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325
Izvestiya, Atmospheric and Oceanic Physics, Vol. 41, No. 3, 2005, pp. 325–341. Translated from Izvestiya AN. Fizika Atmosfery i Okeana, Vol. 41, No. 3, 2005, pp. 360–377.
Original Russian Text Copyright © 2005 by Rusakov.
English Translation Copyright © 2005 by
åAIK “Nauka
/Interperiodica” (Russia).
INTRODUCTION
The fundamental concepts of turbulence are now
being revised. This is reflected, on the one hand, in the
detection of coherence and self-organization in devel-
oped turbulence [1–3] and, on the other hand, in the evi-
dence of the possibility that chaos may occur in a non-
linear dynamic system with even a few degrees of free-
dom [4, 5]. The equations of fluid dynamics are
nonlinear, and the calculated number of degrees of free-
dom for flows, for example, in the atmospheric bound-
ary layer exceeds
10
16
–10
20
. This means that there must
be purely chaotic motions in the atmosphere. However,
the presence of organized (coherent) structures in atmo-
spheric turbulence and the significance of their influ-
ence on flow dynamics are becoming more and more
evident [6].
The semiempirical theories of turbulence [7] and
statistical fluid mechanics [6] provide no description of
physical mechanisms that could explain the origin of
organized structures and preferred wave numbers in a
turbulent medium. An apparent order in the flow struc-
ture is detected by analytical and numerical solutions of
hydrodynamic equations in the analysis of transition to
turbulence [8–10] or in large-eddy simulation modeling
[11]. In the former case, only the initial stage of turbu-
lence with a few degrees of freedom is considered, and
in the latter, the number of degrees of freedom is
reduced by choosing a grid step that provides the stabil-
ity of the solution. However, there is no physical sub-
stantiation of the value of a step. Therefore, the experi-
ment again becomes of primary importance in the study
of turbulence.
There are problems with data interpretation in the
experimental study of a thermally unstable atmospheric
boundary layer (ABL). Field experiments [12–17]
demonstrate a key role of large-scale eddies in heat and
momentum transfer in the ABL. However, the spectra
of meteorological parameters are usually averaged so
that they become smooth and do not reflect important
eddy features [18]. The main goal of most observations
was to check consequences of the Monin–Oboukhov
similarity theory, which disregards the dynamics of
large eddies and mutual coherence of motions in differ-
ent layers of the convective ABL.
Even early satellite pictures showed that clouds of
convective origin are often aligned in cells or rolls
[19]. Somewhat later, Bénard-like patterns, which
were 5–10 km in diameter and 1–2 km in height, were
observed regularly with high-power radars in clear air
[20]. The patterns consisted of thermal-like circular
structures on the order of several hundred meters in size
that moved upward around the periphery of the cells (or
from the center). In an analytical description of such a
flow, turbulent analogues were used instead of the
molecular coefficients of eddy viscosity and diffusivity
[21, 22]. In [23], the assumption was made about their
self-adjustment to the values at which only first modes
of convective instability should occur. This hypothesis
was further developed in [24, 25]. Unfortunately, a
series of studies of this kind was in no demand in the
mid-1970s. At present, a cellular structure of the con-
vective ABL, let alone the presence of preferred wave
numbers in its organization, has as yet no strong exper-
imental support and has been ignored by some authors.
We consider this problem in more detail.
Coherent Oscillations of Meteorological Parameters
in the Convectively Unstable Atmospheric Boundary Layer
Yu. S. Rusakov
Taifun Research and Production Association,
pr. Lenina 82, Obninsk, Kaluga oblast, 249020 Russia
e-mail: rusakov@typhoon.obninsk.ru
Received January 15, 2004; in final form, July 6, 2004
Abstract
—Long-term observations of variability of meteorological parameters in an unstably stratified atmo-
spheric boundary layer (ABL) were carried out using a measuring complex mounted on a tall meteorological
tower and a ground-based network of high-sensitivity pressure sensors. Regular coherent oscillations of mete-
orological parameters under developed convection at a single frequency were first determined experimentally
using a special procedure of bandpass filtering and in-phase analysis. On some days, the oscillation period var-
ied from 20 to 40 min. These oscillations encompassed the surface layer, the free-convection layer, and the
mixed layer and resembled self-oscillations. The periodicity was most distinct in the evolution of the product
of the mixed-layer vertical wind velocity and surface pressure after their filtering in the given frequency range.
A phenomenological description of the proposed structure and of the mechanism of airmass exchange in the
convective ABL is given.
326
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 41
No. 3
2005
RUSAKOV
The hypothesis of coherence of small-scale eddy
motions with height [12] was becoming increasingly
realistic with the advancement of studies of the convec-
tive ABL. The coherence is most apparent in a synchro-
nous occurrence of similar large-scale asymmetric out-
liers (ramp structures) in the temperature and wind-
velocity series at some heights (starting in the surface
layer) [14, 17]. In the scheme proposed in [16], the sur-
face-layer thermals and jets merge in the mixed layer
into mesoscale upward flows (thermal walls), which
resemble the walls of open polygonal cells filling the
entire ABL. At the same time, not a word is said in [16]
about a cellular structure of the ABL.
The hypothesis that ramp structures are quasi-peri-
odic has already been used in [14, 15] in analytical der-
ivations. In [16], on the basis of analysis of the trans-
verse wind component, it is assumed that the updrafts
are probably grouped in a regular, periodic way. The
runs of other wind velocity components did not show
any definite periodicity. It is argued in [17] that the sur-
face-layer ramp structures are certainly associated with
convection cells. At the same time, visual analysis of
many other runs, according to [17], detects no periodic-
ity in the origin of structures. Only sometimes (once or
twice an hour) have the trains of 3–5 structures with a
50-s period been observed.
In the cycle of works on acoustic sounding of the con-
vective ABL (for example, in [26]), it is shown that the
spectra of vertical wind velocity and atmospheric reflec-
tivity have maxima at periods of 6–9 and 20–30 min. The
origin of these maxima is supposedly attributed to
buoyancy waves that form at the top of the troposphere.
In studies of surface-pressure variability, in particular
in [27], it is shown that pressure fluctuations often
resemble coherent oscillations, mostly with periods
from 20 to 40 min. In [27], only those cases were stud-
ied in which the oscillations were observed visually,
having an amplitude of about 30–50 hPa. According to
[27], these oscillations are due to convective storm
activity.
