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Detecting Intermittent Turbulence Using Advanced Signal Processing Techniques
Christina Ho, Xiaoning Gilliam, and
Sukanta BasuTexas Tech University
AIAA – January 8th, 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 thepresence 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