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.

1.
S. N.
Majumdar
, “
Persistence in nonequilibrium systems
,”
Curr. Sci.
77
,
370
375
(
1999
).
2.
A. J.
Bray
,
S. N.
Majumdar
, and
G.
Schehr
, “
Persistence and first-passage properties in nonequilibrium systems
,”
Adv. Phys.
62
,
225
361
(
2013
).
3.
G. M.
Molchan
, “
Maximum of a fractional Brownian motion: Probabilities of small values
,”
Commun. Math. Phys.
205
,
97
111
(
1999
).
4.
F.
Aurzada
and
C.
Baumgarten
, “
Persistence of fractional Brownian motion with moving boundaries and applications
,”
J. Phys. A: Math. Theor.
46
,
125007
(
2013
).
5.
F.
Aurzada
and
T.
Simon
, “
Persistence probabilities and exponents
,” in
Lévy Matters V
(
Springer
,
2015
), pp.
183
224
.
6.
G.
Wang
,
G.
Antar
, and
P.
Devynck
, “
The Hurst exponent and long-time correlation
,”
Phys. Plasmas
7
,
1181
1183
(
2000
).
7.
P.
Perlekar
,
S. S.
Ray
,
D.
Mitra
, and
R.
Pandit
, “
Persistence problem in two-dimensional fluid turbulence
,”
Phys. Rev. Lett.
106
,
054501
(
2011
).
8.
D.
Sornette
,
Critical Phenomena in Natural Sciences: Chaos, Fractals, Self-Organization and Disorder: Concepts and Tools
(
Springer Science and Business Media
,
2006
).
9.
B.
Zheng
, “
Persistence probability in financial dynamics
,”
Mod. Phys. Lett. B
16
,
775
782
(
2002
).
10.
A.
Corral
, “
Long-term clustering, scaling, and universality in the temporal occurrence of earthquakes
,”
Phys. Rev. Lett.
92
,
108501
(
2004
).
11.
D. S.
Grebenkov
,
D.
Holcman
, and
R.
Metzler
, “
Preface: New trends in first-passage methods and applications in the life sciences and engineering
,”
J. Phys. A: Math. Theor.
53
,
190301
(
2020
).
12.
S. O.
Rice
, “
Mathematical analysis of random noise
,”
Bell Syst. Tech. J.
24
,
46
156
(
1945
).
13.
K. R.
Sreenivasan
,
A.
Prabhu
, and
R.
Narasimha
, “
Zero-crossings in turbulent signals
,”
J. Fluid Mech.
137
,
251
272
(
1983
).
14.
R. A.
Antonia
,
H. Q.
Danh
, and
A.
Prabhu
, “
Bursts in turbulent shear flows
,”
Phys. Fluids
19
,
1680
1686
(
1976
).
15.
M. A. B.
Narayanan
,
S.
Rajagopalan
, and
R.
Narasimha
, “
Experiments on the fine structure of turbulence
,”
J. Fluid Mech.
80
,
237
257
(
1977
).
16.
D.
Poggi
and
G. G.
Katul
, “
Evaluation of the turbulent kinetic energy dissipation rate inside canopies by zero- and level-crossing density methods
,”
Boundary-Layer Meteorol.
136
,
219
233
(
2010
).
17.
P.
Kailasnath
and
K. R.
Sreenivasan
, “
Zero crossings of velocity fluctuations in turbulent boundary layers
,”
Phys. Fluids
5
,
2879
2885
(
1993
).
18.
A.
Bershadskii
,
J.
Niemela
,
A.
Praskovsky
, and
K.
Sreenivasan
, “
“Clusterization” and intermittency of temperature fluctuations in turbulent convection
,”
Phys. Rev. E
69
,
056314
(
2004
).
19.
K. R.
Sreenivasan
and
A.
Bershadskii
, “
Clustering properties in turbulent signals
,”
J. Stat. Phys.
125
,
1141
1153
(
2006
).
20.
T.
Kalmár-Nagy
and
Á.
Varga
, “
Complexity analysis of turbulent flow around a street canyon
,”
Chaos, Solitons Fractals
119
,
102
117
(
2019
).
21.
E.
