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Persistence analysis of velocity and temperature fluctuations in convective surface layer turbulence

TL;DR: In this article, the authors carried out a detailed analysis of the statistical characteristics of the persistence probability density functions (PDFs) of velocity and temperature fluctuations in the surface layer of a convective boundary layer using a field-experimental dataset.
Abstract: Persistence is defined as the probability that the local value of a fluctuating field remains at a particular state for a certain amount of time, before being switched to another state. The concept of persistence has been found to have many diverse practical applications, ranging from non-equilibrium statistical mechanics to financial dynamics to distribution of time scales in turbulent flows and many more. In this study, we carry out a detailed analysis of the statistical characteristics of the persistence probability density functions (PDFs) of velocity and temperature fluctuations in the surface layer of a convective boundary layer using a field-experimental dataset. Our results demonstrate that for the time scales smaller than the integral scales, the persistence PDFs of turbulent velocity and temperature fluctuations display a clear power-law behavior, associated with a self-similar eddy cascading mechanism. Moreover, we also show that the effects of non-Gaussian temperature fluctuations act only at those scales that are larger than the integral scales, where the persistence PDFs deviate from the power-law and drop exponentially. Furthermore, the mean time scales of the negative temperature fluctuation events persisting longer than the integral scales are found to be approximately equal to twice the integral scale in highly convective conditions. However, with stability, this mean time scale gradually decreases to almost being equal to the integral scale in the near-neutral conditions. Contrarily, for the long positive temperature fluctuation events, the mean time scales remain roughly equal to the integral scales, irrespective of stability.

Summary (4 min read)

II. DATASET AND METHODOLOGY

  • The dataset being used is from the Surface Layer Turbulence and Environmental Science Test experiment.
  • Note that the authors rotated the coordinate systems of all nine sonic anemometers in the streamwise direction by applying the double-rotation method of Kaimal and Finnigan33 for each 30-min period.
  • The associated probability that the u′ signal stays positive or negative for tp amount of time can be evaluated by constructing the persistence PDFs using standard statistical procedures .

III. RESULTS AND DISCUSSION

  • Before describing the features of the persistence PDFs, it is worthwhile to discuss about the presentation of the results.
  • In the convective surface layer turbulence, it is a common practice to normalize the spatial length scales in the streamwise direction by the height above the surface.
  • Similar to Bershadskii et al.18 and Chamecki,30 the persistence PDFs are computed separately for the positive and negative fluctuations (shown as blue and red markers in Fig. 2) for u′, w′, and T′ signals and compared with the persistence PDFs for the total fluctuations (combining both positive and negative) shown as gray markers.
  • It could be noted that for the highly convective stability class [−ζ > 2, Fig. 2(a)], the persistence PDFs show a slight disparity between the positive and negative However, this difference gradually disappears with the change in stability from highly convective to near neutral [Figs. 2(a)–2(f)].

1. Linkage between the persistence PDFs and asymmetric distribution

  • From phenomenological arguments, the authors will show that such a form of the persistence PDF is equivalent to a timefraction distribution associated with (tpu)/z by directly connecting the premultiplied persistence PDF with the PDF of the corresponding signal itself.
  • The authors emphasize that such a connection is not possible to establish from the persistence PDFs alone (shown in Fig. 2) without considering its premultiplied form.

2. Premultiplied or logarithmic persistence PDFs of velocity and temperature fluctuations

  • Figure 3 shows the logarithmic PDFs of (tpu)/z for the same six different stability classes shown in Fig.
  • These PDFs are computed after taking the logarithm of (tpu)/z in base 10 and dividing the fraction of samples by the logarithmic bin-width d log10[(tpu)/z].
  • This clear disparity between the premultiplied PDFs of positive and negative.
  • This is congruous with the close to Gaussian characteristics of the T′ signal in the near-neutral stability.

B. Scrutiny of persistence PDFs through surrogate data

  • The persistence PDFs are related to the inter-arrival time between the successive zero-crossings of a time series.
  • If these zerocrossings were randomly located being independent of each other, the authors would have expected the persistence PDFs to follow a Poisson distribution, which is exponential in nature.
  • 1,67 However, in a convective surface layer, the persistence PDFs of the turbulent velocity and temperature fluctuations show a power-law structure.
  • Published under license by AIP Publishing 68,69.
  • Since the Fourier amplitudes of the surrogate dataset are kept intact during the process of Fourier phase-randomization (PR), this procedure preserves the Fourier spectrum and hence the auto-correlation function of the time series.

