[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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