Detecting Intermittent Turbulence Using Advanced Signal Processing Techniques

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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