Decomposition nonstationary turbulence velocity in open channel flow Ying-Tien Lin 2005.12.12

Background Laminar flow and turbulent flow

Background Flow velocity profile

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

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

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

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.