Yee
,
P. R.
Kosteniuk
,
G. M.
Chandler
,
C. A.
Biltoft
, and
J. F.
Bowers
, “
Statistical characteristics of concentration fluctuations in dispersing plumes in the atmospheric surface layer
,”
Boundary-Layer Meteorol.
65
,
69
109
(
1993
).
22.
E.
Yee
,
R.
Chan
,
P. R.
Kosteniuk
,
G. M.
Chandler
,
C. A.
Biltoft
, and
J. F.
Bowers
, “
Measurements of level-crossing statistics of concentration fluctuations in plumes dispersing in the atmospheric surface layer
,”
Boundary-Layer Meteorol.
73
,
53
90
(
1995
).
23.
D.
Cava
and
G. G.
Katul
, “
The effects of thermal stratification on clustering properties of canopy turbulence
,”
Boundary-Layer Meteorol.
130
,
307
(
2009
).
24.
D.
Cava
,
G.
Katul
,
A.
Molini
, and
C.
Elefante
, “
The role of surface characteristics on intermittency and zero-crossing properties of atmospheric turbulence
,”
J. Geophys. Res. Atmos.
117
,
D01104
, (
2012
).
25.
G. I.
Barenblatt
,
Scaling, Self-Similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics
(
Cambridge University Press
,
1996
), Vol. 14.
26.
P. A.
Davidson
,
Turbulence: An Introduction for Scientists and Engineers
(
Oxford University Press
,
2015
).
27.
G. G.
Katul
,
J.
Albertson
,
M.
Parlange
,
C.-R.
Chu
, and
H.
Stricker
, “
Conditional sampling, bursting, and the intermittent structure of sensible heat flux
,”
J. Geophys. Res. Atmos.
99
,
22869
22876
, (
1994
).
28.
C. M. A.
Pinto
,
A. M.
Lopes
, and
J. A.
Tenreiro Machado
, “
Double power laws, fractals and self-similarity
,”
Appl. Math. Model.
38
,
4019
4026
(
2014
).
29.
R.
Narasimha
,
S. R.
Kumar
,
A.
Prabhu
, and
S. V.
Kailas
, “
Turbulent flux events in a nearly neutral atmospheric boundary layer
,”
Philos. Trans. R. Soc., A
365
,
841
858
(
2007
).
30.
M.
Chamecki
, “
Persistence of velocity fluctuations in non-Gaussian turbulence within and above plant canopies
,”
Phys. Fluids
25
,
115110
(
2013
).
31.
M.
Metzger
,
B. J.
McKeon
, and
H.
Holmes
, “
The near-neutral atmospheric surface layer: Turbulence and non-stationarity
,”
Philos. Trans. R. Soc. Lond.
365
,
859
876
(
2007
).
32.
H.
Panosfsky
and
J.
Dutton
,
Atmospheric Turbulence: Models and Methods for Engineering Applications
(
John Wiley & Sons
,
1984
).
33.
J. C.
Kaimal
and
J. J.
Finnigan
,
Atmospheric Boundary Layer Flows: Their Structure and Measurement
(
Oxford University Press
,
1994
).
34.
T.
Foken
and
C. J.
Napo
,
Micrometeorology
(
Springer
,
2008
), Vol. 2.
35.
S.
Chowdhuri
,
K. G.
McNaughton
, and
T. V.
Prabha
, “
An empirical scaling analysis of heat and momentum cospectra above the surface friction layer in a convective boundary layer
,”
Boundary-Layer Meteorol.
170
,
257
284
(
2019
).
36.
S.
Chowdhuri
,
S.
Kumar
, and
T.
Banerjee
, “Revisiting the role of intermittent heat transport towards Reynolds stress anisotropy in convective turbulence,” J. Fluid Mech. (in press) (
2020
).e - print
37.
A.
Donateo
,
D.
Cava
, and
D.
Contini
, “
A case study of the performance of different detrending methods in turbulent-flux estimation
,”
Boundary-Layer Meteorol.
164
,
19
37
(
2017
).
38.
J. C.
Kaimal
,
J. C.
Wyngaard
,
Y.
Izumi
, and
O. R.
Coté
, “
Spectral characteristics of surface-layer turbulence
,”
Q. J. R. Meteorol. Soc.
98
,
563
589
(
1972
).
39.
