Decomposition nonstationary turbulence velocity in open channel flow

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Decomposition nonstationary turbulence velocity
in open channel flow

• Ying-Tien Lin
• 2005.12.12

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Background

• Laminar flow and turbulent flow

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Background

• Flow velocity profile

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Background

• Turbulent flow occurs in our daily life.
• put cube sugar into a cup of coffee
• Turbulent model
• Assume

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Background

• Reynolds shear stress

Sediment particles
Shear stress
River
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Background

• Stationary turbulence flow
• Nonstationary turbulence flow (occurs in flooding
  period)

Mean velocity
How to find its time-varying mean velocity?
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Decomposition method

• Fourier decomposition method
• Wavelet transformation
• Empirical mode decomposition

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Fourier decomposition method
DFT
LF
Inv. DFT

• It is unable to show how the frequencies vary
  with time in the spectrum.

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Wavelet transformation
DWT
Threshold
Inv. DWT

• Linear combinations of small wave
• Be able to show the frequency varies with time

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Empirical Mode Decomposition (EMD)

• The upper and lower envelopes of U(t) are
  constructed by connecting its local maxima and
  minima.

Upper envelope
Velocity
Instantaneous velocity
Lower envelope
Time
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Empirical mode decomposition (EMD)

• The mean value of the two envelopes is then
• computed. The difference between the
• instantaneous velocity and the mean value
• is called the first intrinsic mode function
• (IMF), c1(t). IMF is a function that
• 1. has only one extreme between zero
• crossings.
• 2. has a mean value of zero.
• This is called the Sifting Process

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C1(t)
C5(t)
C12(t)
residual(t)
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Results
Add noise
Denoising
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Results
Add noise
Denoising
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Summary

• These three decomposition methods perform good
  fitting with the original functions.
• EMD seems better than the other two methods.