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Angel December 21, 2001 13:12

real velocity field from energy spectrum

I must obtain a real velocity field from a given energy spectrum, but I am having some problems. The velocity field must be real, 3 dimensional and must satisfy the continuity equation for incompressible flows.

Could someone give any reference?

Thank you.


Srinivasan Arunajatesan December 21, 2001 15:10

Re: real velocity field from energy spectrum
I am assuming that the velocity field you are looking for is on a periodic box for an isotropic turbulence case.

There are tons of references for this : you can check a paper in the 97-98 time frame by O'Kongo and Knight in AIAA Reno conference. That paper explains things in gory detail.

The summary of steps is :

you basically take a field of random velcotities, transform them to fourier space, subtract out the divergence from them, rescale the spectrum to match the spectrum you want, and then transform the field back to physical space.

for pressure, you can solve the poisson equation to get the pressure field once the velocity field is done.

You will get a divergence free spectrum, but not a real velocity field. the spatial correlations will be wrong- I know of no way to get that right. What people usually do is to run this a few time steps - the turbulence kinetic energy decays rapidly, but the spatial correlations work themselves out - then you can rescale the field back to get the kinetic energy to the level you want and use this as the initial condition.

hope this is clear enough to help, if you need the exact reference, I can dig it up.


Paul December 26, 2001 09:10

Re: real velocity field from energy spectrum
hi, Srinivasan, seems that I have to ask you to dig that paper up. I am also interested in it.

P.S. I wander how to pronounce your name, and its meaning, if any. :)

Srinivasan December 28, 2001 12:49

Re: real velocity field from energy spectrum

I am out of town this week I will send you the ref. as soon as I get back.


Srinivasan December 29, 2001 11:44

Re: real velocity field from energy spectrum
Hi! Paul,

Dr. Knight has some of his papers online, you can donwnload his AIAA-98-0535 paper from his site :

There are also some other papers that might be of interest to you.


Paul December 30, 2001 22:16

Re: real velocity field from energy spectrum
Hey, Srinivasan, thank you very much!


sylvain January 2, 2002 08:32

Re: real velocity field from energy spectrum
I'm sorry but I can't find the article I have about this subject, but you may look at google with 'langevin spectrum'.

Happy new year.


anzillo December 13, 2013 21:40

Hello everyone

If you receive this message, I would be very thankful if you could reply to the following query:

- I understand that Rogallo's code can be used to generate an random velocity field that is divergence free in wavenumber space.
- Once converted to physical space, it loses its solenoidal character. However, after letting the field decay for a few turn-over times it does show some realistic correlations.

Now, I would like to know how is the 'rescaling' done to match the spectrum that I desire. I generated the field to match a certain spectrum, but the field has now lost its energy due to decay.

Does 'rescaling' mean that I multiply the field variables (velocities) by a value to make sure that the scaled field has the same 'peak value in the desired energy spectrum' although the scaled field might not have exactly the desired spectrum.

It would be great if you could assist me with this.

Thank you ! :)

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