Thus, modern notions of turbulence, including the
atmosphere, admit the origination and existence in it of
large-scale structures that may exhibit frequency and
wave selectivity. Forty years ago, however, turbulence
was treated in another way. Ten years before coherent
structures were recognized, measurements of tempera-
ture and wind-velocity fluctuations under convection
carried out at a 300-m meteorological tower in the city
of Obninsk had detected steady maxima in the spectra
of temperature, wind velocity, heat fluxes, and friction
in the turbulent convective ABL. The coherence of
mesoscale fluctuations of wind speed or temperature
with height was then shown; the hypothesis of self-
adjustment of turbulence coefficients, which is still
important, was proposed; and the model of cellular con-
vection was detailed. An extensive cycle of works in
that period of time was summarized in monograph [28].
These studies have been extended recently in [29],
where a method is proposed for identification of cellu-
lar structures on the basis of the adaptation of the solu-
tion to the classical Rayleigh–Bénard problem for the
interpretation of the results of experiments conducted at
the tall meteorological tower. It is shown that, depend-
ing on the type of cell (hexagon, square, or convective
roll) and on how the cell is orientated relative to the
mean wind, the spectrum of vertical wind velocity
should contain up to three harmonics interrelated by
some formulas.
What is the objective cause of the lack of support
among researchers for the theory of coherent fluctua-
tions in the convective ABL? Probably, this is related to
the maxima observed in the spectra having low statis-
tics due to comparable periods and series length. The
energy of small-scale fluctuations in the lower part of
the ABL usually exceeds the energy of mesoscale fluc-
tuations, which probably reduces the significance of the
latter. Maxima in the spectra of individual parameters
are often not single and may be treated as being caused
by the influence of random eddies, nonstationarity, and
local orography on the flow. Moreover, there are some
problems in the application of a simplified cell model to
the description of the convective ABL. More important,
there is as yet no analysis of mutual coherence of fluc-
tuations of different meteorological parameters at
selected frequencies that provides strong evidence of an
organized structure of the convective turbulent field of
these parameters.
The purpose of this paper is an experimental study
of mesoscale fluctuations of wind components, temper-
ature, and surface pressure for determining the measure
of their mutual coherence in the convectively unstable
ABL and their possible periodicity. Note that we are
dealing here with the properties of a typical convective
ABL that are not related to synoptic processes, oro-
graphic features, or single significant events.
EXPERIMENTAL AREA, INSTRUMENTATION,
AND MEASURING TECHNIQUE
Experiments were performed at the tall meteorolog-
ical tower and in the adjacent areas in July–August
1997 and September 1999. The tower is located in a
gently rolling terrain typical of Russia’s middle zone, at
the center of Obninsk, 100 km southwest of Moscow.
According to [13, 16], the influence of such an under-
lying surface on the characteristics of the free-convec-
tion and mixed layers is insignificant. Wind speeds and
directions and air temperatures were recorded on a
computer once per second with a measuring complex of
the meteorological tower at heights from 2 m (8 m for
wind) to 300 m with 25- to 100-m intervals. The verti-
cal wind velocity was measured with a DAT-300 acous-
tic anemometer (Japan) at a height of 74 m, with an
ATsAT-3 acoustic anemometer at 121 m, and with a
bivane anemometer at 225 m. The last two instruments
were designed at NPO Taifun. The ATsAT-3 was not in
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 41
No. 3
2005
COHERENT OSCILLATIONS OF METEOROLOGICAL PARAMETERS 327
use in 1999. Surface temperatures and winds were mea-
sured at a meteorological site 150 m from the tower.
A more detailed description of the area and instruments
can be found in [28]. In addition, surface air pressure
was recorded at three sites with an accuracy on the
order of
10
–2
hPa in the frequency range from 0 to
10 Hz by sensors designed at the Space Research Insti-
tute, Russian Academy of Sciences [30]. In 1997, the
array of pressure sensors was an approximately equilat-
eral triangle with a side of 300 m, at the center of which
the tower was located. In 1999, the pressure sensors
were arranged at the vertices of a right-angled isosceles
triangle with 1200-m sides. Sensor N1 was mounted at
the measuring center 20 m from the base of the tower.
In 1999, acoustic sounding of the atmosphere was per-
formed simultaneously with tower measurements.
Of one and a half months of continuous measure-
ments in 1997, six diurnal series with typically convec-
tive conditions were selected, with all the sensors being
operated and no atmospheric fronts or precipitation.
The same number of series was selected for September
1999, during the Indian summer. The 1999 diurnal
series were smoothed with a moving average and fur-
ther decimated at 1-min intervals. The 1997 diurnal
series were smoothed and decimated with a 10-s step to
provide the required accuracy in measurements of the
phase difference of pressure fluctuations at the three
sites. The length of the 1997 series was limited by eight
hours to speed up the computations.
In this paper, the emphasis is on 150-min samples in
each series under developed convection. Table 1 shows
the dates and periods of measurement, 150-min average
characteristics of major meteorological parameters, and
their fluctuations. For the reasons given below and in
order to decrease the amount of data, the number of
parameters and characteristics in the table is reduced
relative to the total number of the quantities analyzed.
Beginning at a height of 120 m, the values of the mean
speed differed from one another by no more than 0.5 m/s
(except series 12, where the wind speed increased rap-
idly with height). A constant wind speed above the sur-
face layer is a typical indicator of unstable stratifica-
tion. The mean wind direction remained constant in
height within 10
°
, except series N8 with near-calm con-
ditions. The relative humidity in the samples varied
from 51 to 66%. The mean values of atmospheric pres-
sure were nearly equal. The table lists temperatures at a
height of 2 m. Because surface measurements of verti-
cal turbulent fluxes over a complex local terrain could
not be treated unambiguously, the degree of atmo-
spheric instability was estimated using Turner’s classi-
fication with the IEM correction [31] by the method of
network observations. By this classification, there was
strong to moderate instability of the ABL in series 1–4
and 8–10 and moderate to weak instability in the other
series. Table 1 also displays the convective ABL heights
for 1997 from daily radiosonde data at the town of
Sukhinichi, about 150 km southwest of Obninsk.
The column with turbulent characteristics in Table 1
displays standard deviations
σ
X
of the wind-velocity
modulus and the vertical wind component, temperature
at 225 m, and atmospheric pressure at site 1. For other
heights and sites, these values differed by no more than
a factor of 1.5. In addition, the vertical turbulent heat
and stress fluxes at 74 m normalized by the air density
are shown. It is known [12, 13] that the sign of turbulent
fluxes in the convective ABL reverses with height. Yet
the fact that the change of sign may already take place
at a height of about
0.1
Z
i
is somewhat unexpected.
