[MITgcm-support] Questions: simulating the cooling process of a glass of water

[Oren Raz]

Hi Martin,

Thanks for your detailed answers - they were very useful!

Bests,
Oren

On Tue, Jul 18, 2017 at 5:32 AM, Martin Losch <Martin.Losch at awi.de> wrote:

> Hi Oren,
>
> interesting experiment, but I am not sure you will get anywhere with the
> MITgcm. Keep in mind, that is is primarily an Ocean circulation model,
> which implies a few approximations that you may not want to accept (and
> some of your questions actually reflect this).
>
> > On 13. Jul 2017, at 17:41, Oren Raz <oraz at umd.edu> wrote:
> >
> > Hi,
> > My name is Oren Raz, and I am a postdoc in Chris Jarzynski's research
> group at the department of chemistry, University of Maryland College Park.
> >
> > We are trying to simulate in your software the Mpemba effect, in which a
> glass of hot water cools faster than identical glass filled with cold
> water, when both are placed in a refrigerator. This fact was experimentally
> observed long ago, and recently is under a debate, see e.g. H. C. Burridge
> and P. F. Linden, Scientific Reports 6:37665 (2016). The idea is to use
> your code and run "cooling experiments" from different initial temperature,
> and plot the average temperature as a function of time.
> >
> > After running several simulations, I have several questions which can
> illuminate the results I got so far:
> >
> >       • Using the ``exactConserv.=True" option (see parameters list
> attached in the file "data"), we see that the total volume of the fluid
> does not changes during the experiment. Assuming that the temperature is
> always at least 5 celsius above the freezing point (the refrigerator's
> temperature is 5 celsius), constant volume is unphysical, since the
> expansion coefficient is positive. Is it possible to track the actual
> volume during the cooling process?
> The standard model is a so-called Boussinesq model which implies that
> water is incompressible (div(v) = 0) and conserves volume rather than mass
> (you will notice that bottom pressure changes with temperature). The
> “exactConserv” option refers to volume. You can lift the Boussinesq
> approximation to make the model mass conserving and there’s an example how
> to do that in verification/tutorial_global_oce_in_p and there’s even a
> tutorial description of this experiment: <http://mitgcm.org/public/r2_
> manual/latest/online_documents/node133.html>
> It involves using pressure coordinates and cannot be used together with
> non-hydrostatic dynamics (although I am no longer sure about that, can’t
> find any test/stops for this case). Without pressure coordinates, you can
> still diagnose the change in volume from the change in mass (bottom
> pressure) through scaling with a mean density.
> >       • Our time-steps are extremely shorts: deltaT=1e-3 (seconds). In
> such a short timescale, the change is the destiny might be strongly
> effected by the change in the temperature - which if we understand
> correctly you completely neglect (1.5.1 in the user manual). Is there a way
> to avoid this approximation?
> The change in density due to temperature is accounted for in the equation
> of state (EOS). There are several choices, see the manual for details, you
> use something reasonable for seawater and should be fine. You may have
> misinterpreted section 1.5.1 in the manual: The Boussinesq approximation
> implies that the change of density is only through changes in temperature
> (and salinity) and not through changes in pressure (i.e. incompressibility)
> >       •  Is there a way to make sure which set of equations we are using?
> with your “data” file you use non-hydrostatic, Boussinesq, as described in
> section "1.5.1.3 Incompressible z-coordinate equations”, with linear free
> surface (section 2.4 <http://mitgcm.org/public/r2_manual/latest/online_
> documents/node34.html>)
> >       • Is there an option to set the boundaries (other than the top
> boundary) to a constant temperature with heat exchange through the boundary?
> The ocean is usually in thermal equilibrium with it solid boundaries so
> this option is not directly in the code. You could use “open boundary
> conditions” with zero normal flow through the lateral boundaries and
> prescribed temperatures (package obcs), you’d then have some diffusive heat
> flux across the lateral boundaries. For the bottom there’s the option to
> apply “geothermal heat flux”, not exactly what you want, but no
> temperatures.
> The work around would be the “rbcs” package, where you can specify
> restoring temperatures anywhere in your domain. If you set the restoring
> time scale to your time step, that is almost like prescribing the
> temperature.
>
> hope that helps,
>
> Martin
>
> > Best regards,
> > Oren Raz
> > <data>_______________________________________________
> > MITgcm-support mailing list
> > MITgcm-support at mitgcm.org
> > http://mitgcm.org/mailman/listinfo/mitgcm-support
>
>
> _______________________________________________
> MITgcm-support mailing list
> MITgcm-support at mitgcm.org
> http://mitgcm.org/mailman/listinfo/mitgcm-support
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mitgcm.org/pipermail/mitgcm-support/attachments/20170719/f63eaf47/attachment.htm>