T. Boulard et al. Agricultural and Forest Meteorology 100 2000 169–181 173
Fig. 3. Polar graph of the experimental air velocity in section I.
4. Results
4.1. Tunnel flow field 4.1.1. Polar plots
Figs. 3 and 4 show frequency distributions of air flow directions in the vertical plane u–w as polar
plots at each position of sections I and II. The ori- gin of each plot is the measurement position and the
probability densities were calculated, accumulated and plotted at 10
◦
intervals from 0 to 360
◦
. These val- ues are plotted at the angle representing the interval
mid-points and their extremities connected by a line to form the polar graph. In this way, the mean flow di-
rection in the u, w planes together with the deviations in the flow can be easily represented.
The air-flow pattern Fig. 4 in the vent-opening sec- tion section II was characterised by a very strong air
stream entering through the northern opening, crossing the tunnel and escaping through the southern opening.
As shown in Fig. 3, air speed was much weaker in the mid-section section I, centred between two consec-
utive openings. Here, we observed an airflow pattern characterised by two vortex, one rotating anticlock-
wise and centred on the southern side of the tunnel, and a second, rotating clockwise and centred on the
northern side of the tunnel.
Fig. 4. Polar graph of the experimental air velocity in section II.
4.1.2. Two-dimensional vectors The mean vector fields are presented in Fig. 5
for section II. This shows clearly that the air stream crosses the tunnel and escapes perpendicularly through
the southern vent opening. If we only consider air circulation in section II, mass conservation did not
hold with the inflow exceeding the outflow. As a consequence, and contrary to our initial expectations,
lateral air circulations perpendicular to the mean flow v component were not symmetrical with respect to
the middle of each vent opening.
Vertical profiles of the reduced 3-D resultant air ve- locity in the middle of the tunnel Fig. 6 were sim-
ilar for both sections. Approximately the same val- ues 13U
j
18 were observed between 0.25 and 2.7 m, with a peak value U
∗ j
= 18 at 0.9 m and de- creasing to zero at soil and roof levels. As illustrated
by the horizontal profile at 1 m height Fig. 7, this similarity of profiles was only observed in the mid-
dle section of the greenhouse. Conversely, air velocity was maximum at the air inlet U
∗ j
= 100 and outlet U
∗ j
= 30 of section II and null at the same posi- tions in section I.
4.2. Air-temperature patterns Patterns of reduced air temperature [Tj =
{Tj,t − T
o
t }{T
i
t − T
o
t }] are shown in Figs. 8 and 9
for sections II and I, respectively. Physical values of air-temperature
◦
C differences can be deduced by multiplying T
∗
with the average difference between inside and outside 2.2
◦
C, see Appendix B. Lateral heterogeneity perpendicular to the wind di-
rection was not very significant and the similar pat- terns of temperature, with comparable magnitudes,
were observed in both the sections. On average, sec- tion I was only slightly warmer than section II, be-
cause less cold air penetrated into this section. Lon- gitudinal heterogeneity in the direction of the wind
was much more significant, particularly in section II where a strong north to south gradient, due to the
cold air penetration, was observed. In the north open- ing, and along the north side of the tunnel cover in
section I, the air-inflow temperature was close to the outside temperatures 0 T 0.5. In contrast, the
area situated along the south side of the tunnel and near the southern opening, was significantly warmer
174 T. Boulard et al. Agricultural and Forest Meteorology 100 2000 169–181
Fig. 5. Normalised air velocity expressed as a percentage of outside wind speed distribution measured in section II.
1.5 T 2.5. Solar absorption at soil surface also generated a vertical gradient 1.5 T 2.5 in the
first 20 cm above the soil, i.e. across the soil surface boundary layer.
4.3. Air humidity patterns Normalised air water vapour distributions Xj
= [ {Xj,t − X
o
t }{X
i
t − X
o
t }] are shown in Figs.
10 and 11 for sections I and II. respectively. Similar patterns were observed in both sections, with ‘dry’
regions X 1 situated windward in the northern and upper parts of the tunnel and the more ‘humid’
regions 1.8 X 3 near the soil surface, where water vapour was evaporated, and concentrated in
Fig. 6. Normalised air speed expressed as a percentage of outside wind speed in the middle of the two sections of the tunnel.
the leeward part of the tunnel. This pattern is sig- nificantly different from that of the air temperature
pattern presented above because, contrary to the heat diffusion from the cover to the inside air observed in
Figs. 8 and 9, a gradient of water vapour can only be observed above the soil surface. Yet, water vapour
transfer above the soil surface seemed to be more im- portant than heat diffusion, as indicated by the larger
extension of the areas with 1.8 X 3 as compared to the area with 1.8 T 3. However, one must con-
sider cautiously the humidity measurements because air humidity gradients kg kg
−1
between inside and outside were rather weak see Appendix B.