However, this is unimportant for the subject of our
paper. Overall, it is evident that all the series were per-
formed under conditions of typical convection with a
different degree of development, and characteristics of
the sensors and of the meteorological tower area corre-
sponded to the problem of detection of coherence and
periodicity in the convectively unstable ABL.
METHOD OF IDENTIFICATION
OF QUASI-MONOCHROMATIC OSCILLATIONS
IN THE ABL
This method is based on the solution of two scien-
tific problems. One problem is a search for a parameter
in which an organized structure of the convective ABL
is most clearly defined. The second problem is to
develop a procedure of detection of the frequency–time
variability of this parameter.
The most characteristic feature of thermal convec-
tion over a flat underlying surface is an alternation of
intense updrafts and downdrafts. Unlike the spectra of
temperature, horizontal wind speed, wind direction,
and pressure, the vertical velocity spectra are not dom-
inated by low-frequency fluctuations (about an hour or
more) and these fluctuations are, as a rule, negligible.
Our data and observations [12, 14, 26] usually show a
reasonable consistency of mesoscale (5–40 min) verti-
cal motions in the free-convection and mixed layers.
The structure of the convective ABL appears to be well
reflected in these motions.
Unlike the temperature and wind sensors, which
respond to local characteristics of the turbulent flow,
the pressure sensors integrate the influence of the air
lying above. Large-scale motions encompassing the
entire ABL must also be manifested in the variability of
atmospheric pressure. The use of several ground-based
sites of pressure measurement makes it possible to esti-
mate parameters of large-scale inhomogeneities and the
phase velocity of their propagation, for example, buoy-
ancy waves in the stable ABL [32]. Under the condi-
tions of typical convection with no storm activity, how-
ever, quasi-monochromatic oscillations in the evolution
of atmospheric pressure are visually indiscernible.
It is assumed that the most clearly organized struc-
ture of the convective ABL should be manifested in the
product of vertical wind velocity and surface pressure
after their filtering in the corresponding frequency
328
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 41
No. 3
2005
RUSAKOV
band. Further analysis has confirmed a justification of
the choice of this quantity as a basic parameter.
The filtered time series in narrow frequency bands
provided the basis for the analysis performed. To
improve spectral resolution and to limit edge effects,
the diurnal (8-h) series of a meteorological parameter
was used from which the mean and the linear trend
were removed. In 10% of data at the start and the end of
the series, the fluctuation amplitude was linearly sup-
pressed so that it would be zero at the ends of the series.
Table 1.
Integral characteristics of the samples with developed convection in the ABL
No. 123456789101112
Date 24.07 25.07 28.07 8.08 21.08 24.08 5.09 6.09 7.09 8.09 9.09 10.09
Time, h 11.14 14.36 13.18 11.07 13.5 13.19 13.96 14.79 12.79 13.12 12.12 14.46
Means
V
8
2.3 1.7 2.4 1.5 2.2 1.5 2.2 0.8 0.9 0.8 1.5 3.5
V
225
6.1 3.4 4.5 2.5 4.4 2.9 3.9 0.8 1.6 1.7 3.3 6.7
f
225
108 136 204 337 244 235 322 50 109 176 280 329
T
2
24.2 26.1 27.1 21.9 22.9 25.8 21.5 22.2 22.5 22.7 22.7 18.6
P
1
995 986 989 1002 1002 1000 988 987 986 985 982 983
B
t
576623100342
B
n
464613000332
F
Cu, Ac Cu, Ci Cu, Ac Cu Cu, Ci Cu Ci Cu, Ci Cu, Ci Cu
Z
i
1400 1600 1700 1500 1800 –––––––
n
111122211122
Turbulent characteristics
σ
w
0.69 0.52 0.67 0.38 0.45 0.6 0.42 0.22 0.32 0.41 0.41 0.52
0.38 0.38 0.52 0.28 0.30 0.42 0.33 0.17 0.30 0.35 0.34 0.40
0.30 0.32 0.44 0.23 0.30 0.36 0.28 0.16 0.25 0.28 0.28 0.33
σ
V
1.46 1.10 1.18 0.85 0.89 0.91 0.81 0.45 0.57 0.67 1.03 1.02
0.91 0.74 0.76 0.64 0.57 0.51 0.63 0.38 0.34 0.51 0.62 0.86
0.74 0.61 0.73 0.52 0.51 0.48 0.53 0.33 0.30 0.46 0.56 0.79
σ
T
0.59 0.45 0.85 0.50 0.36 0.33 0.43 0.51 0.44 0.37 0.62 0.37
0.14 0.26 0.20 0.19 0.16 0.15 0.06 0.37 0.23 0.20 0.15 0.1
0.12 0.21 0.18 0.18 0.12 0.15 0.07 0.31 0.20 0.20 0.14 0.09
σ
P
15.6 56.0 14.1 8.8 33.8 47.8 34.3 31.4 24.8 21.2 26.7 10.3
4.46 5.87 4.63 3.60 3.17 3.14 2.02 3.07 2.06 1.72 2.66 2.45
3.56 5.01 4.06 2.90 2.81 2.56 1.82 2.52 2.04 1.71 3.22 2.23
〈
w
74
×
T
74
〉
0.06 0.07 0.11 0.03 0.07 0.08 0.04 –0.07 0.01 –0.02 – 0.04 0.06
〈
w
74
×
V
74
〉
–0.50 –0.17 –0.24 –0.04 –0.09 –0.08 –0.07 0 0 0.06 0.06 0.04
T
m
34.9 28.6 21.8 25.3 28.6 24.7 20.8 28.6 25.9 24.7 37.5 36.6
Note: No. is the series number;
V
,
f
, and
T
are the wind speed (m/s) and direction (deg) and air temperature (deg) at the height given in the
subscript;
P
1
is the surface atmospheric pressure (hPa) at site 1;
B
t
,
B
n
, and
F
are the total and low-level cloud amounts and cloud
type;
Z
i
is the ABL height (m);
n
is the Turner–IEM stability class [31];
σ
X
is the standard deviation of vertical wind velocity (m/s),
wind-velocity modulus (m/s), temperature (deg), and surface pressure (Pa) calculated for the entire sample without limitation of the
frequency band; is the same but for periods of 5–50 min; and is the same but calculated over power spectra for their filtering
in the range 5–50 min. The subscript
X
denotes the parameter for which the standard deviation is calculated (measurements at site
1 are for
P
, and measurements at 225 m are for
w
,
V
, and
T
).
w
74
×
T
74
and
〈
w
74
×
V
74
〉
are turbulent fluxes of heat (m deg/s) and
frictional stress (m
2
/s
2
) in the frequency band 0.5–2
×
10
–4
Hz.
