
[Sponsors] 
May 30, 2022, 04:58 
Turbulent energy spectra

#1 
New Member
Join Date: May 2022
Posts: 18
Rep Power: 4 
Hi everyone,
I study flows in biperiodic channel and I would like to plot turbulent energy spectra in 1D (streamwise direction). I had the instantaneous fields of my 3 velocity components at a fixed distance from the channel wall (y+40). I perform a Fourier transform thanks to Python as follows: 1) I store 1 line of my instantaneous field of U in the streamwise direction in a vector (same for V and W) 2) I perform the FFTs: Code:
FFT_U=abs(np.fft.fft(U))**2 Code:
FFT_V=abs(np.fft.fft(V))**2 Code:
FFT_W=abs(np.fft.fft(W))**2 Code:
0.5(FFT_U+FFT_V+FFT_W) I obtain a 1D spectrum that have a shape in agreement with the literature (at the same friction Reynolds number) but the energy levels are significantly different. I am not sure about the formulae used to compute the kinetic energy spectra. Is the following expression right ? Code:
abs(np.fft.fft(U))**2+abs(np.fft.fft(V))**2+abs(np.fft.fft(W))**2 Sincerely, Boone 

May 30, 2022, 06:37 

#2  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,849
Rep Power: 73 
Quote:
If you search in the forum, you will find several posts that answer you. I personally posted years ago a matlab script for doing that. 

May 30, 2022, 08:28 

#3 
New Member
Join Date: May 2022
Posts: 18
Rep Power: 4 
Dear FMDenaro, thank you for your answer.
I effectively found these posts that help me proposing the expression I wrote in my first message: Plot Turbulence Spectrum Using 2D Spatial FFT Energy spectrumwrong spectrum shape Energy Spectrum for a 3D turbulent Flow Computing the energy spectrum of a turbulent channel flow I plotted (abs(FFT(U)))^2+(abs(FFT(V)))^2+(abs(FFT(W)))^2 as function of the streamwise wave number. I am surprised by the energy levels which are very high when compared to the levels obtained by some author of the literature (see: fig 5. of Spectral analysis of turbulence based on the DNS of a channel flow Igor A. Bolotnov et al. 2010 Computers & Fluids) 

May 30, 2022, 14:31 

#4  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,849
Rep Power: 73 
Quote:
1) if you want to plot the 1D spectra, why do you sum the contribution of U,V and W? 2) If you are working with the nondimensional equations, your velocity fields are already nondimensionalized by u_tau. 

May 31, 2022, 02:54 

#5 
New Member
Join Date: May 2022
Posts: 18
Rep Power: 4 
1) I thought that is was possible to compute the total contribution of the 3 velocities along 1 direction (streamwise, x). My mesh is homogeneous in this direction and in the spanwise direction (z). Isn't it the case ?
2) I am working with dimensional equations. My fields of velocity are in m/s. That is why I normalized by nu*Utau the energy spectrum.  Do you have any other idea that can cause this energy difference ? Is there a difference between the energy spectrum and the density energy spectrum ? Thanks ! 

May 31, 2022, 05:12 

#6  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,849
Rep Power: 73 
Quote:
The velocity is normalized by utau, therefore the first issue is in your computation of u_tau. Then, the kinetic energy is normalized by u_tau^2. 

May 31, 2022, 06:58 

#7 
New Member
Join Date: May 2022
Posts: 18
Rep Power: 4 
In the literature, see: fig 5. of Spectral analysis of turbulence based on the DNS of a channel flow Igor A. Bolotnov et al. 2010 Computers & Fluids, it seems that the energy spectrum is normalized by Utau*nu [m3/s2] which seems coherent to obtain a normalized energy spectrum.
I think that if a want to first normalize the velocity I have to do: abs(np.fft.fft(U/Utau))**2 but the resulting energy spectrum will be homogeneous to meter. 

May 31, 2022, 09:52 

#8 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,849
Rep Power: 73 
Yes. Spectral density has dimension m^3/s^2.
Have a check here to see if your different scaling is due to these issues https://journals.ametsoc.org/view/jo...170056.1.xml 

Tags 
fourier transform, spectral analysis, tke 
Thread Tools  Search this Thread 
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Energy equation  where is the turbulent kinetic energy?  usv001  OpenFOAM Programming & Development  1  January 25, 2022 16:04 
Contributions to turbulent kinetic energy in les  sonsonst  FLUENT  2  November 12, 2021 16:17 
Problem with divergence  TDK  FLUENT  13  December 14, 2018 07:00 
Turbulent kinetic energy at wall?  alanlove  FLUENT  1  November 23, 2012 12:24 
LES and total turbulent kinetic energy  Boerge  FLUENT  1  September 8, 2012 12:41 