Wind Noise and Atmospheric Turbulence

March 20, 2007

NASA – Visible Earth, Madeira Island (visibleearth.nasa.gov)

What is wind noise?

• Not sound

• Very local pressure fluctuations

• Low frequency

How do windscreens work?

• Long standing theory due to Phelps (1930’s)

• Bernoulli equation holds:• At low frequencies velocity variations produce pressure fluctuations,

distributed just like the steady pressure• Pressure measured at the center is average of surface pressures

20 21 vpp

Flow around a cylinder

Many acoustic systems would work much better if we could eliminate low frequency wind noise

Elephant

http://fohn.net/elephant-pictures-facts/

Scott Morgan – University of Mississippi PhD Student“Investigation of the mechanisms of low frequency wind noise generation outdoors.”

Measured pressure fluctuations with a microphone

Measured velocity fluctuations with hot wire anemometer

Wind velocity measurement along one direction

0 100 200 300 400 500 600 700 800 900-5

0

5

10

Time (s)

Vel

ocity

(m

/s)

Scott’s findings

• Found that the pressure fluctuations depend directly on the wind velocity fluctuations U and average wind speed V

• Wind noise depends on the wind screen and atmospheric turbulence

Atmospheric Turbulence

Now we need to understandMeteorology

and

Fluid Dynamics

Turbulence is

a) Three-dimensional

b) Non-linear

c) Random

G.K. Batchelor

The Theory of Homogeneous Turbulence, 1956

Need additional mathematical tools to analyze atmospheric turbulence

Non-Linear and Random – Don’t get the same velocity field

when you repeat an experiment

I. Fourier analysis

II. Correlations

I. Fourier Analysis

Sine waves have two attributes, Frequency and Amplitude

0 500 1000 1500 2000-10

-5

0

5

10

Time

Period = 1/Frequency

Amplitude

Any

Wav

e A

mpl

itude

Wiggly Wave

0 100 200 300 400 500 600 700 800 900 1000-1.5

-1

-0.5

0

0.5

1

1.5

2

Time

Any

Wav

e A

mpl

itude

Fourier showed that any wave can be written as a sum of different sine waves

0 100 200 300 400 500 600 700 800 900 1000

-1

-0.5

0

0.5

1

Time

Am

plitu

de

0 100 200 300 400 500 600 700 800 900 1000-2

-1

0

1

2

Time

Am

plitu

de

Simple Fourier Spectrum

Apply Fourier analysis to atmospheric turbulence

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0

5

10

Time (s)

Ve

loci

ty (

m/s

)

0 100 200 300 400 500 600 700 800 900-5

0

5

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Time (s)

Ve

loci

ty (

m/s

)

Two wind velocity measurements at the university airport taken approximately 30 min apart.

.001 .01 .1 1 10 100

10-5

100

Frequency

Am

plit

ud

e

.001 .01 .1 1 10 100

10-5

100

Frequency

Am

plit

ud

e

Fourier spectra of the two velocity measurements.

Atmospheric Turbulence

“Big whorls have little whorls that feed on their velocity, and little whorls have smaller whorls and so on to viscosity.”

--Lewis Frye Richardson

.001 .01 .1 1 10 100

10-5

100

105

Frequency

Am

plit

ud

e (

En

erg

y)Source(big whorls)

Inertial(smaller whorls)

Slope always the same

Audible range

II. Correlations

A correlation is a measure of how alike two velocity or pressure measurements are.

Rule:Corr = +1 Data sets have same shape

(can be different sizes)

Corr = 0.5 Some similarity

Corr = 0 Data sets randomly related

Corr = -1 Data sets have same shape, but inverted.

0 20 40 60 80 100-20

0

20

0 20 40 60 80 100-20

-10

0

10

0 20 40 60 80 100-5

0

5

10

0 20 40 60 80 100-5

0

5

10

Corr = ?

Corr = ?

Corr = ?

Corr = ?

Rules:

SameCorr = 1

Similar:Corr = 0.5

Random:Corr = 0.0

Inverted:Corr = -1

Let’s train your neural network

Two velocity measurements – look carefully, do you see how they are related?

15 20 25time (s)

Systematically shift the two measurements and repeat the correlation.

0 1 2 3 4 5 6 7 8 9 10-0.5

0

0.5

1

Offset time (s)

What would we expect the graph of the correlations to be?

Correlation versus Distance between two wind velocity measurements?

0 10 20 30 40 50 60 70-0.5

0

0.5

1

Distance (cm)

Co

rre

latio

n

If two microphones are far enough apart, the turbulence and wind noise are random.

What about the sound each receives?

We’ve learned a lot from meteorologists about tools and classification of turbulence.

Meteorologists are interested in atmospheric turbulence because it transports:

-Pollutants-Heat-Water Vapor

But, pressure fluctuations are not important to them.

This leads us to Fluid Dynamics

General equation for incompressible flow

ji

ji

xx

uup

2

2

George uses mathematical Correlations and Fourier Transforms to predict the spectrum of the pressure given only the spectrum of the wind velocity, and compares to measurement.

Our Work! – We apply his methods to wind noise calculations outdoors and compare to measurements.

Experimental Setup

Measured wind velocity spectrumwith fit to the data

Measured pressure spectra with predictions

.001 .01 .1 1 10 10010

-10

10-5

100

105

Frequency

Win

d A

mp

litu

de

.1 1 10 100

10-5

100

Frequency

Pre

ssu

re A

mp

litu

de

Bare Microphone

Great big windscreen

What we’ve learned about windscreens

Recall that at low frequencies the pressure distributions should resemble the steady flow pressure distribution.

Front Middle Back

Ste

ady

Pre

ssur

e

Plan! In order to reduce wind noise, Use lots of little microphones near the windscreen surface and pick ones or combinations with low pressures.

Maybe we should measure the pressure distribution.

Wind

If Phelps is right, what should the correlations look like?

0 5cm 10cm 15cm

0

Higher Velocity

Lower Velocity

Middle Velocity

Phelps model prediction of the correlations between a microphone at the front of the windscreen and a microphone located a distance x around the windscreen

0m 5cm 10cm 15cm

0 50 100 150 200-0.5

0

0.5

1

Pressure Correlations

What, in fact, do they look like?

0m 5cm 10cm 15cm

0 50 100 150 200-0.5

0

0.5

1

Velocity Correlations

0m 5cm 10cm 15cm

What about velocity correlations around the same windscreen?

.1 1 10 100

10-6

10-4

10-2

100

102

Frequency

Pre

ssu

re A

mp

litu

de

Our Prediction

New Understanding

We can predict the wind noise level of a smaller windscreen at low frequency based on the shorter correlation length.

Declare Victory!

• We can exploit the decorrelation for a better design

• But we would like to understand why.

Footnote: What’s left out of Phelps/Bernoulli

General equation:

-1 -0.5 0 0.5 1X

-1

-0.5

0

0.5

1

Y

-1 -0.5 0 0.5 1X

-1

-0.5

0

0.5

1

Y

Images from Xiao-Lun Wu’s presentation “Statistical Fluctuations in Two-Dimensional Turbulence”

ji

ji

xx

uup

2

2

Conclusions

• Wind noise depends on state of the atmospheric turbulence.

• Can calculate lower limit to wind noise from measured wind velocity spectrum

• Can calculate wind noise in a bare microphone from measured velocity spectrum

• Can calculate the wind noise in a small wind screen from the measured wind velocity spectrum and the measured correlation length

• This method replaces the long standing Phelps model of low frequency wind noise reduction by small wind screens