<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto">Hi Xiaozhou,<div><br></div><div>Perfect advection scheme should 1) conserve tracer extrema and 2) conserve total tracer variance. However, when advection is discretized, these two properties cannot be kept simultaneously.</div><div><br></div><div>Centered 2nd scheme keeps minimum spurious diffusion but generates large spurious extrema (noisy field), whereas upwind scheme (code 3) or DST (33) generate less spurious extrema (smooth field) but induce large diffusion.</div><div><br></div><div>If you want a exact control of tracer extrema (e.g., salinity without negative value), you should use flux limiter scheme but generally a little larger spurious diffusion. In case you want a good compromise between the two properties, you should use 7th order scheme (code 7 but more computational load) or Prather scheme (code 80 but more storage as it fit subgrid tracer with polynomials, also suggested by Hill et al. (2012 <a href="https://doi.org/10.1016/j.ocemod.2011.12.001">https://doi.org/10.1016/j.ocemod.2011.12.001</a>)). The actual spurious diffusion depends on your model resolution and flow regime.</div><div><br></div><div>Hope this helps.</div><div><br><div dir="ltr">————————————</div><div dir="ltr">Best regards.</div><div dir="ltr"><br></div><div dir="ltr">Yu-Kun Qian</div><div dir="ltr"><br></div><div dir="ltr">LTO, SCSIO</div><div dir="ltr">Guangzhou, China</div><div dir="ltr"><br><blockquote type="cite">在 2021年1月30日，01:58，Ruan Xiaozhou <saberruan@hotmail.com> 写道：<br><br></blockquote></div><blockquote type="cite"><div dir="ltr">
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Dear MITgcm users,
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<div class="">Hope this message finds you well. I’ve been running simple 2D simulations with internal tides driven by oscillatory mean flows over rough bathymetry. When diagnosing the volume-integrated tracer variance budget, although the l.h.s. (time-tendency)
and r.h.s (advection + diffusion) terms balance exactly, I found some extra destruction of variance coming from the volume integral of the advection term using nonlinear advection schemes (scheme 33) which is as large as the diffusion term. Theoretically this
volume integral of variance advection should vanish... Switching to a centered 2nd order scheme (scheme 2) kills this contribution but the total variance destruction rate becomes about twice as large which, according to the output, can be explained by the
noisy tracer field and thus a larger gradient term.</div>
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<div class="">I was wondering if anyone had experience beating down this *spurious* contribution from the advection term? I noticed this contribution not only in the variance budget but also other 2nd order budgets involving a volume integral.</div>
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<div class="">Cheers,</div>
<div class="">Xiaozhou</div>
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--<br class="">
Xiaozhou Ruan</div>
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Postdoctoral researcher</div>
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Department of Earth, Atmospheric and Planetary Sciences</div>
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Massachusetts Institute of Technology<br class="">
54-1622<br class="">
Cambridge, MA 02139</div>
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email: <a href="mailto:xiaozhour@caltech.edu" class="">xruan@mit.edu</a></div>
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web: <a href="http://www.its.caltech.edu/~xruan" style="orphans: auto; widows: auto;" class="">http://www.mit.edu/~xruan</a></div>
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