1. Phase-randomization and randomization experiments

  • For their purpose, the authors performed the phase-randomization and randomization experiments by varying the strength of the randomization to investigate their gradual effects on the behavior of the persistence PDFs.
  • Figure 4 shows the typical results from these two experiments for the highly convective stability class.
  • This is related to the fact that in phase-randomization experiments, the surrogate time series of temperature fluctuations approach an almost Gaussian distribution at even 20% randomization strength [see Fig. S4(a) of the supplementary material].
  • On the contrary, from Fig. 4(b), the authors note that the power-law structure of the T′ persistence PDFs gradually disappears as the strength of the randomization is increased to 100%.
  • In a turbulent time series, the temporal coherence can be described by the integral time scale, defined as the time up to which the signal remains auto-correlated with itself.

2. Auto-correlation functions and integral scales

  • Figure 5 shows the auto-correlation functions [Rxx(τ), where x can be u′, w′, or T′ signals and τ is the time lag] of u′, w′, and T′ signals, plotted against the lags for the six different stability classes.
  • The auto-correlation functions are plotted against the normalized time lags (τu/z) for u′ (red circles), w′ (blue squares), and T′ (pink inverted triangles) signals for the six different stability classes.
  • As the stability changes from highly convective to near neutral, the coefficients K of T′ signals become closer to u′ signals, implying that the ΛT values approach Λu [Figs. 5(a)–5(f)].
  • Therefore, it indicates that the power-law behavior of the persistence PDFs is connected to the eddies from the inertial subrange of the turbulence spectra (sizes smaller than the integral scales).

C. Scaling the persistence time by the integral scales

  • The authors begin with discussing the logarithmic persistence PDFs, since in that representation, the disparity between the PDFs corresponding to the positive and negative fluctuations at larger Phys.
  • Published under license by AIP Publishing persistence scales is highlighted more clearly (see Fig. 3 in Sec. III A).
  • The persistence time tp of u′, w′, or T′ signals are scaled with the integral time scale (Γ) before computing the logarithmic persistence PDFs.
  • Note that from the application of Taylor’s frozen turbulence hypothesis, this is equivalent to scaling the persistence length with integral scales Λ.

1. Logarithmic persistence PDFs

  • Figure 6 shows the logarithmic persistence PDFs with the persistence times normalized by Γ corresponding to u′, w′, or T′ signals for all six stability classes (Table I).
  • This discrepancy gradually disappears in near-neutral stability [see Figs. 6(a)–6(f)], implying that the non-Gaussian characteristics of the T′ signal are definitely related to the energy containing scales of motions.
  • The exponential decay of the CDFs, F(tp/Γ)∝ exp[−λ(tp/Γ)], (13) in such plots would appear as a straight line with the slope of λ.
  • This indicates that the mean time scales of the long persistent events of negative temperature fluctuations become closer to the integral scale of temperature as the near-neutral stability is approached, while the same remains unchanged for the positive fluctuation patterns.
  • This explains the closeness of the integral scales of w′ and T′ in highly convective stability [Fig. 5(a)].

2. Persistence PDFs

  • So far in Fig. 6, the authors have focused on the characteristics of the long persistent events larger than the integral scales (associated with energy containing eddies) by investigating the logarithmic representation of the persistence PDFs.
  • Since the power-law behavior is best represented in the original PDFs, Fig. 7 shows the persistence PDFs of u′, w′, and T′ signals with tp scaled with Γ. From Fig. 7, one can note the cut-off scale, where the deviation from the power-law behavior begins, is located almost exactly at the integral scale Γ for all three signals.
  • Therefore, in Fig. 7(a) (highly convective stability), the exponents of the power-law functions are determined by performing a linear regression for the range 0.01 ≤ tp/Γ ≤ 1 on the log–log plots.
  • Note that the exponent 1.4 for the T′ signal is very close to 1.37 as reported by Bershadskii et al.18 from their turbulent convection experiments.
  • For the w′ signal, the extent of the power-law behavior gradually decreases with stability.

3. Physical explanation of persistence exponents

  • In general, the exponents of the power-laws in persistence PDFs are non-trivial and difficult to compute analytically, except for simple systems such as fractional Brownian motions.
  • From Eq. (15), one can infer that the difference in the power-law exponents (γ) for u′, w′, and T′ signals is directly related to the different values of the intermittency exponents (μ).
  • Katul, Parlange, and Chu83 and Katul et al.84 demonstrated that in a convective surface layer, the temperature fluctuations are more intermittent compared to the velocity fluctuations, given the presence of sharp drops associated with the cliffs of the ramp-cliff patterns.
  • The reason for this difference is not clear at present.
  • Nonetheless, at present, both of these frameworks based on SOC and fractals seem plausible to connect these power-law exponents with the physical nature of small-scale turbulence, but further research is required to assess their viability.

