[Nek5000-users] turbulent 3d box

Sun Dec 22 09:05:40 CST 2013

Hi Barak,

If your initial condition is:

      ux=(cos(y)+sin(z))
      uy=(cos(z)+sin(x))
      uz=(cos(x)+sin(y))

and your domain is [0,2pi]^3, how is it possible that your velocity magnitude
is less than 2?

What is your measure of velocity magnitude?   When I compute the L2
norm of this initial condition I'm seeing about 2.3+

Paul

________________________________
From: nek5000-users-bounces at lists.mcs.anl.gov [nek5000-users-bounces at lists.mcs.anl.gov] on behalf of nek5000-users at lists.mcs.anl.gov [nek5000-users at lists.mcs.anl.gov]
Sent: Sunday, December 22, 2013 7:53 AM
To: nek5000-users at lists.mcs.anl.gov
Subject: Re: [Nek5000-users] turbulent 3d box

Hi Paul,
It seems that something does not work, comparing my simulations using a standard spectral code (pseudo-spectral). For nu=0.1, I used 16 points for each space direction. Now for this case, the nonlinear terms vanish (just cancel each other) and the solution is just the ABC flow if you set it as initial condition. Then since the forcing is f=nu*ABC the dissipation term (Laplacian) dissipation=-nu*ABC and therefore the initial value (ABC) remains as it is. If we decrease the viscosity above the critical value of 1/12 (if I remember correctly) there is a bifurcation (Hopf...) and we obtain a new periodic solution (in time), where the ABC modes are dominating combined with some high wave numbers that are oscillating.

>From my first tests using NEK, I find that the velocity field (for nu>1/12) does not agree with the above characteristics. For example, the max magnitude of the velocity field should be for the ABC flow sqrt(3), whereas here I get a value close to 2.5.

Do you have any idea what's wrong?
If you wish to read some literature about the ABC flow as a forcing for Navier Stokes or as a prescribed velocity for generation of magnetic field (i.e., kinematic generation of magnetic field MHD):

1. D. Galloway and U. Frisch. A numerical investigation of magnetic field generation in a flow with chaotic streamlines. Geophysical & Astrophysical Fluid Dynamics, 29(1):13–18, 1984.

2. D. Galloway and U. Frisch. Dynamo action in a family of flows with chaotic streamlines.
Geophysical & Astrophysical Fluid Dynamics, 36(1):53–83, 1986.

3. Podvigina, Pouquet, On the non-linear stability of the 1:1:1 ABC flow,
Phys. D, Vol. 75, 4, 1994.

With my best wishes,
Barak

Quoting nek5000-users at lists.mcs.anl.gov<mailto:nek5000-users at lists.mcs.anl.gov>:

Hi Barak,

Thanks for the note about the ABC flow -- that's very useful.

What is your target viscosity?
If you want it to be 0.1, then you would set param 2 in the .rea file to be 0.1.
Setting param 2 = -0.1 would imply that Re=0.1 or equivalently nu=10.
Does this resolve the issue for you?

Once it's working we could add it as a documented example in the example
suite.

Thanks!

Paul
________________________________________
From: nek5000-users-bounces at lists.mcs.anl.gov<mailto:nek5000-users-bounces at lists.mcs.anl.gov> [nek5000-users-bounces at lists.mcs.anl.gov<mailto:nek5000-users-bounces at lists.mcs.anl.gov>] on behalf of nek5000-users at lists.mcs.anl.gov<mailto:nek5000-users at lists.mcs.anl.gov> [nek5000-users at lists.mcs.anl.gov<mailto:nek5000-users at lists.mcs.anl.gov>]
Sent: Saturday, December 21, 2013 5:24 PM
To: nek5000-users at lists.mcs.anl.gov<mailto:nek5000-users at lists.mcs.anl.gov>
Subject: Re: [Nek5000-users] turbulent 3d box

Hi Paul,
Regarding the 3dbox:
The forcing which I propose is known as the ABC flow
(Arnold-Beltrami-Childress) and has steady solutions (in the form of ABC
flow) with Re=1/nu (nu the viscosity) Re=<12 (in periodic box).
The forcing should be in the form:
f=Re*ABC in order to balance the dissipation term.
This settings can serve as a benchmark for pure hydro/mhd problems.

I tried to fix the example which you have sent me, but I don't succeed
retreiving the expected values.
I attach the relevant files( tarball file).
Best regards,
Barak

On 12/18/2013 03:29 AM, nek5000-users at lists.mcs.anl.gov<mailto:nek5000-users at lists.mcs.anl.gov> wrote:

Hi Barak,

I added a 3d periodic box under "3dbox" in the examples
directory.

Paul

Dear nek's,
I would like to run the following problem:
a 3D periodic box, small viscosity and the following forcing:

fx=cos(y)+sin(z)
fy=cos(z)+sin(x)
fz=cos(x)+sin(y)

Do you have a similar example?

Many thanks,
Barak

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