Calculation of spectral transfer flux T(k)

gharek · July 28, 2017, 07:30

Hi guys,

I would like to get your advice on this.

In homogeneous turbulence, a dynamic equation can be written for the 3D energy spectrum E(k), whereby the time rate of Energy spectrum is related to the spectral energy transfer T(k) and dissipation:

dE(k)/dt = T(k) - 2vk^2E(k)

Now, I have calculated E(k) from a 3D data field, and would like to calculate T(k). Is there a direct way to work out T(k)? I have tried to take the Fourier transform of the non-linear triad interactions in physical space, but have not achieved a good result.

Appreciate your help!

FMDenaro · July 28, 2017, 12:53

Without more details I cannot say if you are wrong in the procedure...What is the problem you see? Does the integral of T(k) vanish?

gharek · August 1, 2017, 05:20

Quote:

Originally Posted by FMDenaro

Without more details I cannot say if you are wrong in the procedure...What is the problem you see? Does the integral of T(k) vanish?

The T(k) profile seems to be very noisy. Just to make sure that I am on the right track.. I computed the product u_i*u_j*d(u_i)/dx_j, and then take the Fourier transform of it and obtain the real coefficients.

FMDenaro · August 1, 2017, 13:51

Try to check the expression reported in the book Turbulence of U.Frisch, from sec.6.2.2 it explains the transfer function for homogeneous turbulence

July 28, 2017, 07:30	Calculation of spectral transfer flux T(k)	#1
gharek New Member Gareth Join Date: Apr 2010 Location: Sydney Aus Posts: 14 Rep Power: 16	Hi guys, I would like to get your advice on this. In homogeneous turbulence, a dynamic equation can be written for the 3D energy spectrum E(k), whereby the time rate of Energy spectrum is related to the spectral energy transfer T(k) and dissipation: dE(k)/dt = T(k) - 2vk^2E(k) Now, I have calculated E(k) from a 3D data field, and would like to calculate T(k). Is there a direct way to work out T(k)? I have tried to take the Fourier transform of the non-linear triad interactions in physical space, but have not achieved a good result. Appreciate your help!

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July 28, 2017, 12:53		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,896 Rep Power: 73	Without more details I cannot say if you are wrong in the procedure...What is the problem you see? Does the integral of T(k) vanish?

August 1, 2017, 13:51		#4
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,896 Rep Power: 73	Try to check the expression reported in the book Turbulence of U.Frisch, from sec.6.2.2 it explains the transfer function for homogeneous turbulence