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USING SODAR IN THE STUDY OF WIND FIELD OVER MOSCOW .
*
G. Kurbatov
Moscow State University, Physical Faculty
In examinations of a urban microclimate the main attention is given, " to an island of heat ", performances of
a turbulence and height of a stratum of intermixing, and also measurings of concentrations of contaminatings. Less
operations is devoted to a field of a wind, though the wind streams strongly influence accumulation and allocation of
polluting impurities from urban of radiants. Usually velocity of a wind inside cities is measured in boundary layer [1].
Only in few cities, where there are meteorological towers, measurings vertical lateral views of velocity of a wind were
carried out.
In limits of urban building the convergence of a wind stream, infringement logarithmical of a lateral view of
velocity, magnification of height of the inferior jet flow is observed. The degree of development of such features
depends on a climatic band, orography of terrain, season and synoptic situation, and also from the performances of
the city (its area, density and height of building, etc.); therefore individual performances of a field of a wind in
different cities strongly differ.
From a point of view of local wind circulation Moscow is one of the least investigated cities among other
large cities of a world. Therefore in 2002 on atmospheric division of physics faculty Moscow State University (MSU)
and in Institute of physics of an atmosphere by. And. M. Obuhova (IAP RAS) the program of share examinations
designed which provides regular ultrasonic measurings of vertical lateral views of velocity of a wind in region of an
arrangement MSU and at centre of Moscow.
Principal physics of ultrasonic sondage of an atmosphere
The mechanism of a dispersion of a sound by an atmospheric turbulence
The ultrasonic detection and ranging of an atmosphere grounded on a volumetric dispersion of waves of a
heard gamut by turbulent inhomogeneities of meteorological parameters. The phase velocity of a sound c is
r
determined by a Kelvin temperature of air T and projection of velocity of a wind v to a normal line to front of a sound
wave
r r
k |k | :
r
k
c = (γRT/µ) 1/2 +
r r r
v ⋅ k | k |,
(1)
- wave vector, R - gas constant, γ - relation of heat capacities of air at fixed pressure and volume, µ molar mass of air.
r
v
The atmospheric turbulence calls fluctuations T and
, that gives in occurrence of casual inhomogeneities
of an index of refraction n ' = c0 /c - 1 (c0 - medial velocity of a sound). The reference frequencies of turbulent
fluctuations in an atmosphere are much lower than frequency of a heard sound. Therefore sound is diffused on as the
though frozen inhomogeneities which are carried away by a wind stream. The inhomogeneities of an index of
refraction in an atmosphere are rather small n ' < 10-2 and the intensity of a dispersion on random inhomogeneities is
small. Owing to a constructive interference, the dispersion amplifies in determinate directions, if the inhomogeneities
are periodic, and is satisfied Bregg’s condition:
(2)
lt = λ (2sin ΘB).
Here lt - reference gauge of inhomogeneities, λ - length of a sound wave, ΘB a Bregg’s angle (angle of
indicence equal to half of a scattering angle θ). As the energy distribution of turbulent inhomogeneities in an
atmosphere is continuous, always will discover of a spectral builder of a turbulence K=2/lt satisfying to a requirement
(2), which will determine intensity of a dispersion of a wave with length λ on a angle θ.
Intensity of a dispersion
The quantitative performance of intensity of a dispersion is the effective section σ (θ), having dimensionality
m -1 and equal to that share of power of radiation, which is diffused from single volume in a single spatial angle in a
direction θ. Monin [2] and Tatarsky [3] have expressed σ (θ) through a linear combination of spectral densities of
fluctuations of temperature, ΦT (K), and velocity of a wind, Φv (K):
 Φ (K ) Φ (K )
θ
σ (θ ) = 2πk 4 cos2 θ  T 2 + v 2 cos2  .
c0
2
 4T0
(3)
Here c0 and T0 - average value of velocity of a sound and Kelvin temperature of air, k = 2π/λ - wave number.
Argument of spectral densities K (the module of a vector of a dispersion) represents the module of a difference of
wave vectors of impinging and dispelled waves:
r r
K = | k − k s | ≡ 2k sin(θ / 2) .
(4)
On the basis of qualitative viewing, reduced above, the formulas (3) and (4) allow to use for calculation σ (θ)
a Kolmogorov spectrum of a locally - isotropic turbulence. Really, for a heard sound and wide gamut of scattering
angles reference gauge of scattering inhomogeneities lt =2π/K lays in a so-called inertial interval, L0 > lt > l0, where it
0
is possible to consider a turbulence as isotropic. For audio frequency 2 kHz an inverse (i.e. under a angle 180 ) the
dispersion happens on inhomogeneities to the reference sizes ≈ 8,5 cm.
