The Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2.2 Subgrid-Scale Closure . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.2.3 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.2.4 Description of Surface Drag Elements . . . . . . . . . . . . . . . . . 95
4.3 The Wind Tunnel Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.4.1 Mean Velocity Field . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.4.2 Second Moment Statistics . . . . . . . . . . . . . . . . . . . . . . . . 101
4.4.3 Instantaneous Velocities . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.4.4 Static Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.4.5 Momentum Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.4.6 Scalar Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
References 123
5 Conclusion 127
References 132
vii
viii
List of Figures
(cid:0)1
2.1 Vertical distributionofleafareadensity(m ). Vertical integrationproduces
leaf area indices (LAI) of 2 and 5.. . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Left: Verticalpro(cid:12)lesofhorizontallyaveragedstreamwisevelocitynormalized
by the volume averaged streamwise velocity for weakly convective runs with
an LAI of 5 (Case S7, for the current code) and, Right: Pro(cid:12)les of horizon-
tally averaged streamwise velocity normalized by the canopy-top streamwise
velocityforaweaklyconvectiverunwithanLAIof2(CaseS3),andmeasure-
ments from Gao et al. (1989) in the Borden forest under weakly convective
conditions and an LAI of 1.9. . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Vertical pro(cid:12)les of horizontally averaged Reynolds stress (resolved plus sub-
grid) normalized byeach respective canopy-top value fromweakly convective
LES runs with an LAI of 5 (Case S7, for the current code) and the mea-
sured stress within a deciduous forest canopy with an LAI of 4.9 (Shaw et
al. (1988), circle). Small symbolsare the subgrid-scale contribution fromthe
respective LES runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 Vertical pro(cid:12)le of the total (resolved plus subgrid) turbulent kinetic energy
normalized by the canopy top friction velocity u(cid:3). Small symbols are the
subgrid-scale contribution. Data taken from the same cases as Figure 2.2. . 22
2.5 Vertical pro(cid:12)le of the total (resolved plus subgrid) relative intensities of tur-
bulence (velocity standard deviations divided by the local cup wind speed)
for a neutral LES run (Case S9, solid) and from measurements above and
within the Borden forest (dash-dot) under near-neutral stability and an LAI
of 1.9, from Shaw et al. (1988). . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.6 Verticalpro(cid:12)leoftheresolved-plussubgrid-scalevelocitystandarddeviations
normalized by the friction velocity evaluated at the canopy-top for a neutral
LES run (Case S9, solid) and measurements within and above the Borden
forest (dash-dot) under near-neutral stability and an LAI of 1.9, from Shaw
et al. (1988). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.7 Vertical pro(cid:12)le of the total (resolved plus subgrid) streamwise and vertical
velocity correlation coe(cid:14)cient for a neutral LES run with an LAI of 2 (Case
S9, square), for near neutral conditions in a deciduous forest with an LAI
of 1.9 (Shaw et al. (1988), circle), and for a wind tunnel simulation with
neutral conditions and an LAI of 0.47 (Brunet et al (1994), diamond). . . . 26
2.8 Vertical pro(cid:12)les of velocity skewness for a weakly unstable LES run with an
LAI of 5 (Case S7, square), Shaw and Schumann (1992) (cross), for daytime
(weakly unstable to near neutral) conditions within and above a deciduous
forest with an LAI of 4.9 (Baldocchi and Meyers (1988), circle), and for a
wind tunnelstudy underneutral conditions with a model wheat canopy with
an LAI of 0.47. (Brunet et al. (1994), diamond). . . . . . . . . . . . . . . . 28
2.9 Vertical pro(cid:12)le of the terms in the resolved streamwise momentum budget
2
(normalized by h=u(cid:3)) under the assumption of steady-state and horizontally
homogeneous conditions for a neutral LES run with a leaf area index of 5
(Case S10). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.10 Normalizedone-dimensionallongitudinalspectrafromaneutralstabilitycase
with LAI = 5 (S10) of the u and w velocity components and potential tem-
perature (passive scalar) at heights z/h = 0.5, 1.0, and 2.0. . . . . . . . . . 33
2.11 Time series of potential emperature (cid:13)uctuations at speci(cid:12)ed heights from a
weakly unstable case from the LES (Case S1). . . . . . . . . . . . . . . . . 36
2.12 Normalized instantaneous x,z-slices (at y/h = 4.8) of(a) streamwise velocity,
(b) vertical velocity, and (c) potential temperature (passive scalar) deviation
from the LES volume-mean for a neutral case with LAI = 2 (Case S9). Solid
lines arepositive, dottedlines arenegative, andthedashed-lineisthecanopy
top. In non-dimensional units, the contour intervals are 0.5 for velocity, and
0.4 for potential temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.13 The x,z-distribution of leaf area density (m(cid:0)1) for (a) the square wave case,
