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<p class="MsoNormal"><span style="font-size:11.0pt">Hi Mike,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">I don’t know what You et al 2023 refers to – do you have a journal name?
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">However your question is not very clear. Eq 8 is a barotropic energy equation, and related the barotropic tide divergence to its terms: the conversion to baroclinic motions, C, and the barotropic dissipation
\bar{D} and \bar{\epsilon}. Note this equation is missing non-linear advection of the barotropic energy, but that is often small in deep water.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">15-17 are probably baroclinic dissipations, though confusingly you have u’ and u_{bc}. However, there is of course no dissipation of potential energy in the barotropic equations.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">C should balance the divergence of the energy flux and the dissipation in some volume, plus a non-linear baroclinic advection term.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">\epsilon_{diff} is typically substantially less than \epsilon_{visc}, usually around 20%, though its of course possible to drive it to be different values based on how you choose your viscosities and diffusivities.
You have viscosity 10 times your diffusivity, so I wouldn’t expect \epsilon_{visc} to be too high.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">I always use Kang and Fringer for the energy decompositions (<a href="https://journals.ametsoc.org/view/journals/phoc/42/2/jpo-d-11-039.1.xml">https://journals.ametsoc.org/view/journals/phoc/42/2/jpo-d-11-039.1.xml</a>).
They go through the derivation carefully as does Kang’s thesis. <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">You may find my (outdated) energetics code useful:
<a href="https://github.com/jklymak/MITgcmcode">https://github.com/jklymak/MITgcmcode</a><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Cheers, Jody<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">MITgcm-support <mitgcm-support-bounces@mitgcm.org> on behalf of Mike Fan <ifanliming@outlook.com><br>
<b>Date: </b>Tuesday, June 27, 2023 at 12:23 AM<br>
<b>To: </b>MITgcm Support <mitgcm-support@mitgcm.org><br>
<b>Subject: </b>[MITgcm-support] How to calculate the internal tide disspation from MITgcm output ?<o:p></o:p></span></p>
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<span lang="EN-US" style="font-size:9.0pt;font-family:"MS Gothic";color:#212121">你通常不会收到来自</span><span style="font-size:9.0pt;font-family:"Segoe UI",sans-serif;color:#212121"> ifanliming@outlook.com
</span><span lang="EN-US" style="font-size:9.0pt;font-family:"MS Gothic";color:#212121">的</span><span lang="EN-US" style="font-size:9.0pt;font-family:"PingFang TC",sans-serif;color:#212121">电</span><span lang="EN-US" style="font-size:9.0pt;font-family:"MS Gothic";color:#212121">子</span><span lang="EN-US" style="font-size:9.0pt;font-family:"PingFang TC",sans-serif;color:#212121">邮</span><span lang="EN-US" style="font-size:9.0pt;font-family:"MS Gothic";color:#212121">件。</span><span style="font-size:9.0pt;font-family:"Segoe UI",sans-serif;color:#212121"><a href="https://aka.ms/LearnAboutSenderIdentification"><span lang="EN-US" style="font-family:"MS Gothic"">了解</span><span lang="EN-US" style="font-family:"PingFang TC",sans-serif">这</span><span lang="EN-US" style="font-family:"MS Gothic"">一点</span><span lang="EN-US" style="font-family:"PingFang TC",sans-serif">为</span><span lang="EN-US" style="font-family:"MS Gothic"">什么很重要</span></a><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black">Hello, everyone<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black">Recently I try to get the disspation of internal tide from MITgcm output, I have set the coefficients for constant viscosity, diffusion, and bottom friction. I want to know that, in this way, can
I use the equations(15-18) of You et al. (2023) to do the job?<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><img border="0" width="408" height="42" style="width:4.25in;height:.4375in" id="imageSelected1" src="cid:11fddd70-bb73-4fc8-a7ac-eade39c97c0c"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><img border="0" width="559" height="171" style="width:5.8229in;height:1.7812in" id="imageSelected0" src="cid:9631aa7a-893b-4d27-8daa-788aa288b2cc"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black">In my experience (<span class="contentpasted6"><span style="background:white">in the only M2 internal tide model</span></span>), the uncertainty of dissipation caused by diffusion (Equ.17) is the
greatest. When the density perturbation (rho') is calculated by rho-mean(rho), this term (sum of Equ.(16-18) ~20GW) is absolutely dominant and is obviously larger than that estimated by Equ.8 (rhs ~6GW). When the density
<span style="background:white">perturbation (rho')</span> is calculated by harmonic analysis, the result (<span class="contentpasted7"><span style="background:white">sum of Equ.(16-18) </span></span>~3GW) is smaller than that estimated by
<span class="contentpasted2"><span style="background:white">Equ.8</span></span>. I'm not sure that if the choice of parameterization scheme may lead to differences in the calculation of dissipation, so I would like to ask, in a model with only M2 internal tide,
how can I use the given <span class="contentpasted3"><span style="background:white">constant </span></span>parameters (viscosity, diffusion and bottom friction) to directly obtain the
<span style="background:white">disspation</span> generated by the internal tide?<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black">Here is my "<span class="contentpasted0"><span style="background:white">data" file setting:</span></span><o:p></o:p></span></p>
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<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"># ====================
<o:p></o:p></span></p>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"># | Model parameters |<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"># ====================<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black">#<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"># Continuous equation parameters<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> &PARM01<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> TrefFile='Tannualref',
<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> sRef= 50*34.5,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> viscAh=5.0,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> viscAz=1.5E-4,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> diffKhT=5.0,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> diffKhS=5.0,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> diffKzT=1.5E-5,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> diffKzS=1.5E-5,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> no_slip_sides=.FALSE.,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> no_slip_bottom=.TRUE.,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> bottomDragQuadratic=2.5E-3,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> eosType='LINEAR',<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> staggerTimeStep=.TRUE.,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> tAlpha=2.E-4,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> sBeta =0E-4,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> gravity=9.81,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> implicitFreeSurface=.TRUE.,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> exactConserv=.TRUE.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> nonHydrostatic=.FALSE.,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> useCoriolis=.TRUE.,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> hFacMin=0.2,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> hFacInf=0.2,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> hFacSup=1.8,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> tempStepping=.TRUE.,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> saltStepping=.FALSE.,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black">#- not safe to use globalFiles in multi-processors runs<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black">#globalFiles=.TRUE.,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> readBinaryPrec=64,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> writeBinaryPrec=32,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> writeStatePrec=32,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> useSingleCpuIO=.TRUE.,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"> &<o:p></o:p></span></p>
</div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black">Any reply or suggestion will be greatly appreciated.<o:p></o:p></span></p>
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<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black">-Mike<o:p></o:p></span></p>
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