Wind Noise and Atmospheric Turbulence March 20, 2007

1. Wind Noise and Atmospheric TurbulenceMarch 20, 2007 NASA – Visible Earth, Madeira Island (visibleearth.nasa.gov)

3. What is wind noise? • Not sound • Very local pressure fluctuations • Low frequency

4. 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

5. Flow around a cylinder

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

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

8. 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

9. Wind velocity measurement along one direction

10. 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

11. Atmospheric Turbulence Now we need to understand Meteorology and Fluid Dynamics

12. Turbulence is • Three-dimensional • Non-linear • Random G.K. Batchelor The Theory of Homogeneous Turbulence, 1956

13. 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

14. I. Fourier Analysis Sine waves have two attributes, Frequency and Amplitude Any Wave Amplitude

15. Wiggly Wave

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

17. Simple Fourier Spectrum

18. Apply Fourier analysis to atmospheric turbulence Two wind velocity measurements at the university airport taken approximately 30 min apart.

19. Fourier spectra of the two velocity measurements.

20. Atmospheric Turbulence

21. “Big whorls have little whorls that feed on their velocity, and little whorls have smaller whorls and so on to viscosity.” --Lewis Frye Richardson

22. 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.

23. Let’s train your neural network Corr = ? Rules:SameCorr = 1Similar:Corr = 0.5 Random:Corr = 0.0Inverted: Corr = -1 Corr = ? Corr = ? Corr = ?

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

25. Systematically shift the two measurements and repeat the correlation.

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

27. Correlation versus Distance between two wind velocity measurements?

28. If two microphones are far enough apart, the turbulence and wind noise are random.What about the sound each receives?

29. 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

31. General equation for incompressible flow 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.

32. Experimental Setup

33. Measured wind velocity spectrum with fit to the data Measured pressure spectra with predictions

34. What we’ve learned about windscreens Recall that at low frequencies the pressure distributions should resemble the steady flow pressure distribution. Steady Pressure Front Middle Back

35. 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

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

37. 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

38. What, in fact, do they look like? 0m 5cm 10cm 15cm

39. What about velocity correlations around the same windscreen? 0m 5cm 10cm 15cm

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

41. Declare Victory! • We can exploit the decorrelation for a better design • But we would like to understand why.

42. Footnote: What’s left out of Phelps/Bernoulli General equation: Images from Xiao-Lun Wu’s presentation “Statistical Fluctuations in Two-Dimensional Turbulence”

43. 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