[Nek5000-users] turbulent 3d box

Sun Dec 22 14:24:42 CST 2013

Hi Barak,

When I compute the L2 norm of the function, given as:

       v2 = [ sum_i  vx_i b_i vx_i + vy_i b_i vy_i + vz_i b_i vz_i / sum_i b_i ]^(1/2)

it comes out to ~ 2.23

Note that there are some places where ux==2, uy==0, uz==1,
which would give an L2 norm of

     sqrt (2*2 + 0*0 + 1*1) = sqrt(5) > sqrt(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 11:04 AM
To: nek5000-users at lists.mcs.anl.gov
Subject: Re: [Nek5000-users] turbulent 3d box

Hi Paul,
My definition for velocity magnitude is:
|v|=sqrt(ux^2+uy^2+uz^2)
so if you see, there are two components in the form:
cos^2(x)+sin^2(x)
etc in each direction
so in fact
|v|=sqrt(3) for any x,y,z.
Isn't correct?
Barak

On 12/22/2013 05:05 PM, nek5000-users at lists.mcs.anl.gov wrote:
>
> 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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