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## 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**Background**• Laminar flow and turbulent flow**Background**• Flow velocity profile**Turbulent velocity or Fluctuated velocity**Mean velocity Background • Turbulent flow occurs in our daily life. put cube sugar into a cup of coffee • Turbulent model Assume**Background**• Reynolds shear stress Sediment particles Shear stress River**Background**• Stationary turbulence flow • Nonstationary turbulence flow (occurs in flooding period) Mean velocity How to find its time-varying mean velocity?**Decomposition method**• Fourier decomposition method • Wavelet transformation • Empirical mode decomposition**Fourier decomposition method**• It is unable to show how the frequencies vary with time in the spectrum. DFT LF Inv. DFT**Wavelet transformation**• Linear combinations of small wave • Be able to show the frequency varies with time DWT Threshold Inv. DWT**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**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**C1(t)**C5(t) C12(t) residual(t)**Results**Add noise Denoising**Results**Add noise Denoising**Summary**• These three decomposition methods perform good fitting with the original functions. • EMD seems better than the other two methods.