[Nek5000-users] turbulent 3d box

[nek5000-users at lists.mcs.anl.gov]

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:
> 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  
> [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: Saturday, December 21, 2013 5:24 PM
>   To: 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 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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