T
m
is the period (min) in which a maximum appears in the cross
spectra of
w
225
and
P
1
.
σw
'
σw
''
σV
'
σV
''
σT
'
σT
''
σP
'
σP
''
σX
'
σX
''
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
Vol. 41
No. 3
2005
COHERENT OSCILLATIONS OF METEOROLOGICAL PARAMETERS 329
The series was symmetrically padded at both ends with
zeros so that the number of readings in it would be
equal to the nearest power of two. The fast Fourier
transform was performed. A group of adjacent harmon-
ics was selected in the frequency range with the aid of
a sine-squared window (Hahn window [33]). The
inverse Fourier transform was done. The frequency
window was shifted by a quarter-octave, and the inverse
Fourier transform was performed again. To compensate
the weakening of harmonics due to their weighting, the
adjacent frequency windows were half-overlapped.
There were 40 harmonics in the 20-min window for
diurnal series and 16 for the 8-h series. The data pro-
cessing technique is entirely identical to wavelet filter-
ing [34], and the result of its application is equivalent to
the use of an array of analog quarter-octave filters.
The technique was tested on the model signals
(group of six sinusoids with incomparable frequencies,
different modulations, and superimposed noise) to
determine its amplitude, phase, and dynamic character-
istics and sensitivity to noise. A principal advantage of
the technique was a nearly ideal decomposition of the
signal into components; i.e., the algebraic sum of the
filtered signals within an accuracy up to 1% (3% under
strong nonstationarity) was equal to the original signal
if its spectrum was limited by the frequency band. The
main disadvantage was that the energy of harmonics on
the periphery of the frequency window was strongly
suppressed because of “frequency weighting.” That is,
the signal was decomposed into the sum of dependent
harmonics, and the square of this sum was on average
one-quarter less than the variance of the original pro-
cess. A common drawback inherent in all spectral esti-
mates was “leakage” of energy from the low-frequency
region and expansion of the input signal in the fre-
quency–time region according to the uncertainty prin-
ciple [35].
The bandwidth was
10
–2
–10
–4
Hz. A total of 26 data
series were obtained for each run, which were filtered
in adjacent quarter-octave frequency bands. Of the fil-
tered data series, 150-min samples corresponding to
conditions of developed convection were selected in
accordance with the dates given in Table 1. From the
samples, the power spectrum was calculated as half the
variance of fluctuations in the corresponding quarter-
octave frequency band, the coherence was determined
on the basis of the coefficient of correlation between the
filtered series, and the cross-spectrum modulus was cal-
culated as the mean product of the filtered series after
the removal of the phase shift between them.
APPLICATION OF THE METHOD
TO EXPERIMENTAL DATA
The power spectra of the basic meteorological param-
eters calculated from 150-min samples (900 readings
every 10 s) by the traditional method and by the proce-
dure proposed in this paper are compared in Fig. 1. The
experimental points at frequencies about 1/1300 Hz in
spectra 1 and 3 are averaged over three independent
harmonics, and in spectra 2 and 4, they are averaged
over 15 dependent harmonics (i.e., their cross correla-
tion within the sample is not zero). We can see that the
proposed method provides a better spectral resolution.
The fact that the maximum is not unexpected is evi-
denced by the occurrence of the maximum in the spec-
tra of independent samples of the vertical wind velocity
w
, temperature
T
at several heights, and surface pres-
~
~~
~
~
~~
~
10
–4
10
–3
10
–2
10
–4
10
–3
10–2
ω, Hz
0
0.1
0.2
0.3
S(ω) × ω, m2/s2
0
0.2
0.4
S(ω) × ω/σ'
12
34
w h = 74 m
w h = 121 m
w h = 225 m
V h = 225 m
T h = 225 m
P site 1
Fig. 1. Power spectra of the vertical wind velocity at h = 74 m, 121 m, and 225 m (1, 2) and -normalized power spectra of the
wind-velocity modulus, temperature at 225 m, and atmospheric pressure at site 1 (3, 4). Plots 1 and 3 are obtained by the traditional
calculation of the spectrum; 2 and 4 correspond to the spectrum with an improved resolution of narrow-band oscillations. Series N3.
σX
'
330
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS Vol. 41 No. 3 2005
RUSAKOV
sure P at several sites. The spectrum of the modulus of
wind velocity V has no local maximum in the selected
frequency region. A similar picture is typical of all the
series analyzed.
Analysis of the spectra has shown that the study of
meteorological fluctuations can be limited by frequen-
cies from 1/300 to 1/3000 Hz, because any regular and
power-significant changes in the vertical-wind velocity
in the layer of 74–225 m were absent outside this fre-
quency range. The spectra do not provide an unambig-
uous conclusion that fluctuations are periodic, but only
indicate the presence of disturbances (eddies) of a given
15.515.014.514.0 t, h
V8
V225
13.513.0
4 m/s
15 Pa
1.5°ë
2 m/s
P1
123
T2
T225
w74
w225
w121
Fig. 2. Illustration of the procedure of selecting a quasi-monochromatic signal by example of series N3. Time evolution of meteo-
rological parameters (1) before filtering, (2) after filtering in the range 5–50 min, and (3) after quarter-octave filtering in the region
of maximum correlation between w225 and P1.
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS Vol. 41 No. 3 2005
COHERENT OSCILLATIONS OF METEOROLOGICAL PARAMETERS 331
scale, which do not seem to be correlated in time. To
determine periodicity, the filtered signal should be
expanded in time and its phase should be taken into
account.
Figure 2 demonstrates the transformation of the sig-
nal after its wide-band and narrow-band filtering. As an
example, series N3 is used, in which the quasi-mono-
chromatic oscillations are relatively well expressed.
Another objective of the figure is to clear up a possible
cause of why the periodicity in the structure of the con-
vective ABL was not detected by many investigators.
Figure 2 shows the time variation of the horizontal (V)
and vertical (w) wind velocity, temperature T at a few
heights, and surface pressure P at site 1. The evolution
of the meteorological parameters filtered in the fre-
quency band 1/300–1/3000 Hz (2) and in the quarter-
octave band 1/1190–1/1420 Hz (3), in which there was
a maximum correlation of w225 and P1, is also shown.
