[MITgcm-support] Choosing Leith biharmonic co-efficient?
Malte Jansen
mfj at uchicago.edu
Wed Apr 18 11:42:07 EDT 2018
Hi,
I think the reference that David is bringing up is actually also useful
as a guideline for choosing the Leith and Smagorinsky coeficients for
the existing implementations. Fig. 6 in the paper compares EKE spectra
from a channel simulation using Smagorinsky, the traditional (2D) Leith,
as well as the generalized "QG Leith". The non-dimensional parameters
here have all been set to 1. The figure shows pretty clearly that with
this choice of parameters Smagorinsky is overly dissipative, while the
standard Leith (i.e. Leith_2D in the figure) is not dissipative enough.
This is also consistent with my experience (and with Smagorinsky’s
original paper). Griffies and Hallberg (2000) suggest a large value for
the Smag coefficient (>2.2) based on a conservative upper-limit estimate
of the grid Reynolds number. If I’m doing it right, the same argument
would suggest a minimum of about 2.5 for the Leith coefficient - larger
than what’s typically used (successfully). (And I've also run
simulations with significantly smaller Smagorinsky coefficient stably
and happily.)
So in summary, this seems to suggest viscC[2/4]Leith \gtrsim 1, while
viscC[2/4]Leith \lesssim 1.
To return to Jody's original question about the applicability of Leith
at higher resolution (and when we care about internal waves). I would
argue that in this regime neither Leith nor Smagorinsky are quite
justifiable, so pick your poison… You could maybe even consider to use
a little bit of both. If you include Smagorinsky (even with a relatively
small coefficient) you may be able to get away with setting
viscC4LeithD=0, since the Smagorinsky part should be able to handle a
purely divergent mode. (The divergence-dependent term in the Leith
implementation is basically just a hack to get rid of a purely divergent
grid-scale mode.The latter would be unaffected by the original Leith
formulation, which is based on 2D non-divergent flow.)
Cheers,
Malte
On 4/18/18 9:50 AM, David Ferreira wrote:
> Hi all,
> May be useful to mention that Fox-Kemper et al. have also developed a
> QG Leith scheme, same idea as 2D Leith but viscosity is proportional
> the QG PV gradient, instead of just the vorticity gradient (one may or
> may not add the divergent part to this).
> The claim is that it is slightly more general than the "normal" 2D
> Leith scheme
>
> Bachman, S. D., Fox-Kemper, B., Pearson, B., 2017. A scale-aware
> subgrid model for quasi-geostrophic turbulence. J. Geophys. Res. 122
> (2), 1529– 1554.
>
> There is another paper in Ocean Modelling.
>
> cheers,
> david
>
>
> ------------------------------------------------------------------------
> *From:* MITgcm-support [mitgcm-support-bounces at mitgcm.org] on behalf
> of Jody Klymak [jklymak at uvic.ca]
> *Sent:* Monday, April 16, 2018 10:17 AM
> *To:* mitgcm-support at mitgcm.org
> *Subject:* Re: [MITgcm-support] Choosing Leith biharmonic co-efficient?
>
> Hi all,
>
> Thanks so much for your advice and in particular the Fox-Kemper and
> Menemenlis reference (which Dmitris had given me in another context,
> so I guess I should have read it ;-).
>
> Having quickly read it (on a plane, at 5:30 AM), I’m a little unsure
> about the applicability of Leith once horizontal scales get down to a
> km or so, particularly if one wants to have a reasonable internal wave
> field, there is the statement that the divergence-sensing term will
> negatively impact “high-frequency” internal waves.
>
> I will be playing with this the next couple of months, but wanted to
> know the community insights into these parameterizations. Certainly
> the 10-km spinup expt I’m doing now needed Leith biharmonic
> viscosities to make a nice flow.
>
> Thanks again, Jody
>
>
>
>> On Apr 16, 2018, at 6:27 AM, Ryan Abernathey
>> <ryan.abernathey at gmail.com <mailto:ryan.abernathey at gmail.com>> wrote:
>>
>> Jody,
>>
>> I assume you are talking about the config you got from Dhruv. The
>> values we use in those runs were taken from Dimitris Menemenlis and
>> Chris Hill's LLC simulations. The exact same settings are used for
>> 1/12, 1/24, and 1/48 degree global simulations. (Although I do recall
>> that Dhruv had to make some changes related to boundary conditions.)
>>
>> -Ryan
>>
>> On Mon, Apr 16, 2018 at 8:59 AM, Malte Jansen <mfj at uchicago.edu
>> <mailto:mfj at uchicago.edu>> wrote:
>>
>> Just to add on to this: the Leith viscosity is supposed to be
>> "scale aware" (at least within a QG turbulence regime), such that
>> the non-dimensional coefficient should be independent of the
>> grid-scale.
>>
>> -Malte
>>
>>
>>
>> On 4/16/18 3:16 AM, Martin Losch wrote:
>>
>> Hi Jody,
>>
>> my reference is pkg/mom_common/mom_calc_visc.F where you can
>> find this:
>>
>> C RECOMMENDED VALUES
>> C viscC2Leith=1-3
>> C viscC2LeithD=1-3
>> C viscC4Leith=1-3
>> C viscC4LeithD=1.5-3
>> C viscC2smag=2.2-4 (Griffies and Hallberg,2000)
>> C 0.2-0.9 (Smagorinsky,1993)
>> C viscC4smag=2.2-4 (Griffies and Hallberg,2000)
>>
>> And I think this is where it is described:
>> B. Fox-Kemper and D. Menemenlis. Can large eddy simulation
>> techniques improve mesoscale-rich ocean models? In M. Hecht
>> and H. Hasumi, editors, Ocean Modeling in an Eddying Regime,
>> volume 177, pages 319-338. AGU Geophysical Monograph Series,
>> 2008.
>> http://www.geo.brown.edu/research/Fox-Kemper/pubs/pdfs/FoxKemperMenemenlis08.pdf
>> <http://www.geo.brown.edu/research/Fox-Kemper/pubs/pdfs/FoxKemperMenemenlis08.pdf>
>>
>> Martin
>>
>> On 14. Apr 2018, at 22:42, Jody Klymak <jklymak at uvic.ca
>> <mailto:jklymak at uvic.ca>> wrote:
>>
>>
>> Hi all,
>>
>> Is there a good reference and/or ruls of thumb for
>> choosing the Leith biharmonic co-efficient? i.e.
>> `viscC4Leith` and `viscC4Leithd`, with particular
>> interest in how the size of the grid affects the choice?
>> I’m using someone else’s setup, using Leith works great
>> for making the flow look reasonable, but it would be nice
>> if it was turned down as much as possible, particularly
>> when I downscale to a smaller grid size…
>>
>> Thanks a lot, Jody
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>> --
>> Malte F Jansen
>> Assistant Professor
>> Department of the Geophysical Sciences
>> The University of Chicago
>> 5734 South Ellis Avenue
>> Chicago, IL 60637 USA
>>
>>
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--
Malte F Jansen
Assistant Professor
Department of the Geophysical Sciences
The University of Chicago
5734 South Ellis Avenue
Chicago, IL 60637 USA
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