B. A.
Kader
,
A. M.
Yaglom
, and
S. L.
Zubkovskii
, “
Spatial correlation functions of surface-layer atmospheric turbulence in neutral stratification
,”
Boundary-Layer Meteorol.
47
,
233
249
(
1989
).
40.
B.
Kader
and
A.
Yaglom
, “
Spectra and correlation functions of surface layer atmospheric turbulence in unstable thermal stratification
,” in
Turbulence and Coherent Structures
(
Springer
,
1991
), pp.
387
412
.
41.
K. G.
McNaughton
and
J.
Laubach
, “
Power spectra and cospectra for wind and scalars in a disturbed surface layer at the base of an advective inversion
,”
Boundary-Layer Meteorol.
96
,
143
185
(
2000
).
42.
T.
Banerjee
and
G. G.
Katul
, “
Logarithmic scaling in the longitudinal velocity variance explained by a spectral budget
,”
Phys. Fluids
25
,
125106
(
2013
).
43.
K.
Ghannam
,
G. G.
Katul
,
E.
Bou-Zeid
,
T.
Gerken
, and
M.
Chamecki
, “
Scaling and similarity of the anisotropic coherent eddies in near-surface atmospheric turbulence
,”
J. Atmos. Sci.
75
,
943
964
(
2018
).
44.
A.
Monin
and
A.
Yaglom
,
Statistical Fluid Mechanics: Mechanics of Turbulence
(
MIT Press
,
1971
), Vol. 1.
45.
H.
Tennekes
and
J.
Lumley
,
A First Course in Turbulence
(
MIT Press
,
1972
).
46.
Y.
Malhi
,
K.
McNaughton
, and
C.
Von Randow
, “
Low frequency atmospheric transport and surface flux measurements
,” in
Handbook of Micrometeorology
(
Springer
,
2004
), pp.
101
118
.
47.
K. G.
McNaughton
, “
Attached eddies and production spectra in the atmospheric logarithmic layer
,”
Boundary-Layer Meteorol.
111
,
1
18
(
2004
).
48.
K. G.
McNaughton
, “
Turbulence structure of the unstable atmospheric surface layer and transition to the outer layer
,”
Boundary-Layer Meteorol.
112
,
199
221
(
2004
).
49.
G. E.
Willis
and
J. W.
Deardorff
, “
On the use of Taylor’s translation hypothesis for diffusion in the mixed layer
,”
Q. J. R. Meteorol. Soc.
102
,
817
822
(
1976
).
50.
K.
Christensen
and
N. R.
Moloney
,
Complexity and Criticality
(
World Scientific Publishing Company
,
2005
), Vol. 1.
51.
M. E. J.
Newman
, “
Power laws, Pareto distributions and Zipf’s law
,”
Contemp. Phys.
46
,
323
351
(
2005
).
52.
S.
Pueyo
, “
Diversity: Between neutrality and structure
,”
Oikos
112
,
392
405
(
2006
).
53.
D. W.
Sims
,
D.
Righton
, and
J. W.
Pitchford
, “
Minimizing errors in identifying Lévy flight behaviour of organisms
,”
J. Anim. Ecol.
76
,
222
229
(
2007
).
54.
S.
Benhamou
, “
How many animals really do the lévy walk?
,”
Ecology
88
,
1962
1969
(
2007
).
55.
E. P.
White
,
B. J.
Enquist
, and
J. L.
Green
, “
On estimating the exponent of power-law frequency distributions
,”
Ecology
89
,
905
912
(
2008
).
56.
A.
Dorval
, “
Estimating neuronal information: Logarithmic binning of neuronal inter-spike intervals
,”
Entropy
13
,
485
501
(
2011
).
57.
M. G.
Newberry
and
V. M.
Savage
, “
Self-similar processes follow a power law in discrete logarithmic space
,”
Phys. Rev. Lett.
122
,
158303
(
2019
).
58.
H.
Nakagawa
and
I.
Nezu
, “
Prediction of the contributions to the Reynolds stress from bursting events in open-channel flows
,”
J. Fluid Mech.
80
,
99
128
(
1977
).
59.
G.
Katul
,
C.-I.
Hsieh
,
G.
Kuhn
,
D.
Ellsworth
, and
D.