IV. CONCLUSION

  • The authors report the statistical scaling properties of the persistence PDFs of turbulent fluctuations in streamwise and vertical velocity (u′ and w′) and temperature (T′) from the SLTEST experimental dataset in a convective surface layer.
  • On the other hand, for the long positive T′ events, the mean time scales remain roughly equal to the integral scales, irrespective of stability.
  • T′ events is interpreted to be associated with the change in the topology of the coherent structures from cellular convection patterns in highly convective conditions to horizontal streaks in near-neutral stability.
  • Subsequently, by scaling the persistence time scales with the integral scales, this statistical property of the persistence PDFs has been associated with the turbulent structures in a convective flow.
  • All the authors contributed equally to this work.

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UC Irvine Previously Published Works
Title
Persistence analysis of velocity and temperature fluctuations in convective surface layer
turbulence
Permalink
https://escholarship.org/uc/item/262669qs
Journal
Physics of Fluids, 32(7)
ISSN
1070-6631
Authors
Chowdhuri, S
Kalmár-Nagy, T
Banerjee, T
Publication Date
2020-07-01
DOI
10.1063/5.0013911
Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California

Phys. Fluids 32, 076601 (2020); https://doi.org/10.1063/5.0013911 32, 076601
© 2020 Author(s).
Persistence analysis of velocity and
temperature fluctuations in convective
surface layer turbulence
Cite as: Phys. Fluids 32, 076601 (2020); https://doi.org/10.1063/5.0013911
Submitted: 15 May 2020 . Accepted: 15 June 2020 . Published Online: 01 July 2020
Subharthi Chowdhuri , Tamás Kalmár-Nagy , and Tirtha Banerjee
COLLECTIONS
This paper was selected as Featured

Physics of Fluids
ARTICLE
scitation.org/journal/phf
Persistence analysis of velocity and temperature
fluctuations in convective surface layer
turbulence
Cite as: Phys. Fluids 32, 076601 (2020); doi: 10.1063/5.0013911
Submitted: 15 May 2020 Accepted: 15 June 2020
Published Online: 1 July 2020
Subharthi Chowdhuri,
1,a)
Tamás Kalmár-Nagy,
2,b)
and Tirtha Banerjee
3,c)
AFFILIATIONS
1
Indian Institute of Tropical Meteorology, Ministry of Earth Sciences, Dr. Homi Bhaba Road, Pashan, Pune 411008, India
2
Department of Fluid Mechanics, Faculty of Mechanical Engineering, Budapest University of Technology and Economics,
4-6 Bertalan Lajos u, Budapest 1111, Hungary
3
Department of Civil and Environmental Engineering, University of California, Irvine, California 92697, USA
a)
Author to whom correspondence should be addressed: subharthi.cat@tropmet.res.in
b)
Electronic mail: physfluids@kalmarnagy.com
c)
Electronic mail: tirthab@uci.edu
ABSTRACT
Persistence is defined as the probability that the local value of a fluctuating field remains at a particular state for a certain amount of time,
before being switched to another state. The concept of persistence has been found to have many diverse practical applications, ranging
from non-equilibrium statistical mechanics to financial dynamics to distribution of time scales in turbulent flows and many more. In this
study, we carry out a detailed analysis of the statistical characteristics of the persistence probability density functions (PDFs) of velocity
and temperature fluctuations in the surface layer of a convective boundary layer using a field-experimental dataset. Our results demon-
strate that for the time scales smaller than the integral scales, the persistence PDFs of turbulent velocity and temperature fluctuations
display a clear power-law behavior, associated with a self-similar eddy cascading mechanism. Moreover, we also show that the effects of
non-Gaussian temperature fluctuations act only at those scales that are larger than the integral scales, where the persistence PDFs deviate
from the power-law and drop exponentially. Furthermore, the mean time scales of the negative temperature fluctuation events persisting
longer than the integral scales are found to be approximately equal to twice the integral scale in highly convective conditions. However,
with stability, this mean time scale gradually decreases to almost being equal to the integral scale in the near-neutral conditions. Contrar-
ily, for the long positive temperature fluctuation events, the mean time scales remain roughly equal to the integral scales, irrespective of
stability.
Published under license by AIP Publishing. https://doi.org/10.1063/5.0013911
.,
s
I. INTRODUCTION
Let f (t) denote a stochastic signal fluctuating in time governed
by a particular dynamics. The persistence is then the probability P(t)
that the quantity f (t)f (t) does not change sign up to the time
t,
1,2
where the overbar denotes the time average. Despite its simple
description, only for some specific systems, such as those exhibit-
ing fractional Brownian motions, the persistence probability density
functions (PDFs) could be analytically shown to decay as a power-
law, P(t) t
(1H )
. Here, H is the Hurst exponent (0 <H <1) whose
value of 0.5 indicates simple Brownian motion.
1,3–5
The power-law
form of P(t) dictates that as the H values get larger, the persistence
PDFs decrease more slowly, which seems to be consistent with the
general notion that a stochastic signal displays anti-persistent or per-
sistent behavior depending on whether 0 <H <1/2 or 1/2 <H <1.
6
However, for other complex systems, no theoretical solutions exist
for the persistence PDFs, and these need to be computed empir-
ically from the experimental data at hand.
7
Notwithstanding the
theoretical challenges, the concept of persistence has many practical
applications, such as in the field of biology where one can ask how
long does it take for an epidemic to spread,
8
in financial markets to
assess when does a preferred stock will cross a threshold price,
9
or
Phys. Fluids 32, 076601 (2020); doi: 10.1063/5.0013911 32, 076601-1
Published under license by AIP Publishing