Whereas a considerable portion of the fluctuation
energy at the selected frequencies is visually seen for w,
the same cannot be said about other parameters. Table 1
presents the standard deviations of the correspond-
ing parameters X after their filtering in the frequency
band 1/300–1/3000 Hz for all series. It follows from the
table that most of the energy of fluctuations of temper-
ature and, particularly, air pressure is contained outside
this frequency band. Therefore, one cannot expect a
visual similarity of the evolution of these parameters
and of their filtered values. This demonstrates that a
visual analysis of the series is usually not enough to
σX
'
1
2
Series N2
Series N3
3
4
19181716151413 17161514131211
Series N12
5
6
7
8
Series N9
Local time, h
Normalized fluctuation amplitude
–5
0
5
–5
0
5
Fig. 3. Time variation of -normalized fluctuations of (1, 3, 5, 7) vertical wind velocity w225 and (2, 4, 6, 8) surface atmospheric
pressure P1 filtered in the frequency bands 1/300–1/3000 Hz and ωm(1 ± 0.125) in four 6-h runs.
σX
'
332
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS Vol. 41 No. 3 2005
RUSAKOV
detect quasi-monochromatic signals in atmospheric
turbulence, and special filtering techniques are
required.
Figure 3 displays the time evolution of the vertical
wind velocity w225 (odd numbers) and air pressure P1
(even numbers) normalized by , which are filtered at
1/300–1/3000 Hz (thin lines) and in the quarter-octave
frequency band centered at ωm (thick lines). Hereafter,
ωm is the central frequency of a bandpass filter for
which there is a maximum in the correlation and coher-
ence of w225 and P1. Four 6-h samples with a 1-min
interval are shown, including the periods given in
Table 1. The frequency selectivity in the evolution of
the meteorological parameters was most distinctive in
series N2, N3, and N9. It is seen from the figure that the
selected quarter-octave bands contain a significant por-
tion of the energy of the w and P fluctuations in the
range of periods from 5 to 50 min. The vertical wind
velocity obviously contains, along with Tm = 1/ωm,
higher frequency scales of the fluctuations in the region
5–10 min. In the evolution of air pressure, the charac-
teristic scale of variability approximately coincides
with Tm. Moreover, the figure demonstrates that the
relation between the amplitudes of quasi-monochro-
matic oscillations of w and P is complicated. The fluc-
tuations of P at the frequency ωm usually appear during
the day, varying in amplitude by a factor of 3–4 on aver-
age. The oscillations in w persist for 3–5 h, varying in
amplitude by an order of magnitude or more.
The frequency selectivity and periodicity of the con-
vective ABL can be most clearly seen in Fig. 4. Isolines
of the modulus of the product of the quarter-octave fil-
tered w225 and P1 after removal of the mean phase shift
between them are shown for the same samples as those
in Fig. 3. As in Fig. 3, the abscissa is the local time and
the interval when the series was performed, and the
ordinate is the period T = 1/ω on a logarithmic scale.
Overall, 14 filtered time series filling the frequency
band from 1/300 to 1/3000 Hz were used. The contour
interval is 10% of the maximum product, 0.87 Pa m/s
for series N2, 1.02 Pa m/s for series N3, 0.33 Pa m/s for
series N9, and 0.25 Pa m/s for series N12.
A single frequency range dominates in series 2, 3,
and 9. In series 12, there are several selected frequency
regions. We see not only a strong interaction between
w225 and P1 at a given frequency, but also that this pro-
cess is periodic and extended in time. Figure 4, as the
previous figures, is in fact a qualitative illustration of
the frequency–wave selectivity in the convective ABL.
The arguments that leave no doubt about this conclu-
sion are discussed in the next section.
CROSS SPECTRA AND COHERENCE
OF METEOROLOGICAL VALUES
Figure 5 shows the plots of the frequency depen-
dence of the correlation between the vertical wind
σx
'
velocity w225 and surface pressure P1 and with other
basic meteorological parameters after their filtering in
the quarter-octave frequency band. Before being multi-
plied, one filtered sample from the pair was shifted so
as to remove the sample-mean phase shift between
them. In fact, these are the plots of the modulus of cross
spectra Wxy(ω) integrated in the quarter-octave fre-
quency band for the 150-min samples shown in Table 1.
The determining frequency for the plots was ωm at
which the filtered w225 and P1 had maximum correla-
tion. The values of Tm = 1/ωm for each series are given
in Table 1.
To make it easier to compare the spectra, the
abscissa is the binary logarithm of the frequency
divided by ωm, and the amplitudes of the spectra are
normalized by the product of the corresponding stan-
dard deviations . The values of (or ) for
each meteorological parameter were determined from
its power spectrum so that the sum of all 14 readings of
the spectrum in the range from 1/300 to 1/3000 Hz was
exactly equal to ()
2/2. Because of the aforemen-
tioned properties of the filtering technique, was
somewhat different from , which can be seen from
Table 1. The power spectra of fluctuations of the basic
parameters normalized by ()
2 are shown in Fig. 6 for
all 12 series.
The series numbers are indicated in Fig. 5a and are
arranged vertically so that the frequency selectivity of
the convective ABL is most distinct in the upper plots
and weak in the lower plots. The same numbering of
series is retained in Figs. 6a and 7a. The spectra in
Figs. 5–7 are located from left to right in accordance
with our estimates of their significance. Analogous
plots (but on a doubled scale along the ordinate axis)
averaged over all 12 series are shown in Figs. 5b–7b
along with standard deviations. Although the main fea-
tures are clearly seen in the average spectra, the origin,
statistics, and relationship of these features can be bet-
ter analyzed using individual spectra obtained for dif-
ferent conditions.
The cross spectra of w225 and P1 are the starting
point for analysis of the frequency selectivity of the
convective ABL (plots 1 in Fig. 5). All series show a
distinct maximum at ω = ωm. In 11 out of 12 series, this
is an absolute maximum. The position of this maximum
on the frequency axis was always coincident with the
position of a local maximum in the pressure spectrum
(plots 2 in Fig. 6). However, the spectrum of P usually
contained energetically more significant low-frequency
oscillations, which were weak in the (ω) spec-
trum. There was nearly always a local maximum at the
frequency ωm in the cross spectrum of atmospheric
pressure at sites 1 and 2 and 1 and 3 (plots 2 in Fig. 5).
σx
''σy
'' σx
'' σy
''
σx
''
σx
''
σx
'
σx
''
Ww225 P1
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS Vol. 41 No. 3 2005
COHERENT OSCILLATIONS OF METEOROLOGICAL PARAMETERS 333
1000
300
Oscillation period T, s
Series N2
3000
1000
300
Series N3
3000
1000
300
Series N9
3000
1000
300
Series N121 h Local time t, h
3000
Fig. 4. Representation of the modulus of the product of the vertical wind velocity in the convective mixed layer and the surface
pressure filtered in 14 quarter-octave frequency bands for four series. Contour interval is 0.1 of the maximum product in the
series.
