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<div style="direction: ltr;font-family: Tahoma;color: #000000;font-size: 10pt;">Hi all,<br>
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).<br>
The claim is that it is slightly more general than the "normal" 2D Leith scheme<br>
<br>
<p><span style="font-size: 12.000000pt; font-family: 'CMR12'">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.
</span></p>
There is another paper in Ocean Modelling.<br>
<br>
cheers,<br>
david<br>
<br>
<br>
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<div style="direction: ltr;" id="divRpF97212"><font face="Tahoma" color="#000000" size="2"><b>From:</b> MITgcm-support [mitgcm-support-bounces@mitgcm.org] on behalf of Jody Klymak [jklymak@uvic.ca]<br>
<b>Sent:</b> Monday, April 16, 2018 10:17 AM<br>
<b>To:</b> mitgcm-support@mitgcm.org<br>
<b>Subject:</b> Re: [MITgcm-support] Choosing Leith biharmonic co-efficient?<br>
</font><br>
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<div>Hi all,
<div class=""><br class="">
</div>
<div class="">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 ;-).</div>
<div class=""><br class="">
</div>
<div class="">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. </div>
<div class=""><br class="">
</div>
<div class="">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.</div>
<div class=""><br class="">
</div>
<div class="">Thanks again, Jody</div>
<div class=""><br class="">
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<div class=""><br class="">
<div><br class="">
<blockquote type="cite" class="">
<div class="">On Apr 16, 2018, at 6:27 AM, Ryan Abernathey <<a href="mailto:ryan.abernathey@gmail.com" class="" target="_blank">ryan.abernathey@gmail.com</a>> wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<div dir="ltr" class="">Jody,
<div class=""><br class="">
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<div class="">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.)</div>
<div class=""><br class="">
</div>
<div class="">-Ryan</div>
</div>
<div class="gmail_extra"><br class="">
<div class="gmail_quote">On Mon, Apr 16, 2018 at 8:59 AM, Malte Jansen <span dir="ltr" class="">
<<a href="mailto:mfj@uchicago.edu" class="" target="_blank">mfj@uchicago.edu</a>></span> wrote:<br class="">
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex; border-left:1px #ccc solid; padding-left:1ex">
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.<br class="">
<br class="">
-Malte
<div class="HOEnZb">
<div class="h5"><br class="">
<br class="">
<br class="">
On 4/16/18 3:16 AM, Martin Losch wrote:<br class="">
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex; border-left:1px #ccc solid; padding-left:1ex">
Hi Jody,<br class="">
<br class="">
my reference is pkg/mom_common/mom_calc_visc.F where you can find this:<br class="">
<br class="">
C RECOMMENDED VALUES<br class="">
C viscC2Leith=1-3<br class="">
C viscC2LeithD=1-3<br class="">
C viscC4Leith=1-3<br class="">
C viscC4LeithD=1.5-3<br class="">
C viscC2smag=2.2-4 (Griffies and Hallberg,2000)<br class="">
C 0.2-0.9 (Smagorinsky,1993)<br class="">
C viscC4smag=2.2-4 (Griffies and Hallberg,2000)<br class="">
<br class="">
And I think this is where it is described:<br class="">
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.<br class="">
<a href="http://www.geo.brown.edu/research/Fox-Kemper/pubs/pdfs/FoxKemperMenemenlis08.pdf" rel="noreferrer" class="" target="_blank">http://www.geo.brown.edu/resea<wbr class="">rch/Fox-Kemper/pubs/pdfs/FoxKe<wbr class="">mperMenemenlis08.pdf</a><br class="">
<br class="">
Martin<br class="">
<br class="">
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex; border-left:1px #ccc solid; padding-left:1ex">
On 14. Apr 2018, at 22:42, Jody Klymak <<a href="mailto:jklymak@uvic.ca" class="" target="_blank">jklymak@uvic.ca</a>> wrote:<br class="">
<br class="">
<br class="">
Hi all,<br class="">
<br class="">
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…<br class="">
<br class="">
Thanks a lot, Jody<br class="">
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<span class="HOEnZb"><font class="" color="#888888">-- <br class="">
Malte F Jansen<br class="">
Assistant Professor<br class="">
Department of the Geophysical Sciences<br class="">
The University of Chicago<br class="">
5734 South Ellis Avenue<br class="">
Chicago, IL 60637 USA</font></span>
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