Physics of Fluids
ARTICLE
scitation.org/journal/phf
in the field of geophysics to predict when will the next earthquake
have a dangerously high magnitude.
10
Note that, depending on the
context, the persistence could also be referred to as distributions of
the first-passage time, survival probability distributions, return-time
distributions, or the distributions of the inter-arrival times between
the successive zero-crossings.
11
In turbulent flows, the interest in the concept of persistence or
zero-crossings grew with the analytical result from Rice
12
through
which it was possible to show that the frequency of the zero-
crossings in a turbulent signal was related to the Taylor microscale.
13
This connection was intriguing because it implied that the dissipa-
tion rate of the turbulent kinetic energy could be directly computed
from the zero-crossing frequencies. Since then, several studies are
carried out in wall-bounded turbulent flows to verify this result, and
the agreements obtained with the theoretical prediction are more
or less satisfactory.
13–16
However, there has been a fair amount of
disagreement among different experiments regarding the statistical
characteristics of the PDFs of the inter-arrival times between the suc-
cessive zero-crossings (hereafter, the persistence PDFs). Narayanan,
Rajagopalan, and Narasimha
15
found that in a turbulent boundary
layer, the persistence PDFs of the velocity fluctuations were log-
normal to a good approximation. Later, Sreenivasan, Prabhu, and
Narasimha
13
and Kailasnath and Sreenivasan
17
found that the per-
sistence PDFs of the velocity fluctuations and momentum flux sig-
nals were double-exponential in nature. Their interpretation of this
behavior was that the long intervals are a consequence of the large-
scale structures passing the sensor and the short intervals are a con-
sequence of the impinging small-scale motions superposed on the
large-scale structures. Subsequently, Bershadskii et al.
18
showed that
the persistence PDFs of temperature fluctuations from a turbulent
convection experiment followed a power-law distribution, which
indicates scale-free behavior. In a follow up study, Sreenivasan and
Bershadskii
19
commented that when the temperature behaved like
an active scalar in convective turbulence, the persistence PDFs fol-
lowed a power-law distribution. On the other hand, when the tem-
perature behaved like a passive scalar in shear-driven turbulence,
the persistence PDFs followed a log-normal distribution. Recently,
Kalmár-Nagy and Varga
20
noted that the persistence PDFs of veloc-
ity fluctuations followed a log-normal distribution in a turbulent
flow around a street canyon.
In atmospheric turbulence, the investigation of the statisti-
cal properties of the persistence PDFs of turbulent fluctuations is
quite rare. Nevertheless, there are a few limited studies available
from the atmospheric surface layer, which report the persistence
PDFs of velocity and scalar fluctuations.
21–24
The atmospheric sur-
face layer is a generalization of the inertial layer of unstratified
wall-bounded flows by including the effect of buoyancy, where the
effects of surface roughness are no longer important and the mod-
ulations by the outer eddies are not too strong.
25,26
Yee et al.
21,22
reported that the persistence PDFs of scalar concentrations dis-
played a double power-law in a near-neutral surface layer. Later,
Katul et al.
27
also observed the same, when they investigated the
persistence PDFs of the burst events in the sensible heat flux in
a convective surface layer. Pinto, Lopes, and Tenreiro Machado
28
showed that the double power-law feature in a distribution func-
tion is related to the presence of two sets of fractals with two dif-
ferent fractal dimensions associated with two different scale-free
processes. However, Narasimha et al.
29
found that the persistence
PDFs of the momentum flux events in a near-neutral surface layer
followed an exponential distribution, suggestive of a Poisson type
process. Recently, Cava and Katul
23
demonstrated that the persis-
tence PDFs of the velocity and scalar fluctuations in a canopy sur-
face layer turbulence could be power-laws with log-normal cutoffs
or log-normal distributions depending on the measurement height
in the canopy. In due course, Cava et al.
24
showed that the persis-
tence PDFs of the velocity and scalar fluctuations in the canopy and
atmospheric surface layer turbulence could be modeled as a power-
law distribution with an exponential cutoff in convective conditions.
Chamecki
30
lent support for this model by investigating the per-
sistence PDFs of velocity fluctuations above and within a cornfield
canopy.
Therefore, from this brief review, it is apparent that there is a
very little consensus about the statistical characteristics of the per-
sistence PDFs for both laboratory and atmospheric turbulent flows.
Nevertheless, in a convective atmospheric surface layer, a detailed
understanding of the persistence properties of velocity and temper-
ature fluctuations is important since it holds the key to explain the
quadrant cycles of the heat and momentum fluxes. This is because
the switching patterns of the heat and momentum fluxes from one
quadrant to the other are dependent on the zero-crossings of the
component signals, as described by their persistence PDFs. Thus, we
define our objectives for this study as follows:
1. To carry out a detailed analysis to establish the statistical scal-
ing properties of the persistence PDFs of velocity and temper-
ature fluctuations in a convective surface layer.
2. To empirically connect the statistical scaling properties of the
persistence PDFs with the turbulent structures in a convective
surface layer.
This study is organized as follows: In Sec. II, we provide the
descriptions of the field-experimental dataset and methodology used
in this study; in Sec. III, we present and discuss the results; and
finally, in Sec. IV, we conclude by presenting our findings and
providing the future research direction.
II. DATASET AND METHODOLOGY
In this study, the dataset being used is from the Surface Layer
Turbulence and Environmental Science Test (SLTEST) experiment.
The SLTEST experiment ran continuously for nine days from 26
May 2005 to 03 June 2005, over a flat and homogeneous terrain at
the Great Salt Lake desert in UT, USA (40.14
N, 113.5
W), with
the aerodynamic roughness length (z
0
) being z
0
5 mm.
31
During
this experiment, nine north-facing time synchronized CSAT3 sonic
anemometers were mounted on a 30-m mast, spaced logarithmically
over an 18-fold range of heights, from 1.42 m to 25.7 m, with the
sampling frequency being set at 20 Hz.
During the daytime convective periods, the standard practice is
to compute the turbulent statistics in the atmospheric surface layer
over a 30-min period.
32–34
Therefore, the data from all nine sonic
anemometers were restricted to rain-free daytime convective periods
and subsequently being divided into 30-min sub-periods, contain-
ing the 20-Hz measurements of the three wind components and
the sonic temperature.
35
To select the 30-min periods for the per-
sistence analysis, we followed the detailed data selection methods as
Phys. Fluids 32, 076601 (2020); doi: 10.1063/5.0013911 32, 076601-2
Published under license by AIP Publishing

