<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Hi Flynn,<div class=""><br class=""></div><div class="">the reason why the off-diagonal k12 and k21 are set to 0 is because the antisymmetric component of that tensor is associated with the “bolus-velocity”, which needs to be incompressible. This point is lucidly explain in Vallis textbook (2017 edition) in chapter 13.6 (pages 490-493). In Vallis’ example the component set to zero is k31 and k13, but this is irrelevant: you can set any of the three antisymmetric components to zero, and guarantee that the resulting “bolus-velocity” is incompressible in 3-D.</div><div class=""><br class=""></div><div class="">In the implementation of Kgm in the MITgcm that I am familiar with, the antisymmetric component is explicitly determined in terms of a streamfuction associated with the bolus velocity, making sure that it also satisfies the boundary conditions on solid boundaries and on the free surface. You can read about it here: <a href="https://www.sciencedirect.com/science/article/pii/S1463500310000065" class="">https://www.sciencedirect.com/science/article/pii/S1463500310000065</a></div><div class=""><br class=""></div><div class="">In summary, I recommend that you implement your large slope scenario on the existing components of knm, without adding a third antisymmetric part which would mess up incompressibility of the bolus velocity. The diffusive part of the tensor is in the diagonal components.</div><div class=""><br class=""></div><div class="">Cheers,<br class=""><div class="">
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line-break: after-white-space;" class=""><div dir="auto" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div dir="auto" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div dir="auto" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div dir="auto" style="text-align: start; text-indent: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div dir="auto" style="text-align: start; text-indent: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div dir="auto" style="text-align: start; text-indent: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="text-align: start; text-indent: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="text-align: start; text-indent: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="text-align: start; text-indent: 0px;"><span style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); font-variant-caps: normal; letter-spacing: normal; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px; font-style: normal;" class="">Paola</span><br class=""><br class=""></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div><div><blockquote type="cite" class=""><div class="">On Apr 26, 2023, at 5:21 AM, Flynn Ames <<a href="mailto:f.ames@pgr.reading.ac.uk" class="">f.ames@pgr.reading.ac.uk</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta charset="UTF-8" class=""><div class="elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;">Hi Martin,</div><div class="elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;"><br class=""></div><div class="elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;">Thanks for getting back to me on this. This is helpful!</div><div class="elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;"><br class=""></div><div class="elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt;">Flynn</div><div id="appendonsend" style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""></div><hr tabindex="-1" style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; display: inline-block; width: 904.53125px;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class=""></span><div id="divRplyFwdMsg" dir="ltr" style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><font face="Calibri, sans-serif" style="font-size: 11pt;" class=""><b class="">From:</b><span class="Apple-converted-space"> </span>MITgcm-support <<a href="mailto:mitgcm-support-bounces@mitgcm.org" class="">mitgcm-support-bounces@mitgcm.org</a>> on behalf of Martin Losch <<a href="mailto:Martin.Losch@awi.de" class="">Martin.Losch@awi.de</a>><br class=""><b class="">Sent:</b><span class="Apple-converted-space"> </span>25 April 2023 9:44 AM<br class=""><b class="">To:</b><span class="Apple-converted-space"> </span>MITgcm Support <<a href="mailto:mitgcm-support@mitgcm.org" class="">mitgcm-support@mitgcm.org</a>><br class=""><b class="">Subject:</b><span class="Apple-converted-space"> </span>Re: [MITgcm-support] GMREDI without the small slope approximation</font><div class=""> </div></div><div style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 18px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; line-break: after-white-space;" class="">Hi Flynn, <div class=""><br class=""></div><div class="">I am not really qualified to answer this, so take my comments with a grain of salt.<div class=""><br class=""></div><div class="">As far as I can see, the missing tensor components (basically k12=Kuy and k21=Kvx) need to be defined and computed and you are right that these are small and straightforward changes to the code (gmredi_calc_tensor.F). But you will also need to code the action of these tensor components on the \nabla(u) in the right place (k12*dv/dy in xtranport and k21*du/dy in ytransport?, involves some averaging of the derivatives). I find this hard to figure out, because there are so many different options in pkg/gmredi, but it should be possible.</div><div class=""><br class=""></div><div class="">Martin<br class=""><div class=""><br class=""><blockquote type="cite" class=""><div class="">On 21. Apr 2023, at 18:38, Flynn Ames <<a href="mailto:f.ames@pgr.reading.ac.uk" class="">f.ames@pgr.reading.ac.uk</a>> wrote:</div><br class="x_Apple-interchange-newline"><div class=""><div class="x_elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255);">Dear MITgcm community,</div><div class="x_elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255);"><br class=""></div><div class="x_elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255);">Hello - I'm wondering if anyone has ever tried implementing (or has implemented) GMREDI into the MITgcm without making the small slope approximation?</div><div class="x_elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255);"><br class=""></div><div class="x_elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255);">This is something I would like to do as I'm modelling a deep, ice-covered ocean where the steep isopycnals that develop violate the small slope approximation over much of the domain.</div><div class="x_elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255);"><br class=""></div><div class="x_elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255);">I may be being naive here, but looking at the MITgcm documentation, the terms that are neglected in the REDI projection tensor when making the small slope approximation appear to consist of quantities that are already computed in the model (Sx, Sy etc.).</div><div class="x_elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255);">I'm hoping to ask: Does anyone know if it would just be a case of putting these extra terms into the REDI tensor in the model? or is there a lot that I'm missing here? - I'm guessing the latter :<span id="x_��" class="">)</span></div><div class="x_elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255);"><br class=""></div><div class="x_elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255);">Thank you for your time!</div><div class="x_elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255);">Flynn</div><div class="x_elementToProof" style="font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255);"><br class=""></div><span style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; float: none; display: inline !important;" class="">_______________________________________________</span><br style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none;" class=""><span style="font-family: Helvetica; font-size: 12px; 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