170 T. Boulard et al. Agricultural and Forest Meteorology 100 2000 169–181
investigated the detailed temperature and air-flow patterns under conditions of free convection in a
greenhouse equipped with roof openings. All these numerical studies require further empirical validation
particularly in the case of turbulent characteristics, which represent the most critical factors to take into
account in simulations Mohammadi and Pironneau, 1994.
Further insight into the turbulent air flow and asso- ciated sensible heat exchange in a naturally ventilated
bi-span greenhouse was provided by measurements with an ultrasonic anemometer operated in a horizon-
tal plane at the level of continuous openings Boulard et al., 1997. Similar data is lacking for tunnel-type
greenhouses, a fact that provides the primary motiva- tion for the current study. This paper deals with the
characterisation of mean and turbulent air flows and patterns of air temperature and humidity inside a clas-
sical 8-m wide tunnel house. The tunnel under study was sheltered upwind by other tunnels and oriented
perpendicularly to the dominant wind direction as is usual in this region. Natural ventilation was provided
by means of discontinuous openings placed every 4 m on either side of the tunnel. Such conditions are
common in southern France and in all other Mediter- ranean regions where the use of tunnel houses is
widespread.
The present study builds upon measurements of mean and fluctuating air speeds, and fluctuations in
temperature and humidity to: 1. characterise patterns of air flow and the microcli-
matic heterogeneity in vertical cross sections of a tunnel; and
2. evaluate the mean and turbulence characteristics of air velocity components.
2. Theory
For the convenience of the reader, we present a brief summary of the equations used in our anal-
yses. For more details, the reader is referred to Kaimal and Finnigan 1994 for a general review
of boundary-layer turbulence and to Heber and Boon 1993 and Heber et al. 1996 for discus-
sion of the patterns of air flow and turbulence in barns.
2.1. Mean and turbulent air velocities Mean air velocity measured over a period 1t is:
u = 1
1t Z
1t
u dt
1 where u, the instantaneous air velocity, is represented
using the Reynold’s decomposition: u = ¯
u + u
′
2 as the sum of time-mean value ¯
u and a fluctuating
component u
′
. 2.2. The discrete energy spectrum
The structure of turbulence is commonly investi- gated by means of frequency domain analysis of the air
velocity data. A large data record can be conveniently reduced to a spectrum of velocity fluctuations called
the discrete energy spectrum Ef m
2
s
−1
. Its density, often plotted vs. frequency on a log–log graph, pro-
vides even for indoor conditions a useful description of the air flux components Lay and Bragg, 1988.
The energy spectrum can be integrated over all fre- quencies f Hz for all variance spectra to yield the
total variance: σ
2
= Z
∞
Ef df
3 If Rt is a decaying oscillating function determined
by the correlation between air velocities at a fixed position at two different instants, t
′
and t
′
+ t Rt =
u
′
t
′
u
′
t
′
+ t σ
2 u
4 Pasquill and Smith 1983 defined the integral turbu-
lence time scale as the integral of Rt over time from zero to the first zero crossing, t
int
, such as Rt = 0:
t
R
= Z
t
Rt dt
5 and L
int
, the integral turbulence length scale as: L
R
= | ¯ u| t
R
6
T. Boulard et al. Agricultural and Forest Meteorology 100 2000 169–181 171
2.3. Turbulent kinetic energy k and dissipation rate ε
The microscale of turbulence λ is a measure of the dimension of eddies mainly responsible for the
dissipation of turbulent energy into heat.
λ = ¯
u
2
σ
2
2π R
∞
f
2
Ef df
0.5
7 If k, the total turbulent kinetic energy, is calculated as
k = 1
2 σ
2 u
+ σ
2 v
+ σ
2 w
8 where σ
u
, σ
v
, σ
w
, respectively, are the standard devi- ations of the velocity fluctuations in the x, y, z direc-
tions, the turbulence energy dissipation rate is: ε = k
32
λ
−1
9
3. Experimental setup