Physics of Fluids
ARTICLE
scitation.org/journal/phf
TABLE I. The six different stability classes formed from the ratio ζ = z/L in an unstable atmospheric surface layer flow, where z is the height above the surface and L is the
Obukhov length. The ratios span from highly convective (ζ > 2) to near-neutral (0 < ζ < 0.2) conditions. The number of 30-min runs and the associated heights with each
of the stability classes are given. The total numbers of zero-crossings (No. ZC) in u
, v
, w
, and T
signals associated with each stability class are also provided.
Number of
Stability class 30-min runs Heights u
(No. ZC) v
(No. ZC) w
(No. ZC) T
(No. ZC)
ζ >2 55 z = 6.1 m, 8.7 m, 12.5 m, 17.9 m, 25.7 m 116 459 86 576 142 751 127 633
1 <ζ <2 53 z = 3 m, 4.3 m, 6.1 m, 8.7 m, 12.5 m, 17.9 m, 25.7 m 119 511 92 236 189 131 138 785
0.6 <ζ <1 41 z = 2.1 m, 3 m, 4.3 m, 6.1 m, 8.7 m, 12.5 m, 17.9 m 97 575 73 884 184 652 115 173
0.4 <ζ <0.6 34 z = 1.4 m, 2.1 m, 3 m, 4.3 m, 6.1 m, 8.7 m 90 551 70 957 193 302 107 356
0.2 <ζ <0.4 44 z = 1.4 m, 2.1 m, 3 m, 4.3 m, 6.1 m 128 538 98 123 293 816 154 774
0 <ζ <0.2 34 z = 1.4 m, 2.1 m, 3 m 114 383 95 228 285 961 143 470
outlined in Ref. 36. Note that we rotated the coordinate systems of all
nine sonic anemometers in the streamwise direction by applying the
double-rotation method of Kaimal and Finnigan
33
for each 30-min
period.
A total of 261 combinations of the stability ratios (ζ = z/L,
where L is the Obukhov length) were possible for the selected 30-min
periods from the convective conditions (L >0). The stability ratio
z/L is the ratio between the turbulent kinetic energy generated due
to buoyancy and due to shear, with the Obukhov length (L) being
defined as
L =
u
3
T
0
k
v
gH
0
, (1)
where T
0
is the surface air temperature, g is the acceleration due to
gravity (9.8 m s
2
), H
0
is the surface kinematic heat flux, k
v
is the
von Kármán constant (0.4), and u
is the friction velocity. It is to be
noted that these are the same set of runs used by Chowdhuri, Kumar,
and Banerjee
36
for their study of turbulence anisotropy. The entire
range of ζ (12 ζ 0.07) was divided into six stability classes
and considered for the persistence analysis (see Table I). For each
30-min run, the turbulent fluctuations of the three velocity com-
ponents in the streamwise (u
), cross-stream (v
), and vertical (w
)
directions along with the fluctuations in the sonic temperature (T
)
were computed by removing the linear trend from the 30-min period
associated with the respective variables.
37
A graphical illustration of the persistence phenomenon is pro-
vided in Fig. 1, where a 120-s long section of u
signal is shown for a
particular 30-min run, corresponding to a ζ = 10.6. Figure 1 shows
that the u
signal displays persistent positive or negative (i.e., above
or below the mean) values for a particular amount of time, denoted
as t
p
. Note that the persistence time t
p
can also be interpreted as the
inter-arrival time between the subsequent zero-crossings where the
u
signal changes its sign. The zero-crossings are identified by using
the telegraphic approximation (TA) of the u
signal as
(u
)
TA
=
1
2
u
(t)
u
(t)
+ 1 (2)
FIG. 1. A 120-s long section of a time
series of u
from a highly convective sur-
face layer corresponding to ζ = 10.6
is shown for (a) actual values and (b)
its telegraphic approximation (TA), where
u
> 0 is denoted as 1 and u
< 0 is
denoted as 0. The red horizontal line
denotes the position of zero, and the red-
crosses show the points where the u
signal changes its sign from positive to
negative or vice versa (zero-crossings).
To provide an example, two particular
regions of the u
signal are highlighted
where the positive and negative values
persist for a time t
p
(around 30 s–50 s).
Phys. Fluids 32, 076601 (2020); doi: 10.1063/5.0013911 32, 076601-3
Published under license by AIP Publishing

Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors apply the telegraphic approximation (TA) to the streamwise velocity component and air temperature time series acquired in the first metre above the salt flats of Utah, USA.
Abstract: The physicist and mathematician Shang-Keng Ma once commented that “the simplest possible variable is one that can have two values. If there is only one value, no variation is possible." Guided by this dictum, the telegraphic approximation (TA) is applied to the streamwise velocity component and air temperature time series acquired in the first metre above the salt flats of Utah, USA. The TA technique removes amplitude variations and retains only zero-crossing behaviour in a turbulent series, thereby allowing for an isolated examination of the role of clustering in intermittency. By applying the TA technique, clustering properties are analyzed to uncover dissimilarity in temperature and velocity across unstable, near-neutral, and stable atmospheric stratification. The spectral exponents of the original and of the TA series are examined, with the inertial-subrange behaviour conforming to prior empirical relations and the energy-containing range exhibiting deviations. These two distinct scale regimes are observed in the standard deviations of the running density fluctuations of the TA series, delineating scaling behaviour between fine and large scales. In the fine scales, clustering is not appreciably affected by the stability regime and is higher than in the large scales. In the large scales, the temperature series exhibits stronger clustering with increasing stability, and higher clustering compared with the streamwise velocity component series under stable conditions. Amplitude variations are shown to mitigate intermittency in the small scales of velocity, but play only a minor role in intermittency for temperature. Last, the inter-pulse period probability distributions are explored and implications to self-organized criticality as models for TA turbulence are discussed.

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Journal ArticleDOI
TL;DR: In this article, the authors investigate the switching patterns of intermittently occurring turbulent fluctuations from one state to another, a phenomenon called persistence, and uncover power-law scaling and length scales of turbulent motions that cause this behavior.
Abstract: The characterization of heat and momentum fluxes in wall-bounded turbulence is of paramount importance for a plethora of applications ranging from engineering to Earth sciences. Nevertheless, how the turbulent structures associated with velocity and temperature fluctuations interact to produce the emergent flux signatures has not been evident until now. In this work, we investigate this fundamental issue by studying the switching patterns of intermittently occurring turbulent fluctuations from one state to another, a phenomenon called persistence. We discover that the persistence patterns for heat and momentum fluxes are widely different. Moreover, we uncover power-law scaling and length scales of turbulent motions that cause this behavior. Furthermore, by separating the phases and amplitudes of flux events, we explain the origin and differences between heat and momentum transfer efficiencies in convective turbulence. Our findings provide a new understanding of the connection between flow organization and flux generation mechanisms, two cornerstones of turbulence research.

7 citations


Cites background or methods from "Persistence analysis of velocity an..."

  • ...Note that, in the parlance of non-equilibrium statistical mechanics, the distribution of zero-crossing time intervals in a stochastic signal is equivalent to the persistence PDFs, where persistence is the probability P (t) that the signal does not change its sign up to the time t (Majumdar, 1999; Chowdhuri et al., 2020a)....