and (b) the sine wave case. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.14 The vertical pro(cid:12)le of horizontally averaged streamwise velocity normalized
by the canopy-top friction velocity for three di(cid:11)erent canopies. . . . . . . . 42
2.15 The vertical pro(cid:12)le of horizontally averaged total turbulent kinetic energy
normalized by the square of the horizontally averaged friction velocity at the
canopy top for the three canopy descriptions. . . . . . . . . . . . . . . . . . 43
2.16 Vertical pro(cid:12)les of horizontally averaged total turbulent kinetic energy nor-
malized by the square of the horizontally averaged friction velocity at the
canopy top for the four di(cid:11)erent values of (cid:11), and the percent contribution
from the SGS energy to to the total for each case. . . . . . . . . . . . . . . 45
2.17 The vertical pro(cid:12)le of horizontally averaged streamwise velocity normalized
by the volume averaged streamwise velocity for the four di(cid:11)erent values of (cid:11). 48
2.18 Normalized one-dimensional longitudinal spectra at z/h = 0.5 from neutral
stability, LAI = 5 cases of the u and w velocity components and potential
temperature (passive scalar) with (cid:11) = 0.00, 0.25, 0.50, and 1.00. . . . . . . 49
(cid:0)1
3.1 Vertical distribution of leaf area density (m ). Integration gives leaf area
indicies (LAI) of 2 and 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2 Normalized resolved-scale TKEbudgetfor simulation S1, h/L = -0.024. Plot
labels refer to budget terms in Equation (3.12), where TT refers to the sum
of T and T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
t sgs
ix
3.3 Normalized components of the turbulent transport term (TT) for simulation
S1. T is the resolved-scale component. S and S represent the normal
t n s
and shear components of subgrid-scale di(cid:11)usion of resolved-scale TKE (T )
sgs
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.4 Normalized resolved-scale TKEbudgetfor simulation S5, h/L = -0.017. Plot
labels refer to budget terms in Equation (3.12), where TT refers to the sum
of T and T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
t sgs
3.5 Normalized resolved-scale TKEbudgetfor simulation S8, h/L = -1.252. Plot
labels refer to budget terms in Equation (3.12), where TT refers to the sum
of T and T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
t sgs
3.6 Normalized turbulent transport (TT) for a dense canopy (LAI = 5). Plot
labels are ordered in terms of increasingly negative h/L; S5 (h/L = -0.017),
S6 (-0.064), S7 (-0.153), S8 (-1.252). . . . . . . . . . . . . . . . . . . . . . . 79
3.7 Normalized pressure transport (T ) for a dense canopy (LAI = 5). Plot
p
labels are ordered in terms of increasingly negative h/L; S5 (h/L = -0.017),
S6 (-0.064), S7 (-0.153), S8 (-1.252). . . . . . . . . . . . . . . . . . . . . . . 80
4.1 The arrangement in the wind tunnel. Not drawn to scale. . . . . . . . . . . 96
4.2 An x,z plot of the streamwise velocity (cid:12)eld averaged over both the cross-
stream direction and 10,000 timesteps. All velocities are scaled by the factor
needed to force the x-averaged streamwise velocity at z/H = 2 to 12 m/s.
Each tick mark on the axes represents one grid point or a 2 cm distance. . . 98
4.3 An x,z plot of vertical velocity averaged over both the cross-stream direction
and 10,000 timesteps. All velocities are scaled by the factor needed to force
the x-averaged streamwise velocity at z/H = 2 to 12 m/s. Each tick mark
on the axes represents one grid point or a 2 cm distance. . . . . . . . . . . . 99
4.4 Vertical pro(cid:12)les of streamwise velocity at speci(cid:12)ed x-locations upstream and
downstream of the fence. Dashed lines represent time-averaged wind tunnel
measurements (U), andsolidlinesrepresentthespanwise-andtime-averaged
LES results (hjuji ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
y;t
4.5 Vertical pro(cid:12)les of streamwise velocity variance at speci(cid:12)ed x-locations up-
stream and downstream of the fence. Dashed lines represent time-averaged
wind tunnel measurements (u2), and solid lines represent the spanwise- and
002 2 0
time-averaged LES results (hu i +h ei ). . . . . . . . . . . . . . . . . 102
y;t 3 y;t
4.6 Vertical pro(cid:12)lesofvertical velocity varianceatspeci(cid:12)edx-locations upstream
and downstream of the fence. Dashed lines represent time-averaged wind
tunnel measurements (w2), and solid lines represent the spanwise- and time-
averaged LES results (hw002i +h2e0i ). Note scale di(cid:11)erence from Figure
y;t 3 y;t
4.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.7 Vertical pro(cid:12)les of Reynolds stress at speci(cid:12)ed x-locations upstream and
downstream of the fence. Dashed lines represent time-averaged wind tunnel
measurements (uw), and solid lines represent the cross-stream and time-
00 00
averaged LES results (hu w i +h(cid:28) i ). . . . . . . . . . . . . . . . . . . 104
y;t xz y;t
4.8 An x,z plot of the spanwise- and time-averaged turbulent kinetic energy
00 00 0 2 2
(hu u =2i +hei ) from the LES. The contour values are in m =s . . . . 105
i i y;t y;t
x