4.4. Air turbulence characteristics 4.4.1. Turbulent kinetic energy distribution
Fig. 12 shows the map of the normalised and time averaged turbulent kinetic energy kj = 12
[ {u
′2
j,t + v
′2
j,t + w
′2
j,t }U
2 o
t] × 100, obtained using least-squares methods for section II. Turbu-
lence intensity was weak in the centre of the tunnel, and increased strongly toward the windward opening,
Fig. 7. Normalised air speed expressed as a percentage of outside wind speed in the two sections at 1-m height of tunnel.
T. Boulard et al. Agricultural and Forest Meteorology 100 2000 169–181 175
Fig. 8. Normalised temperature distribution Tj = [ {Tj,t − T
o
t }{T
i
t − T
o
t }] measured in section I. Tj,t, T
o
t and T
i
t are the mean temperatures
◦
C measured at time t at positions j, outside the greenhouse and inside in the middle of the greenhouse, respectively.
Fig. 9. Normalised temperature distribution Tj = [ {Tj,t − T
o
t }{T
i
t − T
o
t }] measured in section II. Tj,t, T
o
t and T
i
t are the mean temperatures
◦
C measured at the t time at positions j, outside the greenhouse and inside in the middle of the greenhouse, respectively.
where kj was ten times larger than at the centre. The value of kj in the northern opening and in the
areas situated just leeward reached 10. It increased moderately in the leeward opening kj ≈ 4, when
compared to the values measured in the centre of the tunnel kj 2. However, even the stronger val-
ues measured in the opening were rather low when compared to external wind conditions k = 26,
Fig. 10. Normalised water vapour distribution Xj = [ {Xj,t − X
o
t }{X
i
t − X
o
t }] measured in section I. Xj,t, X
o
t and X
i
t are the mean air humidities kg kg
−1
measured at time t at positions j, outside the greenhouse and inside in the middle of the greenhouse, respectively.
measured outside at 1.8 m. Lateral v-component variations in turbulence intensity were also signifi-
cant, kj being much lower in section I kj 2 than in section II. Longitudinal heterogeneity in sec-
tion I was also characterised by decreasing values of k from the centre of the tunnel where the mean
wind speed was at a maximum to the tunnel cover and soil surface.
176 T. Boulard et al. Agricultural and Forest Meteorology 100 2000 169–181
Fig. 11. Normalised water vapour distribution Xj = [ {Xj,t − X
o
t }{X
i
t − X
o
t }] measured in section II Xj,t, X
o
t and X
i
t are the mean humidities kg kg
−1
measured at time t at positions j, outside the greenhouse and inside in the middle of the greenhouse, respectively.
Fig. 12. Normalised turbulent kinetic energy kj = 12[ {u
′2
j,t + v
′2
j,t + w
′2
j,t }U
2 o
t] × 100 distribution measured in section II. The values are expressed as percentages.
4.4.2. Turbulent energy dissipation rate distribution Turbulent energy dissipation rate, ε, was calcu-
lated both from spectral density analysis and from Eq. 3 and Eqs. 7–9. The spatial distribution of
ε obtained by least-squares analyses of sections II
Fig. 13 and I not shown followed the distribu- tion of turbulent kinetic energy in both the sections.
However, while the order of magnitude of varia-
Fig. 13. Distribution of the energy dissipation rate ε m
2
s
−2
of velocity component u in section II.
tions in ε was approximately the same in the two sections, the rate of turbulent kinetic energy was ap-
proximately five times greater in section II than in section I.
