Detecting Intermittent Turbulence Using Advanced
Signal Processing Techniques
Christina Ho, Xiaoning Gilliam,
and
Sukanta Basu
Texas Tech University
AIAA
–
January 8
th
, 2009
Motivation
Wind Turbine Inflow Generation
t = 0
t = T
TurbSim
User’s Guide
Wind Turbine Inflow Generation: IEC Spectral Models
Kaimal’s
Spectral Model (neutral boundary layer)
Several other models: e.g., Mann’s Uniform Shear Model
Nighttime (Intermittent) Turbulence
Observation (stable boundary layer)
CASES

99,
Poulos
et al. (2002)
Over the US Great Plains, intermittent
turbulence frequently occurs in the
presence of nocturnal low

level jets.
Background
The Atmospheric Boundary Layer (ABL)
ABL (~ 1km)
•
Turbulent fluxes of heat, momentum, and moisture are driving forces in
hydrologic, weather, and climate systems
Source: NASA
Atmospheric Boundary Layer (Cont…)
Original Source
: Stull (1988
);
Courtesy: Jerome Fast
Stable vs. Convective Boundary Layer (Potential Temp.)
TTU

LES:
stable boundary layer
TTU

LES
: convective boundary layer
Flow Visualization
of
Boundary
Layers
Turbulence

generation
by mechanical shear competes with turbulence
destruction by (negative) buoyancy forces
Ohya (2001
)
Near

Neutral
Very Stable
Nocturnal Low

Level Jets (LLJs)
Wind Speed
Wind Direction
Storm et al. (2008)
Beaumont ARM Profiler
Strong wind speed and directional shear
Large

Eddy Simulation
of
LLJs
What is Intermittency?
Definition of Intermittency
“The
term
intermittency
is
somewhat
ambiguous
in
that
all
turbulence
is
considered
to
be
intermittent
to
the
degree
that
the
fine
scale
structure
occurs
intermittently
within
larger
eddies
.
The
intermittency
within
a
given
large
eddy
is
referred
to
as
fine
scale
intermittency
.
Global
intermittency
defines
the
case
where
eddies
on
all
scales
are
missing
or
suppressed
on
a
scale
which
is
large
compared
to
the
large
eddies
.
”
(
Mahrt
,
1999
)

extended
quiescent
periods
interrupted
occasionally
by
‘bursts’
of
activity
(Coulter
and
Doran,
2002
)
Causes of Turbulence Intermittency
Intermittent turbulence
associated with:
(i) a density current,
(ii) solitary waves, and
(iii) downward propagating
waves from a LLJ.
Sun et al. (2002)
A Multi

scale Phenomenon
Outstanding Questions
What
are
the
statistical

dynamical
properties
of
these
intermittent
bursting
events?
What
is
the
statistical
distribution
of
the
on

off
phases?
Is
there
any
‘strong’
relationship
between
atmospheric
stability
and
intermittency?
“Turbulence
is
normally
considered
to
be
more
intermittent
in
very
stable
conditions
.
However,
some
studies
have
observed
intermittent
periods
of
relatively
strong
turbulence
in
less
stable
conditions,
in
contrast
to
background
weak
turbulence
in
very
stable
conditions
.
”
(
Mahrt
,
1999
)
Do
different
‘events’
(
e
.
g
,
density
current
vs
.
solitary
waves)
give
different
intermittency
signatures?
Can
we
numerically/synthetically
generate
these
bursting
events?
Detection & Analysis of Intermittency
Continuous Wavelet Transform (CWT)
Morlet
Wavelet
CWT of Observed and Simulated Turbulence
Observed
TurbSim
GP_LLJ
Statistical Hypothesis Testing
In
signals
with
a
highly
stochastic
nature,
the
wavelet
transform
often
replaces
a
complicated
one

dimensional
signal
representation
with
an
even
more
complex
two

dimensional
representation
.

we
replace
informal
interpretation
of
pictures
with
a
rigorous
statistical
test
.
Surrogate/Exemplar Analysis
Introduced
by
Theiler
et
al
.
(
1992
)
for
nonlinearity
testing

generalizations
and
modifications
by
several
others
Observed
Surrogate
IAAFT Algorithm (following Schreiber and Schmitz, PRL 1996)
Venema et
al. (2006)
Iterative Amplitude Adjusted Fourier Transform (IAAFT) =>
identical
pdf
, (almost) identical spectrum (but randomized phases)
Surrogate/Exemplar
Analysis (Cont…)
Observed
Surrogate
Surrogate/Exemplar
Analysis (Cont…)
Intermittency Detection
Framework
Original Series
CWT
Surrogate Series 1
Surrogate Series 2
Surrogate Series M
CWT
CWT
CWT
max
W(
b,a
)
b
max
W(
b,a
)
b
max
W(
b,a
)
b
Order
Statistics
T(a,
)
p

value
Graph
Thresholded
WT
max
W(
b,a
)
b
Intermittency Detection
Framework (Cont…)
TurbSim

IECKAI
TurbSim
–
GP_LLJ
Intermittency Detection
Framework (Cont…)
Observed
Thresholded CWT
Generation of intermittent bursting events will require a novel
nonlinear
approach.
Can We Fool the Intermittency Detection Framework?
AR(2) process with periodically
modulated variance
(Schreiber,
1998
)
p

Value Graph of the Modulated AR(2) Process
An Existing Solution
TurbSim
Kelley and Jonkman (2008)
Implications for Wind Energy Research
LLJ
Climatology & Wind Resource
Bi

Annual Low

Level Jet Frequency and Wind Resource (Smith 2003)
Modern Wind Turbines
Low Level Jets during
CASES

99 Field Campaign
CASES

99 Experiment (Banta et al. 2002)
Coincidence?
Storm and Basu (2009);
Based on Hand
(2003)
Recap: Neutral Flows vs. Low

level Jets
Wind profile: logarithmic
(approximated by a power

law)
Nominal wind speed shear (
α
~0.14)
Nominal wind directional shear
Bottom

up boundary layer
(turbulence is generated near the
surface)
Global

scale intermittency is absent
Wind profile: jet

type
Extreme wind speed shear (
α
>>0.14)
Strong wind directional shear
Bottom

up boundary layer
(turbulence is generated near the
surface); Upside

down boundary layer
structure is also possible (turbulence is
generated near the LLJ

core)
Global

scale intermittency is
observed quite frequently
Neutral
LLJ
To be continued…
On

Off Intermittency (aka Modulational Intermittency)
Toniolo et al.,
2002
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