In order to describe reasonably the turbulent characteristics of wind velocity fluctuations near the surface of cultivated field, the empirical turbulent energy spectra are introduced as follows:
F
u(N/N
0u)=2/3N/N
0u/{1+(N/N
0u)
2}
4/3 and F
w(N/N
0w)=2/3N/N
0w/{1+(N/N
0w)
2}
4/3, where
N denotes the passage-frequency of turbulon, and
N0u and
N0w do those of the largest (or coupling) turbulon for
u-and
w-component respectively. These spectra represent the -5/3 power relation at large
N and the 1 power at small
N.
By means of the partial integration and the Fourier transform of the above spectra, the influence of the change in averaging procedure on the observed turbulent energy and the functional form of the Eulerian correlation coefficient of velocity fluctuations in particular for the range of not necessarily small process time
t, are obtained. These theoretical results are compared to those obtained in practical observations reported in the last paper (part 3) of the same authors, and the particular characteristics of the latter are shown to be explained as follows:
(1) When the averaging-time T* is sufficiently larger than the passage-time of the largest turbulon, the change in
T* does not cause any remarkable increase in ‹u′
2›, whereas when
T* is sufficiently smaller than the passage-time of the largest turbulon, ‹u′
2› increases with
T*
2/3.
(2) When the averaging-time is too much large compared to the passage-time of the largest turbulon, sometimes the contributions of the larger-scale turbulons caused topographically, geographically, thermally and so on, to the observed turbulent energy ‹u′
2› predominate. These contributions seem to cause the vertical gustiness distribution independent of height, and to give rise to the result of ‹u′
2›
1/2=const.
U(z)=const. log (
z-d), where
z, d and
U(z) mean the observation height, the zero-plane displacement and the mean wind velocity at the height
z, respectively. However, according to the conditions whether the former be sufficiently smaller than the latter or be of the just same order, the vertical gustiness distribution increases with or independent of the height. Therefore, any simple empirical laws of gustiness distribution seem difficult to be universal.
(3) In order to obtain the Eulerian correlation coefficient corresponding to the well-known form of
R(t)=1-const.
t2/3, the process-time
t is much smaller than the passage-time of the largest turbulon. However, when the former is much larger than the latter, the functional form of
R(t) is rather approximated fairly well by 1-const.
t1/3, where
R(t)≤0.4.
(4) The practically observed results seem to suggest that the passage-time of the largest turbulon is almost given by 10(
z-d)/U(z). The characteristic time
Tz≡(
z-d)/U(z) is tentatively called the equivalent passage-time of wind at the height
z.
Furthermore, making use of these results, the necessary response time *
T of the anemometer and the necessary length
T* of averaging time for the measurement of the intermediate turbulon range (or the inertial subrange) are suggested to be given by *
T=(
z-d)/U(z) and
T*=100(
z-d)/U(z) respectively.
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