4.4.3. Integral length and time scales Integral length scales of turbulence Table 2 show
size of eddies in the flow field for cross-sections I and
T. Boulard et al. Agricultural and Forest Meteorology 100 2000 169–181 177
Table 2 Integral length scale of the three velocity components outside
position 0 and inside positions 1 to 24 the tunnel at sections I and II
Positions Section I
SectiomII integral length
integral length scale m
scale m L
int,u
L
int,v
L
int,w
L
int,u
L
int,v
L
int,w
8.97 13.03
0.59 8.97
13.03 0.59
1 0.29
0.71 0.10
0.22 3.08
0.08 2
0.17 0.99
0.33 1.27
2.46 0.36
3 0.28
0.59 0.32
8.73 3.76
0.61 4
1.40 0.43
0.10 1.09
0.45 0.11
5 0.53
0.48 0.14
5.96 0.60
0.41 6
0.44 0.58
0.42 5.30
1.02 0.54
7 0.85
0.68 0.08
1.05 0.48
0.09 8
0.56 1.15
0.19 0.78
0.23 0.21
9 0.88
0.86 0.31
1.07 0.31
0.51 10
0.94 0.72
0.27 0.58
0.47 0.11
11 0.89
0.65 0.14
0.94 0.31
0.16 12
0.70 0.63
0.33 0.75
0.73 0.22
13 0.60
0.60 0.22
1.32 0.35
0.20 14
1.74 0.87
0.15 1.46
2.16 0.13
15 0.83
0.66 0.09
2.47 0.94
0.08 16
1.01 0.43
0.24 0.87
0.65 0.28
17 0.77
0.42 0.79
1.01 0.89
0.24 18
0.98 0.69
0.25 1.76
0.79 0.39
19 2.62
1.45 0.07
1.23 0.39
0.07 20
2.81 1.08
0.24 0.74
0.34 0.27
21 0.46
3.82 0.20
0.56 3.38
0.21 22
0.23 1.19
0.77 2.13
1.89 2.07
23 0.50
0.94 1.25
1.62 0.82
1.35 24
0.22 0.47
0.34 0.85
2.90 0.57
Min 0.17
0.42 0.07
0.22 0.23
0.07 Max
2.81 3.82
1.25 8.73
3.76 2.07
Mean 1.19
1.36 0.32
2.11 1.70
0.39
Fig. 14. Integral length scale L
int,u
m distribution of velocity component u in section II.
II. It should be noted that the mean integral length scales for the u, v and w directions were always higher
than the path distance of the sonic anemometer, and was consequently only slightly modified by our mea-
surement system. The integral length scale of the u velocity component decreases strongly from the jet in-
side the North vent opening, where it reaches 8.7 m - the same value as for outside. Towards the interior of
the tunnel, the turbulence is characterised by smaller eddies, with integral length scales ranging, on aver-
age, between 1.8 and 0.38 m in section II and only be- tween 0.87 and 0.3 m in section I. The distribution of
the integral length scale in the u-direction in section II is shown in Fig. 14.
The time required for an eddy to flow past a fixed position may be characterised by the integral time
scale. Integral time scales of velocity for u, v, w di- rections were on average similar in both, sections I
and II, with higher values confined close to the roof measurement positions Nos. 14 and 18 and the soil
surface positions no. 15 and 19 in section II, and between the northern wall and the soil surface point
Nos. 22 and 23 in section I.
4.4.4. Microscale of turbulence The microscale of turbulence in the u-direction
ranged between 0.012 point No. 9 in section I near the roof mid-way between two openings to 1.12 point
No. 6 in section II in the windward opening Fig. 15. It is much larger in the jet situated in the windward
opening and decreased as air flowed inside the tunnel. The distribution of average air velocity and microscale
of turbulence were similar, as shown by the linear de- pendence of λ on ¯
u λ
u
= 0.334 ¯u + 0.056, R
2
= 0.97,
178 T. Boulard et al. Agricultural and Forest Meteorology 100 2000 169–181
Fig. 15. Microscale λ m distribution of velocity component u in section II.
48 points in section II. An equivalent dependence was earlier signalled by Heber et al. 1996 in a
barn.
4.4.5. Energy spectra Comparison of the energy spectra of the external
wind Fig. 16, in the vent opening at position No. 3 Fig. 17 and that inside the tunnel at position No. 23
in section I Fig. 18, show that the air current in the windward opening was the most turbulent, followed
by the outside wind. The lowest values were found at position no. 23 between two openings. All locations
had similar spectral levels at higher frequencies in the dissipation region. However, the behaviour at lower
frequencies was quite divergent. In the vent opening, spectral densities at lower frequencies followed the
dominance of outside conditions. Most positions with low average air speed showed very similar curves
for u-, v- and w-components see position No. 23,
Fig. 16. Spectral energy distribution of the wind at a height of 1.65 m outside the greenhouse tunnel.
section I, with a spectral decay rate correspond- ing to the high frequency spectral energies equal to
about −53, as it is normally the case for isotropic turbulence.
5. Discussion
