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Hi Barak,
<div><br>
</div>
<div>If your initial condition is:</div>
<div><br>
</div>
<div>
<div> ux=(cos(y)+sin(z))</div>
<div> uy=(cos(z)+sin(x))</div>
<div> uz=(cos(x)+sin(y))</div>
<div><br>
</div>
<div>and your domain is [0,2pi]^3, how is it possible that your velocity magnitude</div>
<div>is less than 2?</div>
<div><br>
</div>
<div><br>
</div>
<div>What is your measure of velocity magnitude? When I compute the L2</div>
<div>norm of this initial condition I'm seeing about 2.3+</div>
<div><br>
</div>
<div>Paul</div>
<div><br>
</div>
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<div id="divRpF377696" style="direction: ltr; "><font face="Tahoma" size="2" color="#000000"><b>From:</b> nek5000-users-bounces@lists.mcs.anl.gov [nek5000-users-bounces@lists.mcs.anl.gov] on behalf of nek5000-users@lists.mcs.anl.gov [nek5000-users@lists.mcs.anl.gov]<br>
<b>Sent:</b> Sunday, December 22, 2013 7:53 AM<br>
<b>To:</b> nek5000-users@lists.mcs.anl.gov<br>
<b>Subject:</b> Re: [Nek5000-users] turbulent 3d box<br>
</font><br>
</div>
<div></div>
<div>
<p>Hi Paul,<br>
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
<span class="spellcheckCorrected">nonlinear</span> 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.<br>
<br>
>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.<br>
<br>
Do you have any idea what's wrong?<br>
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):<br>
<br>
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.</p>
<div dir="ltr" style="font-size:15.9403px; font-family:serif; left:526.24px; top:384.86px">
2. D. Galloway and U. Frisch. Dynamo action in a family of flows with chaotic streamlines.</div>
<div dir="ltr" style="font-size:15.9403px; font-family:serif; left:377.599px; top:404.22px">
Geophysical & Astrophysical Fluid Dynamics, 36(1):53–83, 1986.</div>
<p>3. Podvigina, Pouquet, On the non-linear stability of the 1:1:1 ABC flow,<br>
Phys. D, Vol. 75, 4, 1994.<br>
<br>
<br>
With my best wishes,<br>
Barak<br>
</p>
<p><br>
</p>
<p>Quoting <a href="mailto:nek5000-users@lists.mcs.anl.gov" target="_blank">nek5000-users@lists.mcs.anl.gov</a>:</p>
<blockquote type="cite" style="border-left:2px solid blue; margin-left:8px; padding-left:8px">
<p>Hi Barak,<br>
<br>
Thanks for the note about the ABC flow -- that's very useful.<br>
<br>
What is your target viscosity?<br>
If you want it to be 0.1, then you would set param 2 in the .rea file to be 0.1.<br>
Setting param 2 = -0.1 would imply that Re=0.1 or equivalently nu=10.<br>
Does this resolve the issue for you?<br>
<br>
Once it's working we could add it as a documented example in the example<br>
suite.<br>
<br>
Thanks!<br>
<br>
Paul<br>
________________________________________<br>
From: <a href="mailto:nek5000-users-bounces@lists.mcs.anl.gov" target="_blank">nek5000-users-bounces@lists.mcs.anl.gov</a> [<a href="mailto:nek5000-users-bounces@lists.mcs.anl.gov" target="_blank">nek5000-users-bounces@lists.mcs.anl.gov</a>] on behalf of
<a href="mailto:nek5000-users@lists.mcs.anl.gov" target="_blank">nek5000-users@lists.mcs.anl.gov</a> [<a href="mailto:nek5000-users@lists.mcs.anl.gov" target="_blank">nek5000-users@lists.mcs.anl.gov</a>]<br>
Sent: Saturday, December 21, 2013 5:24 PM<br>
To: <a href="mailto:nek5000-users@lists.mcs.anl.gov" target="_blank">nek5000-users@lists.mcs.anl.gov</a><br>
Subject: Re: [Nek5000-users] turbulent 3d box<br>
<br>
Hi Paul,<br>
Regarding the 3dbox:<br>
The forcing which I propose is known as the ABC flow<br>
(Arnold-Beltrami-Childress) and has steady solutions (in the form of ABC<br>
flow) with Re=1/nu (nu the viscosity) Re=<12 (in periodic box).<br>
The forcing should be in the form:<br>
f=Re*ABC in order to balance the dissipation term.<br>
This settings can serve as a benchmark for pure hydro/mhd problems.<br>
<br>
I tried to fix the example which you have sent me, but I don't succeed<br>
retreiving the expected values.<br>
I attach the relevant files( tarball file).<br>
Best regards,<br>
Barak<br>
<br>
<br>
<br>
On 12/18/2013 03:29 AM, <a href="mailto:nek5000-users@lists.mcs.anl.gov" target="_blank">
nek5000-users@lists.mcs.anl.gov</a> wrote:</p>
<blockquote type="cite" style="border-left:2px solid blue; margin-left:8px; padding-left:8px">
<p>Hi Barak,<br>
<br>
I added a 3d periodic box under "3dbox" in the examples<br>
directory.<br>
<br>
Paul<br>
<br>
<br>
Dear nek's,<br>
I would like to run the following problem:<br>
a 3D periodic box, small viscosity and the following forcing:<br>
<br>
fx=cos(y)+sin(z)<br>
fy=cos(z)+sin(x)<br>
fz=cos(x)+sin(y)<br>
<br>
Do you have a similar example?<br>
<br>
Many thanks,<br>
Barak<br>
<br>
<br>
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