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Isotropic Turbulence IC / Rogallo-procedure

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Old   February 20, 2013, 12:55
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Hi LNA,

Just dropping a quick question, when you had "small strange oscillations at the large wave numbers" i.e. that little weird peak, do you have data readily available to plot with that version of your code, I was hoping you could obtain this function just so I can confirm something im not seeing in my DNS, the function is;

E(kappa)*kappa^(5/3)/epsilon^(2/3)=C_kol

i.e. a plot of C_kol vs kappa*eta with logarithmic x and y axis, Its a compensated kolmogorov energy spectrum function

If you could upload a plot that would be awesome!!
Thanks in advance!
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Old   October 16, 2013, 07:49
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Hello

Thanks for telling us about the correction. I wanted to know how could one use the same code (for 3D) to generate a 2D velocity field.

Thank you.

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Old   October 27, 2013, 17:43
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I'm not sure I understand your question...are you asking about the exact solution to the 2D problem?
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Old   October 28, 2013, 05:02
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Hello !

Thank you for your response. What I meant was if Rogallo's procedure could be modified to generate a 2D velocity field that is homogeneous and isotropic, for a given energy spectrum.

I managed to do that with a little modification. However, the velocity field is not divergence free so to speak, the divergence is about 10^(-3) which is okay with regard to the solution's accuracy. But I would be more content if I could get the divergence to say 10^(-5).

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Old   December 14, 2013, 22:05
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Hello Everyone

Does anyone know why does the velocity field lose its solenoidal character after being converted to physical space from wavenumber space by using an IFFT?

I used Rogallo's procedure to generate the field (took care of the 'minus' sign) and made sure that the field matrix is conjugate symmetric before using the IFFT (all done in MATLAB).

I would be grateful to receive some help.

Thank you !

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Old   December 15, 2013, 08:08
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It all depends on how you compute the divergence in physical space. If you are not using a spectral method to do that (I am assuming that you are not), then you won't get a discrete divergence free condition. The way you are computing derivatives / divergence in both spaces (wave and physical) is not compatible, so you cannot expect symmetries etc. to hold.
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Old   December 15, 2013, 09:22
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Thank you for your prompt reply.

So, one can never convert a the spectral field generated with Rogallo's code into a divergence free velocity field in physical space?

That is why most authors simulate turbulence with spectral approach and mention that the field is divergence free (in spectral space)?
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Old   December 15, 2013, 09:45
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Quote:
Originally Posted by anzillo View Post
Thank you for your prompt reply.

So, one can never convert a the spectral field generated with Rogallo's code into a divergence free velocity field in physical space?

That is why most authors simulate turbulence with spectral approach and mention that the field is divergence free (in spectral space)?

as previously said, you can compute in physical space the continuos velocity field using the same spectral reconstrution that derive from your computation
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Old   December 15, 2013, 09:54
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Originally Posted by FMDenaro View Post
as previously said, you can compute in physical space the continuos velocity field using the same spectral reconstrution that derive from your computation
Hello Filippo

Thank you for your reply and apologies for repeating my question again. However, I did not understand the meaning of"

"compute in physical space the continuos velocity field using the same spectral reconstrution that derive from your computation"

I would glad if you could elaborate the meaning of the above sentence. I am not familiar with spectral related things because my code is meant for physical space.

Thank you !
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Old   December 15, 2013, 10:18
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Quote:
Originally Posted by anzillo View Post
Hello Filippo

Thank you for your reply and apologies for repeating my question again. However, I did not understand the meaning of"

"compute in physical space the continuos velocity field using the same spectral reconstrution that derive from your computation"

I would glad if you could elaborate the meaning of the above sentence. I am not familiar with spectral related things because my code is meant for physical space.

Thank you !

when you use a spectral code, you solve for the time evolution of the Fourier coefficients but that implies that you have the possibility to compute the velocity field by using the same coefficients in a discrete sum of a finite number of wavenumber components Ui(k)*epx(i*k*x). This will be your "continuous" velocity field in physical space.
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Old   December 15, 2013, 11:39
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Okay I got it now. Thank you
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