*
Corresponding author address: Mr Gegory Kurbatov Atmospheric Division, Physics Faculty Moscow State University 119899 Moscow, Russia
The spectral densities
of temperature,
C
2
T
Φ T (K )
and
, and velocity of a wind,
C
Φ v (K )
2
v
in an inertial interval express through structural parameters
[3].
Section of a dispersion:
σ (θ ) = 0,03k
13
θ −11/ 3
CT2 Cv2
θ
2 
(sin )
cos θ 0,54 2 + 2 cos2  .
2
2
4T0 c0

(5)
From angular dependence (5) follows, that the main body of power is diffused in a forward hemisphere, the
dispersion on a angle θ = 900 does not happen, and the dispersion on a angle θ = 1800 happens only on temperature
inhomogeneities.
Frequency of a dispelled signal
The motion of scattering inhomogeneities which are carried away by a wind stream with velocity
Doppler detrusion of frequency of a dispelled signal, fs, concerning frequency of an incident wave, f [4]:
fD ≡ ( fs − f ) =
1
2π
r
v , gives in
r r r
(k s − k ) ⋅ v .
(6)
The measuring of frequency of a dispelled signal enables definitions of a projection of velocity of a wind on a
direction of a vector of a dispersion
r r
r
K ≡ (k s − k ) .
Ultrasonic locators (sodars)
In the monostatic plan of sodar radiation and the reception of a sound is carried out the same sound
antenna, i.e. are used "inverse" a dispersion (on a angle θ = 1800). For a backscattering of the formula (6) and (5)
acquire a simple view:
c
0
σ (180o ) = 0,004k 1 3 CT2 T02 v r = f D 2 f
,
,
(7)
vr - projection of velocity of a wind to a direction of a beam of a locator. In three-component monostatic
sodar radiation and the reception of a sound is yielded in vertical and in two oblique directions (unfolded under a
angle 900 on an azimuth), that allows to measure a complete vector of velocity of a wind. The continuous reception of
2
an echo - signal after dispatching a sound impulse gives vertical lateral views CT and velocities of a wind.
Monostatic Doppler sodar "Echo - 1D" has 3 acoustic antennas placed in the sound shields. A type of the
antenna is horn speaker in parabolic focus. The antennas are mounted on the building roof, at the height of about 40
m above the underlying surface. The sodar circuit, and the table of parameters are given in a fig. 1.
The strip
amplifier,
equaliser
devergense
Aerial the
amplifier
The block of
measurement of
amplitude of a signal
Tilt of
antennas
?
24
Carrying
frequency
1700 Hz
Consecutive connection
of aerials. Switching
reception - transfer
The amplifier
of capacity
The block of
measurement Doppler’s
shift of frequency
The interface of input,
micro-computer
Wave- Electrical
length
power
0,2 m
100 W
Output
power
3W
The block of
generation and
synchronization
Fig. 1.
Hmin
Hmax
Resolution
50 m
800 m
25 m
Time of
measurement
20 sec
Time of
averaging
1 - 60 min
Visualization of turbulence structure
Echograms of scattered signal amplitude in "attitude - time" coordinates give an evident picture of ABL
turbulence structure and its dependence on atmospheric stratification. An example of such echogram, received by an
Echo - 1D sodar, is presented on a fig. 2.
Fig. 2
Measurements of the wind speed
The examples of 30-minute averaged profiles of the wind speed and direction are presented on a fig. 3.
Fig. 3.
Profiles of the wind speed and the directions change strongly, both within day, and with synoptic situation
change.
Examinations of vertical structure of a field of a wind is the important part of study of the blanket and
individual performances of a microclimate of large cities.
Obtained earlier in IAP RAS the datas have revealed some idiosyncrasies of velocity of a wind above
Moscow. However, similar separate series of measurings in one item do not give sufficient reason for reliable
deductions. The carried out preparation and trials of the equipment for regular sodar’s measurings of lateral views of
a wind in two items in territory of Moscow will ensure more convincing statistical datas, which are supposed to be
used for an estimation of potential of contaminating of city both model operation of allocation and transport of
impurities in its air pool.
REFERENCES
1.
2.
3.
4.
Landsberg, H. E., 1981:The Urban Climate. Geophysics Series, 28, Academic Press
Monin, A.C., 1962, Characteristics of the scattering of sound in the turbulent atmosphere. Sov. Phys.
Acoust., Engl. Transl., 7, 370-373.
Tatarskii, V.I.,1971, The Effects of the Turbulent Atmosphere on Wave Propagation. Transl. from Russian
(Jerusalem: Israelien Program for Scientific Translation).
Blokhintzev, D.I., 1981, The Propagation of Sound in an Inhomogeneous and Moving Medium (In Russian),
Moscow, Nauka.