Nie
, “
Turbulent eddy motion at the forest-atmosphere interface
,”
J. Geophys. Res. Atmos.
102
,
13409
13421
, (
1997
).
60.
C. R.
Chu
,
M. B.
Parlange
,
G. G.
Katul
, and
J. D.
Albertson
, “
Probability density functions of turbulent velocity and temperature in the atmospheric surface layer
,”
Water Resour. Res.
32
,
1681
1688
, (
1996
).
61.
L.
Liu
,
F.
Hu
, and
X.
Cheng
, “
Probability density functions of turbulent velocity and temperature fluctuations in the unstable atmospheric surface layer
,”
J. Geophys. Res. Atmos.
116
,
D12117
, (
2011
).
62.
A.
Garai
and
J.
Kleissl
, “
Interaction between coherent structures and surface temperature and its effect on ground heat flux in an unstably stratified boundary layer
,”
J. Turbul.
14
,
1
23
(
2013
).
63.
R.
Lyu
,
F.
Hu
,
L.
Liu
,
J.
Xu
, and
X.
Cheng
, “
High-order statistics of temperature fluctuations in an unstable atmospheric surface layer over grassland
,”
Adv. Atmos. Sci.
35
,
1265
1276
(
2018
).
64.
R. J.
Adrian
,
R. T. D. S.
Ferreira
, and
T.
Boberg
, “
Turbulent thermal convection in wide horizontal fluid layers
,”
Exp. Fluids
4
,
121
141
(
1986
).
65.
S.
Chowdhuri
,
T. V.
Prabha
,
A.
Karipot
,
T.
Dharamraj
, and
M. N.
Patil
, “
Relationship between the momentum and scalar fluxes close to the ground during the indian post-monsoon period
,”
Boundary-Layer Meteorol.
154
,
333
348
(
2015
).
66.
S.
Chowdhuri
and
T. V.
Prabha
, “
An evaluation of the dissimilarity in heat and momentum transport through quadrant analysis for an unstable atmospheric surface layer flow
,”
Environ. Fluid Mech.
19
,
513
542
(
2019
).
67.
M.
Santhanam
and
H.
Kantz
, “
Return interval distribution of extreme events and long-term memory
,”
Phys. Rev. E
78
,
051113
(
2008
).
68.
D.
Poggi
and
G.
Katul
, “
Flume experiments on intermittency and zero-crossing properties of canopy turbulence
,”
Phys. Fluids
21
,
065103
(
2009
).
69.
G.
Lancaster
,
D.
Iatsenko
,
A.
Pidde
,
V.
Ticcinelli
, and
A.
Stefanovska
, “
Surrogate data for hypothesis testing of physical systems
,”
Phys. Rep.
748
,
1
60
(
2018
).
70.
T.
Maiwald
,
E.
Mammen
,
S.
Nandi
, and
J.
Timmer
, “
Surrogate data—A qualitative and quantitative analysis
,” in
Mathematical Methods in Signal Processing and Digital Image Analysis
(
Springer
,
2008
), pp.
41
74
.
71.
J.
Wyngaard
,
Turbulence in the Atmosphere
(
Cambridge University Press
,
2010
).
72.
G.
Katul
,
C.-I.
Hsieh
, and
J.
Sigmon
, “
Energy-inertial scale interactions for velocity and temperature in the unstable atmospheric surface layer
,”
Boundary-Layer Meteorol.
82
,
49
80
(
1997
).
73.
D.
Li
,
G. G.
Katul
, and
E.
Bou-Zeid
, “
Mean velocity and temperature profiles in a sheared diabatic turbulent boundary layer
,”
Phys. Fluids
24
,
105105
(
2012
).
74.
K. G.
McNaughton
,
R.
Clement
, and
J.
Moncrieff
, “
Scaling properties of velocity and temperature spectra above the surface friction layer in a convective atmospheric boundary layer
,”
Nonlinear Process. Geophys.
14
,
257
(
2007
).
75.
T.
Banerjee
,
G. G.
Katul
,
S. T.
Salesky
, and
M.
Chamecki
, “
Revisiting the formulations for the longitudinal velocity variance in the unstable atmospheric surface layer
,”
Q. J. R. Meteorol. Soc.
141
,
1699
1711
(
2015
).
76.
S.
