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<p>Hi,</p>
<p><br>
</p>
<p>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.)</p>
<p>So in summary, this seems to suggest viscC[2/4]Leith \gtrsim 1,
while viscC[2/4]Leith \lesssim 1.<br>
</p>
<br>
<p>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.)<br>
</p>
<p><br>
</p>
<p>Cheers,</p>
<p>Malte<br>
</p>
<p><br>
</p>
<br>
<div class="moz-cite-prefix">On 4/18/18 9:50 AM, David Ferreira
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:14B4C99DAD42E249A01406B0B97F754B0134BBD1F4@OC11EXPO27.exchange.mit.edu">
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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>
<div style="font-family: Times New Roman; color: #000000;
font-size: 16px">
<hr tabindex="-1">
<div style="direction: ltr;" id="divRpF97212"><font size="2"
face="Tahoma" color="#000000"><b>From:</b> MITgcm-support
[<a class="moz-txt-link-abbreviated" href="mailto:mitgcm-support-bounces@mitgcm.org">mitgcm-support-bounces@mitgcm.org</a>] on behalf of Jody
Klymak [<a class="moz-txt-link-abbreviated" href="mailto:jklymak@uvic.ca">jklymak@uvic.ca</a>]<br>
<b>Sent:</b> Monday, April 16, 2018 10:17 AM<br>
<b>To:</b> <a class="moz-txt-link-abbreviated" href="mailto:mitgcm-support@mitgcm.org">mitgcm-support@mitgcm.org</a><br>
<b>Subject:</b> Re: [MITgcm-support] Choosing Leith
biharmonic co-efficient?<br>
</font><br>
</div>
<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="">
</div>
<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" moz-do-not-send="true">ryan.abernathey@gmail.com</a>>
wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<div dir="ltr" class="">Jody,
<div class=""><br class="">
</div>
<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" moz-do-not-send="true">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" moz-do-not-send="true">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"
moz-do-not-send="true">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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<pre class="moz-signature" cols="72">--
Malte F Jansen
Assistant Professor
Department of the Geophysical Sciences
The University of Chicago
5734 South Ellis Avenue
Chicago, IL 60637 USA</pre>
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