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  • ...Note that, the persistence PDFs are computed via logarithmic binning and subsequent transformation to the linear space using a change of variable, as illustrated by Chowdhuri et al. (2020a)....

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  • ...Since the measurements from the near-neutral stability class belong to the lowest three SLTEST levels, the shrinkage in the power-law regime is related to insufficient sampling of the small scale eddies at 20-Hz sampling frequency (Chowdhuri et al., 2020a)....

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  • ...Since Λw is of the same order as z (Chowdhuri et al., 2020a), such discrepancy reflects distinct attributes of turbulent transport associated with the detached and attached eddies, characterized by length scales smaller and larger than z (Marusic and Monty, 2019)....

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  • ...Besides, Chowdhuri et al. (2020a) reported the respective power-law exponents to be equal to −1.6, −1.25, and −1.4 for the u′, w′, and T ′ signals....

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Journal ArticleDOI
TL;DR: In this paper , the authors proposed a method based on a multipoint statistical description of turbulent velocity fields that consists of a superposition of multivariate Gaussian statistics with fluctuating covariances, which can be constrained on a certain number of real-world measurement data points from a meteorological mast array.
Abstract: Accurate models of turbulent wind fields have become increasingly important in the atmospheric sciences, e.g., for the determination of spatiotemporal correlations in wind parks, the estimation of individual loads on turbine rotor and blades, or the modeling of particle-turbulence interaction in atmospheric clouds or pollutant distributions in urban settings. Because of the difficult task of resolving the fields across a broad range of scales, one oftentimes has to invoke stochastic wind field models that fulfill specific, empirically observed, properties. Whereas commonly used Gaussian random field models solely control second-order statistics (i.e., velocity correlation tensors or kinetic energy spectra), we explicitly show that our extended model emulates the effects of higher-order statistics as well. Most importantly, the empirically observed phenomenon of small-scale intermittency, which can be regarded as one of the key features of atmospheric turbulent flows, is reproduced with a very high level of accuracy and at considerably low computational cost. Our method is based on a multipoint statistical description of turbulent velocity fields that consists of a superposition of multivariate Gaussian statistics with fluctuating covariances. We propose a new and efficient sampling algorithm for this Gaussian scale mixture and demonstrate how such “superstatistical” wind fields can be constrained on a certain number of real-world measurement data points from a meteorological mast array.Received 12 April 2022Revised 26 July 2022Accepted 22 August 2022DOI:https://doi.org/10.1103/PRXEnergy.1.023006Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAtmospheric scienceBoundary layersShear flowsStochastic processesStructure & turbulence of boundary layersSustainabilityTurbulenceWind energyEnergy Science & TechnologyNonlinear DynamicsFluid DynamicsStatistical Physics

5 citations

Journal ArticleDOI
TL;DR: In this article, a case study where a sudden drop in temperature was noted at heights within the surface layer during the passage of a gust front in the afternoon time, this temperature drop created an interface which separated two different turbulent regimes.
Abstract: The simultaneous observations from a Doppler weather radar and an instrumented micrometeorological tower, offer an opportunity to dissect the effects of a gust front on the surface layer turbulence in a tropical convective boundary layer. We present a case study where a sudden drop in temperature was noted at heights within the surface layer during the passage of a gust front in the afternoon time. Consequently, this temperature drop created an interface which separated two different turbulent regimes. In one regime the turbulent temperature fluctuations were large and energetic, whereas in the other regime they were weak and quiescent. Given its uniqueness, we investigated the size distribution and aggregation properties of the turbulent structures related to these two regimes. We found that, the size distributions of the turbulent structures for both of these regimes displayed a clear power-law signature. Since power-laws are synonymous with scale-invariance, this indicated the passing of the gust front initiated a scale-free response which governed the turbulent characteristics of the temperature fluctuations. We propose a hypothesis to link such behaviour with the self organized criticality as observed in the complex systems. However, the temporal organization of the turbulent structures, as indicated by their clustering tendencies, differed between these two regimes. For the regime, corresponding to large temperature fluctuations, the turbulent structures were significantly clustered, whose clustering properties changed with height. Contrarily, for the other regime where the temperature fluctuations were weak, the turbulent structures remained less clustered with no discernible change being observed with height.

4 citations

References
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Book
01 Jan 1972
TL;DR: In this paper, the authors present a reference record created on 2005-11-18, modified on 2016-08-08 and used for the analysis of turbulence and transport in the context of energie.
Abstract: Keywords: turbulence ; transport ; contraintes ; transport ; couche : limite ; ecoulement ; tourbillon ; energie Reference Record created on 2005-11-18, modified on 2016-08-08

8,276 citations

Journal ArticleDOI
TL;DR: It is shown that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point, and flicker noise, or 1/f noise, can be identified with the dynamics of the critical state.
Abstract: We show that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point. Flicker noise, or 1/f noise, can be identified with the dynamics of the critical state. This picture also yields insight into the origin of fractal objects.

