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#1 |
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Aru
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I am computing energy spectrum for computationally obtained turbulence data, which is statistically homogeneous in 2 directions (X & Z). The energy spectrum is calculated for a homogeneous plane, using Fourier transforms of the spatial data.
![]() The calculated spectrum shows a 'bump' at higher wavenumbers (not the highest). It is prominent in a semilog plot (attached). I am wondering what could have resulted in this anomalous behaviour. I assume it is associated with some error in calculating the spectrum but has nothing to do with the physics. However, I am unable to find any error in the calculation. I would like to know if anybody in the community has encountered a similar erroneous spectrum, and what could cause such anomaly? |
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#2 |
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Uwe Pilz
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You may look whether the wavelength of your bump region coincides with the size of the mesh.
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Uwe Pilz -- Die der Hauptbewegung überlagerte Schwankungsbewegung ist in ihren Einzelheiten so hoffnungslos kompliziert, daß ihre theoretische Berechnung aussichtslos erscheint. (Hermann Schlichting, 1950) |
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#3 |
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Aru
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Hi piu58,
I should have mentioned my mesh and domain earlier. ![]() There are 512x128 points in the XZ plane which has a physical dimension ![]() ![]() ![]() ![]() ![]() ![]() I understand that under-resolved data results in oscillations at highest wavenumbers.In this case, I am perplexed by the smooth spectrum beyond ![]() |
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#4 |
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Filippo Maria Denaro
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What problem are you solving, a plane channel flow? And what about the Re_tau of your problem? what about y+ of the computed spectrum?
What I do not understand is the fact you have the spectrum extending over the Nyquist frequency... Or am I wrong in understanding your comment? Then, the magnitude of E(k) is very high, why? |
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#5 |
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Aru
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The problem under consideration is temporal mixing layer.
On the x-axis I have ![]() ![]() As of now, both k and E(k) are not scaled. My objective of plotting the spectrum is to make sure I am resolving the scales sufficiently. |
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#6 |
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Filippo Maria Denaro
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Quote:
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#7 | ||
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Aru
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Quote:
Quote:
To summarise, can I attribute the "bump" to the method where I am going above the Nyquist limit? |
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#8 |
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Filippo Maria Denaro
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Compute the 1d spectra but perform the spatial averaging along the normal direction
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#9 | |
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Aru
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Quote:
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#10 | |
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Filippo Maria Denaro
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Quote:
No, you compute first the FFT and then you perform the average of the coefficients |
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#11 |
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Aru
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The calculated one-dimensional spectrum is attached.
A smooth curve is not obtained even after averaging FFT coefficients in the Z direction. Is it required to perform an average in time to obtain a smooth spectrum? |
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#12 |
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Filippo Maria Denaro
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That looks quite correct ... have a look at sec.5.2 here
https://www.researchgate.net/publica...-uniform_grids and Ref.42 in the reference |
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#13 |
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Aru
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One dimensional spectra,
![]() ![]() In this reference, the spectrum is calculated as ![]() which seems to be an averaging in the non-homogeneous direction. If so, what difference this makes to the spectrum? |
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#14 |
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Filippo Maria Denaro
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Your results seems physically acceptable.
You can have two choices: 1) the averaging along the non-homogeneous domain give the total energy content of the mixing layer for each wavenumber component. 2) computing and analysing spectra at several stations along y+. This is for example the standard procedure for a channel flow. Both are correct and the choice depends on what you want to analyse. I used the averaging along y to compare the solutions with the paper of Lesieur. |
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#15 | ||
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Aru
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Dear FMDenaro,
Thank you for your valuable suggestions. Can you provide some clarification regarding the 'binning' procedure? Quote:
Quote:
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#16 |
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Filippo Maria Denaro
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The plot is versus the frequency or the integer wavenumber, the relation being k=n*2*pi/L (n=0,1,2..,Nmax). The Nyquist frequency is kmax=pi/h. This is for each direction Lx and Lz.
What do you mean exactly for "binning procedure"? |
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#17 |
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Aru
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The length of the domain in x direction is
![]() In the latter plot, I have used only integer values of wavenumber on the x-axis. The energy of non-integer wavenumbers is rounded off to nearest integer k. For example, E(1) is the sum of all u(k)^2 for k=4/8,5/8,.....,10/8,11/8. This procedure was described in a reference, but I couldn't trace it now. |
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#18 |
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Filippo Maria Denaro
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After you perform the FFT, you have a vector of the complex Fourier coefficients for each integer n=0,1,... Thus, you can plot (in a log scale) the modulus versus these non-dimensional numbers or you simply convert the integers in the dimensional spatial frequency k = n*2*pi/L.
No "binning" in such procedure... |
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