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ulrich bieder June 23, 1999 07:54

turbulent energy spectra
hi there, i am calculating the flow around a circular cylinder at Re=3900 using LES. The energy spectra in the near wake is rather k~-3 than k~-5/3. This corresponds to our experimental results in the near wake of TWO cylinders at Re=1000. Where can i get experimental values of the energy spectra in the near wake of one cylinder (Re=3900)?

thank you

Patrick Godon June 23, 1999 10:50

Re: turbulent energy spectra
Hi here,

Are you simulating a full 3D problem or just a 2D cut of the flow (in a plane perpandicular to the cylinder).

your results seems to imply that the flow has a two-dimensional behaviour. log(Ek)~-5/3 is for homogeneous 3D, while log(Ek)~-3 is more 2D like.

In the 2 cylinders cases I understand that the 2 cylinders defined a plane (between them) and therefore the flow there is really 2D, if the simulations is really 3D.

The Reynolds number should not affect too much the inertial range of the energy spectrum. The viscous dissipation should occur at the highest wavenumbers with a very steep slope especially if you use a hyperviscosity of high power. If you don't, then you might cut-off the inertial range and get the slope of the viscous dissipation of the spectrum.

Cheers, Patrick.

ulrich bieder June 23, 1999 12:16

Re: turbulent energy spectra
hi patrick;

for sure i am simulating a full 3D problem.

our experimental result of the two cylinders does not show any 2d "symmetry" plan. Rather the flow is real 3D. This is why i suppose that the calculated log e(k)~-3 spectra might be correct.

thank you for the comment


Patrick Godon June 23, 1999 13:19

Re: turbulent energy spectra

I would still look for two-dimensional effects in the flow.

1) near the cylinder the flow is actually rotating around the cylinder (rolling over). Rotation is known to affect the Energy spectrum and to introduce a two-dimensional effect in flows. But this might be true only in the immediate vicinity of the cylinder. There, for sure, the boundary layer (and its detachment) are certainly also affecting the flow.

2) the Von Karman VOrtex street forming downstream the cylinder is really a two-dimensional 'sheet', and the turbulence there might be 2D (if the cylinder is much longer than thick, then for sure it is inhomogeneou). I guess the same might happen with 2 cylinders.

I am not sure how far from the cylinder you are simulating. And I am just trying to see if simple analysis can help to explain the results.


Patrick Godon June 23, 1999 14:18

Re: turbulent energy spectra
Hi Ulrich,

just in case you did not get my email:

From the picture you sent the turbulence is inhomogeneous and two-dimensional on the large scale. The turbulence seems three-dimensional on the small scale. If d is the radius of the cylinder, and l the scale of the turbulent eddies, then near the cylinder at r~d, one has l is smaller than d and 3D turbulence, further away it looks like r larger than d however l~d and the turbulence is 2D.

So the spectrum at small wavenumbers k (large scale length) is like log(Ek)~-3; at high wavenumbers (small scale length) the spectrum should be more like log(Ek)~-5/3 (Kolmogorov). At even higher wavenumbers the spectrum should be cut off sharply with a sharp slope due to the (hyper)viscosity.

If you observed only a slope of -3, it could just be that that you don't have enough resolution or that the viscosity is affecting the inertial range of the 3D homogeneous turbulence (you might have an hyperviscosity with a too small power - exponential power I mean).

You could try to check the spectrum in the vicinity of the cylinder in a volume d**3, to see if it is ~-5/3.

Cheers, Patrick.

Gary Dantinne June 24, 1999 03:19

Re: turbulent energy spectra

You can have a look at the DNS results (and LES results) published by G. E. Karniadakis in Fluid Dynamics Research 24 (1999) pp 34-362

For this kind of problem you may also find interesting to look at numerical results obtained through vortex particle methods which are better in this case than any grid-based methods. I don't have any precise references but Leonard 's papers must surely be a good start.

Hope it helps

Ravi Krishnamurthy June 24, 1999 13:51

Re: turbulent energy spectra
The best the I can find closest to what you want is the work of Rajat Mittal in the

Annual Research Briefs, 1995 of Center for Turbulence Research (CTR), Stanford Univeristy.

You can check this out online in the CTR site at

The paper is "Large Eddy Simulation of flow past a circular cylinder "


Adrin Gharakhani June 24, 1999 14:34

Re: turbulent energy spectra
The vortex particle simulation that was mentioned is by Koumoutsakos and Leonard in JFM (post-1993, I forget the exact date). However, it is a 2D (not 3D) DNS simulation for short times.

The most accurate 2D DNS simulation of flow over cylinders by the vortex element method, however, has thus far been conducted by Dr. Shankar Subramaniam. His results at Re=3000 compare very well with experiments and at Re=9500 the results compare excellently with the spectral element simulations of Kruse and Fisher.

Unfortunately, he hasn't published his results in any journals. But they are available in his thesis "A new mesh-free vortex method" The Florida State university, 1996.

Adrin Gharakhani

olus boratav June 25, 1999 10:27

Re: turbulent energy spectra

In 3D large resolution simulations using an array of vortices as the initial condition, there is a very violent (early) interaction phase where the spectrum is around k^-4, k^-3.

Following this phase, the vortices break up and Kolmogorov regime is attained having the k^-5/3 with slight corrections.

See Boratav and Pelz (1994), Physics of Fluids 6(8) second column on page 2770.

One has to check the resolution for sure. It is also possible that the small scales are not formed yet (either it is not late enough or the Reynolds number is not high enough). The existence of sheet-like objects would lead to a k^-3 type of spectra as well.

Olus Boratav

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