6,486 citations


"Persistence analysis of velocity an..." refers background in this paper

  • ...Recently, to explain these power-law exponents, Cava and Katul (2009) and Cava et al. (2012) have proposed an ambitious connection with the self-organized criticality (SOC) observed in the sandpile model of Bak et al. (1987, 1988)....

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Journal ArticleDOI
TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.
Abstract: In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of I(t). The first six sections are concerned with the probability distribution of I(t) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of I(t). Fluctuations of integrals involving I2(t) are discussed in section 3.9. The probability distribution of a sine wave plus a noise current is given in 3.10 and in 3.11 an alternative method of deriving the results of Part III is mentioned. Prof. Uhlenbeck has pointed out that much of the material in this Part is closely connected with the theory of Markoff processes. Also S. Chandrasekhar has written a review of a class of physical problems which is related, in a general way, to the present subject.22

5,806 citations


"Persistence analysis of velocity an..." refers background in this paper

  • ...…ph ys ic s. fl udy n] 1 1 M In turbulent flows, the interest in the concept of persistence or zero-crossings grew with the analytical result from Rice (1945), through which it was possible to show that the frequency of the zero-crossings in a turbulent signal was related to the Taylor…...

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Journal ArticleDOI
TL;DR: Some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them are reviewed.
Abstract: When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, forest fires, solar flares, moon craters and people's personal fortunes all appear to follow power laws. The origin of power-law behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them.

4,734 citations


"Persistence analysis of velocity an..." refers background or methods in this paper

  • ...…the PDFs of such variables is to take the logarithmic transformation and then binning the transformed variables in the logarithmic space (Christensen and Moloney, 2005; Newman, 2005; Pueyo, 2006; Sims et al., 2007; Benhamou, 2007; White et al., 2008; Dorval, 2011; Newberry and Savage, 2019)....

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  • ...…of the avalanches associated with sandpile models (Christensen and Moloney, 2005), identifying the lévy flight patterns in animal displacements (Benhamou, 2007; Sims et al., 2007), and in many other practical cases (see Newman (2005) and the references therein for a detailed review on this topic)....

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  • ...Additionally, the CDFs also have an inherent advantage of being bin-independent with a smooth convergence towards 1 (Newman, 2005; White et al., 2008)....

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  • ...…to the hypothesis of Yee et al. (1995) and Cava et al. (2012) where they connected this power law behaviour in the persistence PDFs with self-similar Richardson cascading mechanism, given the implied scale invariance associated with power-law distributions (Newman, 2005; Verma et al., 2006)....

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  • ...(2012) where they connected this power law behaviour in the persistence PDFs with self-similar Richardson cascading mechanism, given the implied scale invariance associated with power-law distributions (Newman, 2005; Verma et al., 2006)....

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Journal ArticleDOI
TL;DR: In this article, the authors show that certain extended dissipative dynamical systems naturally evolve into a critical state, with no characteristic time or length scales, and the temporal fingerprint of the self-organized critical state is the presence of flicker noise or 1/f noise; its spatial signature is the emergence of scale-invariant (fractal) structure.
Abstract: We show that certain extended dissipative dynamical systems naturally evolve into a critical state, with no characteristic time or length scales. The temporal ``fingerprint'' of the self-organized critical state is the presence of flicker noise or 1/f noise; its spatial signature is the emergence of scale-invariant (fractal) structure.

3,828 citations


"Persistence analysis of velocity an..." refers background in this paper

  • ...Recently, to explain these power-law exponents, Cava and Katul (2009) and Cava et al. (2012) have proposed an ambitious connection with the self-organized criticality (SOC) observed in the sandpile model of Bak et al. (1987, 1988)....

    [...]

Frequently Asked Questions (2)
Q1. What contributions have the authors mentioned in the paper "Persistence analysis of velocity and temperature fluctuations in convective surface layer turbulence" ?

In this study, the authors carry out a detailed analysis of the statistical characteristics of the persistence probability density functions ( PDFs ) of velocity and temperature fluctuations in the surface layer of a convective boundary layer using a field-experimental dataset. Moreover, the authors also show that the effects of non-Gaussian temperature fluctuations act only at those scales that are larger than the integral scales, where the persistence PDFs deviate from the power-law and drop exponentially. Furthermore, the mean time scales of the negative temperature fluctuation events persisting longer than the integral scales are found to be approximately equal to twice the integral scale in highly convective conditions. 

Since the persistence PDFs are related to the time spent between the zero-crossings in a signal, the future research questions are as follows: 1. How the persistence PDFs of the heat and momentum fluxes are related to the persistence PDFs of the velocity and temperature fluctuations ? 2. How much of the flux variation can be described by the persistence properties of the component signals ?