Khanna
and
J. G.
Brasseur
, “
Three-dimensional buoyancy- and shear-induced local structure of the atmospheric boundary layer
,”
J. Atmos. Sci.
55
,
710
743
(
1998
).
77.
S. T.
Salesky
,
M.
Chamecki
, and
E.
Bou-Zeid
, “
On the nature of the transition between roll and cellular organization in the convective boundary layer
,”
Boundary-Layer Meteorol.
163
,
41
68
(
2017
).
78.
M. K.
Verma
,
S.
Manna
,
J.
Banerjee
, and
S.
Ghosh
, “
Universal scaling laws for large events in driven nonequilibrium systems
,”
Europhys. Lett.
76
,
1050
(
2006
).
79.
P.
Bak
,
C.
Tang
, and
K.
Wiesenfeld
, “
Self-organized criticality: An explanation of the 1/f noise
,”
Phys. Rev. Lett.
59
,
381
384
(
1987
).
80.
P.
Bak
,
C.
Tang
, and
K.
Wiesenfeld
, “
Self-organized criticality
,”
Phys. Rev. A
38
,
364
(
1988
).
81.
K. R.
Sreenivasan
,
A.
Bershadskii
, and
J. J.
Niemela
, “
Multiscale soc in turbulent convection
,”
Physica A
340
,
574
579
(
2004
).
82.
H. J.
Jensen
,
K.
Christensen
, and
H. C.
Fogedby
, “
1/f noise, distribution of lifetimes, and a pile of sand
,”
Phys. Rev. B
40
,
7425
(
1989
).
83.
G. G.
Katul
,
M. B.
Parlange
, and
C. R.
Chu
, “
Intermittency, local isotropy, and non-Gaussian statistics in atmospheric surface layer turbulence
,”
Phys. Fluids
6
,
2480
2492
(
1994
).
84.
G. G.
Katul
,
M. B.
Parlange
,
J. D.
Albertson
, and
C. R.
Chu
, “
Local isotropy and anisotropy in the sheared and heated atmospheric surface layer
,”
Boundary-Layer Meteorol.
72
,
123
148
(
1995
).
85.
H. J.
Catrakis
and
P. E.
Dimotakis
, “
Scale distributions and fractal dimensions in turbulence
,”
Phys. Rev. Lett.
77
,
3795
(
1996
).
86.
P. E.
Dimotakis
and
H. J.
Catrakis
, “
Turbulence, fractals, and mixing
,” in
Mixing
(
Springer
,
1999
), pp.
59
143
.
87.
H. J.
Catrakis
, “
Distribution of scales in turbulence
,”
Phys. Rev. E
62
,
564
(
2000
).
88.
K. R.
Sreenivasan
and
C.
Meneveau
, “
The fractal facets of turbulence
,”
J. Fluid Mech.
173
,
357
386
(
1986
).
89.
A.
Scotti
,
C.
Meneveau
, and
S. G.
Saddoughi
, “
Fractal dimension of velocity signals in high-Reynolds-number hydrodynamic turbulence
,”
Phys. Rev. E
51
,
5594
(
1995
).
90.
K. R.
Sreenivasan
, “
Fractals and multifractals in fluid turbulence
,”
Annu. Rev. Fluid Mech.
23
,
539
604
(
1991
).
91.
H. J.
Catrakis
, “
The multiscale-minima meshless (M3) method: A novel approach to level crossings and generalized fractals with applications to turbulent interfaces
,”
J. Turbul.
9
,
N22
(
2008
).
92.
H.
Panofsky
and
G.
Brier
,
Some Applications of Statistics to Meteorology
(
Pennsylvania State University, University Park
,
1958
).
93.
J.
Lumley
,
Stochastic Tools in Turbulence
(
Academic Press
,
1970
).
94.
J. V.
Selinger
,
N. V.
Kulagina
,
T. J.
O’Shaughnessy
,
W.
Ma
, and
J. J.
Pancrazio
, “
Methods for characterizing interspike intervals and identifying bursts in neuronal activity
,”
J. Neurosci. Methods
162
,
64
71
(
2007
).
95.
J.
Strecker
, Fractional Brownian motion simulation: Observing fractal statistics in the wild and raising them in captivity, 2004, http://www.cs.umd.edu/strecker/jstreckerIS-pdflatex.pdf.

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