334
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS Vol. 41 No. 3 2005
RUSAKOV
It could be suggested that the maximum in
(ω) is due only to a larger amplitude of the
selected oscillations of pressure fluctuations. However,
the maximum at the frequency ωm typically appears in
Ww225 P1
the usual spectra of vertical wind velocity and temper-
ature at different altitudes (plots 1, 3–5 in Fig. 6) and in
the cross spectra of these meteorological parameters
(plots 5, 6, 8 in Fig. 5). In addition to , crossWw225 P1
0.1
0.2
Scale
(a)
(b)
6
–1 0 1 2 –1 0 log2ω/ωm
Wxy(ω)/σ''
xσ''
y
5
–1 0 1 2–1 0 1 2–1 0 1 2–1 0 1 2
4321
–1 0 1 2 012 –1 0 1 2 –1 0 1 2 –1 0 1 2 –1 0 1 log2ω/ωm
N12
N7
N6
N1
N4
N10
N11
N8
N5
N9
N3
N2
0.1
(b)
log2ω/ωm
–1 0 1 2
7
–1 0 1 2 –1 0 1 log2ω/ωm
–1 0 1 2 –1 0 1 2 –1 0 1 2 –1 0 1 2 –1 0 1 2 –1 0 1
8 9 10 11 12
–1 0 1 2 –1 0 1 2 –1 0 1 2 –1 0 1 2 –1 0 1 2
13
0.2
Wxy(ω)/σ''
xσ''
yScale
(a)
Fig. 5. Normalized moduli of cross spectra (1) w225P1, (2) P1P2, (3) P1T225, (4) P1V225, (5) w225T225, (6) w225w74, (7) P1T2,
(8) w225T2, (9) w225V225, (10) P1V8, (11) w225V8, (12) T2T225, and (13) V8V225 in (a) series from 1 to 12 and (b) all series on average.
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS Vol. 41 No. 3 2005
COHERENT OSCILLATIONS OF METEOROLOGICAL PARAMETERS 335
1
0.1
Scale
(a)
(b) –1 0 1 2 1 2 –1 0 1 2 –1 0 1 2 –1 0 1 2 –1 0 1 2 –1 0 log2ω/ωm
2 3 4 5 6 7
–1 0 1 2 1 2 –1 0 1 2 –1 0 1 2 –1 0 1 2 –1 0 1 2 –1 0 log2ω/ωm
–1
Ex(ω)/σ''
xσ''
x
0.2
Fig. 6. Normalized power spectra of (1) w225, (2) P1, (3) T225, (4) T2, (5) w74, (6) V225, and (7) V8 in (a) series from 1 to 12 and (b) all series on average.
336
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS Vol. 41 No. 3 2005
RUSAKOV
–1 0 1 2 –1 0 1 2–1012–1 0 1 2–1012–1 0 1 2–1 0 1 2–1 0 1 2–1012–1 0 1 2–1012–1 0 1 2
–1 0 1 2 –1 0 1 2–1012–1 0 1 2–1012–1 0 1 2–1 0 1 2–1 0 1 2–1012–1 0 1 2–1012–1 0 1 2
1 2 3 4 5 6 7 8 9 10 11 12 13
0.01
0.02
Scale
〈f'2
xy〉/max〈f'2
xy〉
(a)
(b)
–1 log2ω/ωm
–1 log2ω/ωm
Fig. 7. Frequency dependence of the variance of the phase difference of oscillations (1) w225P1, (2) P1P2, (3) P1T225, (4) P1V225, (5) w225T225, (6) w225w74, (7) P1T2, (8) w225T2,
(9) w225V225, (10) P1V8, (11) w225V8, (12) T2T225, and (13) V8V225 in (a) series from 1 to 12 and (b) all series on average.
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS Vol. 41 No. 3 2005
COHERENT OSCILLATIONS OF METEOROLOGICAL PARAMETERS 337
spectra , , , and have the
largest average amplitude at the frequency ωm (plots 2,
3, 7, 12 in Fig. 5b). This indicates that the pressure,
temperature, and vertical velocity fluctuations at a
given frequency are closely related in the entire convec-
tive ABL.
The cross spectra of atmospheric pressure or the
vertical wind velocity with the horizontal wind velocity
in the mixed layer (plots 4, 9 in Fig. 5) also have local
maxima at ωm. In the fluctuations of surface wind V8,
however, the oscillations at ωm are weak (plots 7 in
Fig. 6 and 10, 11, 13 in Fig. 5) possibly because V8 is
strongly affected by the friction of the flow against the
underlying surface.
Thus, analysis of the set of cross spectra demon-
strates a regular occurrence in the convective ABL of a
structure that induces a narrow-band oscillation of the
basic parameters. On some days, the period of this
oscillation varied from 20 to 40 min. Figure 7 shows
that not only is this oscillation selective in amplitude
but it is also ordered in phase; i.e., it is coherent. In the
figure, the frequency dependence of the variance of the
oscillation phase difference is shown for all meteoro-
logical parameters for which the cross spectra were cal-
culated. The phase difference was read when the fil-
tered values crossed zero. For example, there were
18 readings in the 150-min joint sample of two meteo-
rological parameters for the filter centered at 10–3 Hz.
From these readings, the data series were formed from
which the mean (average phase shift) and the linear
trend were removed. The variances 〈(fxy)'2〉 were calcu-
lated for each series. It can be shown that the theoreti-
cally maximum possible variance max(〈(fxy)'2〉) in this
case equals (180Lω)2/48 deg2, where L = 9000 s is the
length of the run. The variance was divided by this
value so as to make the ordinate axis dimensionless, as
in Figs. 5 and 6. The variance 〈(fxy)'2〉 in the frequency
range ωm was found to decrease sharply to very small
values. For this minimum to be displayed in the plot,
the maximum variance was limited by 10/(Lω)2, i.e.,
10 deg2 per oscillation period.
The plots averaged over all series are shown in
Fig. 7b. Because of the large fluctuations of 〈(fxy)'2〉
between the series, median averaging is used. As can be
seen in Fig. 7, the degree of coherence of the oscilla-
tions of various parameters increases with decreasing
frequency, which is logical. Surprisingly, the variance
of the phase difference of oscillations usually decreases
sharply at ωm, forming a local minimum. This is partic-
ularly evident in the behavior of the variance of the
phase difference between w225 and P1 (plots 1 in Fig. 7),
where the above is valid for 11 out of 12 series. On
average, 〈()'
2〉 at the frequency ωm is 12 times
lower than in the adjacent quarter-octave frequency
regions. It is quite evident that the indicated parameters
are synchronized in phase at a given frequency, which
WP1P2
WP1T225
WP1T2WT225T2
fw225 P1
is the main evidence of self-oscillations in an open dis-
sipative system [3, 4].
