1. Decomposition nonstationary turbulence velocity in open channel flow
Ying-Tien Lin

2. Background
Laminar flow and turbulent flow

3. Background
Flow velocity profile

4. Background Turbulent flow occurs in our daily life.
put cube sugar into a cup of coffee
Turbulent model
Assume
Turbulent velocity or Fluctuated velocity
Mean velocity

5. Background
Reynolds shear stress
Sediment particles
Shear stress
River

6. Background Stationary turbulence flow
Nonstationary turbulence flow (occurs in flooding period)
Mean velocity
How to find its time-varying mean velocity?

7. Decomposition method Fourier decomposition method
Wavelet transformation
Empirical mode decomposition

8. Fourier decomposition method
DFT LF
Inv. DFT
It is unable to show how the frequencies vary with time in the spectrum.

9. Wavelet transformation
DWT
Threshold
Inv. DWT
Linear combinations of small wave
Be able to show the frequency varies with time

10. 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

11. 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

12. C1(t)
C5(t)
C12(t)
residual(t)

13. Results
Add noise
Denoising

14. Results
Add noise
Denoising

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