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 SpeedWind 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 ObservedTurbSim 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 SeriesCWT Surrogate Series 1 Surrogate Series 2 Surrogate Series M 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 NeutralLLJ

To be continued…

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