The variance of the phase difference of pressure
fluctuations at three ground-based sites also has a local
minimum at the frequency ωm (plots 2 in Fig. 7). How-
ever, this minimum is weaker because the tendency
toward coherence in the region of low-frequency fluc-
tuations is most pronounced in the variability of atmo-
spheric pressure. Mesoscale fluctuations of other
parameters are also synchronized around ωm, but to a
lesser extent. The phase synchronization is weak only
between fluctuations of surface wind and other param-
eters for the above-mentioned reason (plots 10, 11,
plots 13 in Fig. 7). Thus, the experimental results dem-
onstrate that coherent oscillations of the meteorological
parameters in the convectively unstable ABL occur at a
single frequency.
MECHANISM OF COHERENT OSCILLATIONS
OF METEOROLOGICAL PARAMETERS
IN THE CONVECTIVE ABL
What are the causes for the occurrence of mesoscale
fluctuations at a certain frequency and for the synchro-
nization at this frequency of the phase of oscillations of
meteorological parameters in the convectively unstable
ABL? What is the mechanism of specifying this fre-
quency? It is logical to suppose that the coherent oscil-
lations of meteorological parameters at the measure-
ment site are induced by a “frozen” periodic stationary
structure transported by the background wind through
this site [29]. Such structures of thermogravity flows
arise in laboratory experiments as cells at some Ray-
leigh numbers. A reasonable hypothesis is proposed in
[23]. The coefficients of eddy viscosity and heat diffu-
sivity are assumed to be close to the values at which
Ra = g ∆T/Tsνχ lies within a critical range from
1500 to 5000. Here, ν and χ are the coefficients of kine-
matic viscosity and heat diffusivity, ∆T is the difference
of potential temperature across the layer of thickness Zi,
g is the acceleration of gravity, and Ts is the mean layer
temperature. To estimate these coefficients in the ABL,
we set the Prandtl number equal to about unity and
make use of a rough analogy between molecular and
turbulent mass-transport processes. With the character-
istic fluctuation velocity in the convective ABL being
close to 1 m/s and the mixing length of large thermals
and jets on the order of 0.1 Zi, we obtain Ra = 3500 at
∆T = 1°C in the 1-km-thick layer.
One more argument in favor of this hypothesis is
that the direction of circulation in the cells generated in
laboratory conditions is consistent with that observed in
the convective ABL. It is found [8] that molecular vis-
cosity, due to its temperature dependence, is always
less in the downward branch of the cell. There is a sim-
ilar situation (but due to other physical mechanisms) in
the convective ABL. Atmospheric turbulence, in partic-
ular, the structure characteristics of the wind and tem-
Zi
3
338
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS Vol. 41 No. 3 2005
RUSAKOV
perature field, is generally more intense in updrafts than
in downdrafts. This is evidenced by numerous studies
[16, 26] and our results, which are in part described in
[36].
The following qualitative model of a periodic struc-
ture of the convective ABL can be proposed. As the
underlying surface warms up, more and more layers of
the ABL are turbulized by unorganized convection in
the form of thermals and jets. Around midday, turbu-
lence is intensified to such an extent that the coeffi-
cients of eddy viscosity and heat diffusivity approach
critical values. The ABL becomes sensitive to weak
external disturbances of a certain frequency. These may
be quasi-monochromatic pressure fluctuations con-
stantly occurring in the atmosphere [27]. In particular,
such pressure fluctuations can generate buoyancy
waves in the overlying layers of the atmosphere [26]. In
the ABL, a cellular structure develops with an approxi-
mately constant spacing between the cells, which drifts
with the geostrophic wind as a whole. Measurements at
one site detect quasi-monochromatic variability of the
set of meteorological parameters with a period depen-
dent on the step of a cell and on its orientation with
respect to the wind.
Organized convection in the ABL has an important
distinction from sinusoidal convection in a laminar
medium. In addition to cell-induced mass transfer, the
mass is transported upward by local eddy structures
similar to a turbulent vortex ring (TVR). This agrees
with radar observations of the atmosphere [20]. It is
found [37] that TVR dynamics is critically dependent
on weak (~0.1 m/s) updrafts and downdrafts in the
environment. Downdrafts sharply decelerate the TVR,
and updrafts increase the velocity of its rise with the
accompanying fluid. Closed streamlines in the cell
cause the equality of mass fluxes in its upward and
downward branches. Therefore, the turbulent convec-
tive mass transfer in the ABL leads to a strengthening
of the updraft region and to an expansion of the down-
draft region. This explains the known (see [28, 29])
asymmetry of the distribution histogram of vertical
wind velocity w and the presence of additional high-fre-
quency maxima in the velocity spectrum (plots 1, 5 in
Fig. 6). The strength of these maxima in the w spectrum
decreases with height, which agrees with a gradual dis-
sipation of local eddies due to the entrainment of the
ambient air into eddies when they rise.
An obvious fact in the model of advection of the
convective roll encompassing the entire ABL is that the
correlation and coherence of oscillations of atmo-
spheric pressure and vertical wind velocity have a dis-
tinct maximum at a single selected frequency. Probably,
the integral pattern of pressure makes it possible to
smooth the specific features in the nonsinusoidal struc-
ture of cells that are manifested in multimode spectra of
temperature and wind velocity. As a result, in the case
of complicated forms of cells, only one wave number is
identified in the surface pressure field that is associated
with a convective structure of the ABL and is deter-
mined by a characteristic size of the cell.
The cellular circulation that develops in the ABL
influences the fields of all meteorological parameters.
Correlations appear, which are displayed in Table 2.
The correlation coefficients are shown for the meteo-
rological parameters that are filtered in the range 5–
50 min. The varying sign of the correlation coefficient
of w225T225 is noteworthy. At the same time, the correla-
tion w225T2 had a positive sign in all series. This is prob-
ably because thermal instability of the atmosphere is
mainly localized in the surface layer. Above, the strati-
Table 2. Correlation coefficients rXY of 150-min samples of the parameters X and Y filtered in the frequency band 1/300–1/3000
in the period of developed convection
No.123456789101112
w225P1–0.32 –0.16 –0.39 –0.5 –0.41 – 0.11 – 0.28 – 0.23 – 0.39 – 0.29 – 0.19 – 0.26
P1P20.92 0.94 0.9 0.88 0.79 0.71 0.52 0.91 0.78 0.21 0.71 0.36
P1T225 –0.24 –0.46 –0.61 0 – 0.24 – 0.32 – 0.09 0.27 0.1 –0.21 –0.15 –0.26
P1V225 0.31 0.18 0.08 0.17 0.2 –0.07 0.24 0.2 –0.3 –0.01 0 0.29
w225T225 0.58 0.19 0.4 –0.07 –0.12 –0.4 –0.13 –0.65 –0.61 –0.43 –0.09 0.27
w225w74 0.61 0.73 0.71 0.74 0.68 0.66 0.54 0.41 0.62 0.54 0.54 0.53
P1T2–0.22 –0.37 –0.53 –0.4 –0.42 – 0.14 – 0.41 – 0.08 0.16 –0.27 – 0.27 – 0.39
w225T20.41 0.14 0.45 0.1 0.14 0.42 0.23 0.21 0.17 0.21 0.43 0.26
w225V225 –0.6 –0.13 – 0.33 – 0.25 – 0.16 – 0.25 – 0.14 0.06 –0.14 – 0.07 – 0.4 –0.53
P1V80.1 –0.07 0.38 0.03 0.18 0.09 0.29 0.09 –0.26 0.07 0.05 0.1
w225V8–0.39 0.15 – 0.03 – 0.29 – 0.19 – 0.32 – 0.23 – 0.19 0.08 –0.22 – 0.31 – 0.14
T225T20.54 0.81 0.39 0.48 0.75 0.05 0.21 – 0.27 –0.24 0.31 0.4 0.4
V225V80.36 0.29 0.71 0.38 0.29 0.3 0.2 –0.04 0.13 0.11 0.21 0.27
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS Vol. 41 No. 3 2005
COHERENT OSCILLATIONS OF METEOROLOGICAL PARAMETERS 339
fication may be neutral or even weakly stable. Moving
upward by inertia, the eddy structures cool adiabati-
cally, and, hence, their temperature at a sufficient alti-
tude in the mixed layer may become even lower than
the ambient temperature. This could explain the mea-
sured values of the heat fluxes in Table 1. The wind
velocity modulus has the least correlation with the
other parameters. It can be suggested that the function
of the wind is to transport organized fields of vertical-
velocity, temperature, and pressure fluctuations.
Because of friction against the underlying surface, the
wind speed below decreases and deformations develop
in the cellular structure, which can disorganize it when
the wind increases.
The relation between pressure and vertical velocity
fluctuations is as yet not treated with certainty. Under
the assumption that a plane pressure wave appears at
the frequency ωm, it is possible to calculate its phase
velocity and orientation relative to the wind from pres-
sure measurements at three sites. These values for all
series are presented in Table 3. In 9 out of 12 series, the
transverse size of the plane wave agrees roughly with a
theoretical value for cellular structures λ ~ 3Zi [21, 22]
The phase velocity of the wave is close to the wind
speed in the ABL. Slightly higher wind speeds, how-
ever, were measured under the tropopause layer in
1997.
Analysis of the diurnal evolution of the amplitude of
pressure fluctuations at ωm points clearly to an ampli-
tude increase under developed convection. In 6 out of
12 series, the phase shift between w225 and P1 was
95° ± 15°. In [38], it is argued that hydrostatic pressure
fluctuations induced by vertical air motions are to be
taken into account because they serve as a buffer when
the vertical motions develop in the ABL. In our case, it
is possible that the development of cellular convection
is prevented by the intensifying vertical motions that
generate pressure fluctuations at the frequency ωm. Sur-
face pressure fluctuations are also apparently related to
fluctuations of wind speed and, particularly, of temper-
ature. Preliminary analysis of the entire set of parame-
ters has so far failed to determine how they are interre-
lated in the vicinity of the frequency of natural oscilla-
tions of the ABL. This problem needs further
consideration.
CONCLUSIONS
Measurements at a single site or several sites under
conditions of developed convection regularly detect
coherent oscillations of all meteorological and turbu-
lent characteristics for at least one frequency. Quasi-
monochromatic oscillations with a period from 20 to
40 min develop in the surface layer, free-convection
layer, and mixed layer and seem to be mainly a conse-
quence of the advection of a periodic structure of the
convectively unstable ABL.
The periodicity is most clearly defined in the evolu-
tion of the product of the mixed-layer vertical wind
velocity and the surface atmospheric pressure after they
are filtered out in the indicated frequency range.
The frequency ωm of synchronous oscillations of all
meteorological parameters in the convective ABL can
be determined from surface-pressure measurements at
several sites because a distinct local maximum of cor-
relation and a minimum of the variance of the phase dif-
ference between pressure fluctuations are usually
observed at this frequency.
The model of cellular convection is most consistent
with the data. The cells develop in the unstable subin-
version layer of the atmosphere when the turbulent
Rayleigh number approaches critical values. Periodic-
ity in the readings appears when the cells drift with the
wind through the sensors.
The periodic structure and oscillations of the con-
vective ABL, which resemble self-oscillations, may be
initiated by the quasi-monochromatic variability of
atmospheric-pressure fluctuations.
There are complicated feedbacks near the frequency
of natural oscillations of the ABL between the vertical
wind speed in the mixed layer, surface atmospheric
pressure, and surface air temperature. Determining the
functional form of these feedbacks requires a separate
study.
ACKNOWLEDGMENTS
I am grateful to V.N. Ivanov for formulating the
problem of using pressure fluctuations in the set of tur-
bulent characteristics of the convective ABL and their
correlations with other parameters, as well as detecting
quasi-monochromatic oscillations of the meteorologi-
cal elements. I thank V.M. Linkin and B.V. Zubkov for
Table 3. Transverse size (λ), phase velocity (Wv), and the angle between the front of a plane pressure wave at the frequency
ωm and the wind direction at 225 m (Ψ)
No.123456789101112
λ, km 3.1 9.0 6.7 6.1 3.8 4.5 7.3 29.4 6.7 6.5 33.0 18.4
Wv, m/s 2.5 5.2 5.2 4.0 2.2 3.1 5.8 17.1 4.3 4.4 14.7 8.4
Ψ, deg 15 90 45 20 45 45 45 80 45 10 30 45
340
IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS Vol. 41 No. 3 2005
RUSAKOV
placing the unique sensors of pressure fluctuations at
our disposal.
This work was supported by the Russian Foundation
for Basic Research, project nos. 01-05-64362 and 04-
05-65064. The Russian Ministry of Science, Industry,
and Technologies helped with the maintenance of the
unique tall meteorological tower and testing area.
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Translated by N. Tret’yakova
