[MITgcm-support] Spurious mixing with internal tides

[Yu-Kun Qian]

Hi Xiaozhou,

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.

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.

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 https://doi.org/10.1016/j.ocemod.2011.12.001)).  The actual spurious diffusion depends on your model resolution and flow regime.

Hope this helps.

————————————
Best regards.

Yu-Kun Qian

LTO, SCSIO
Guangzhou, China

> 在 2021年1月30日，01:58，Ruan Xiaozhou <saberruan at hotmail.com> 写道：
> 
> 
> Dear MITgcm users,
> 
> 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.
> 
> 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.
> 
> Cheers,
> Xiaozhou
> --
> Xiaozhou Ruan
> Postdoctoral researcher
> Department of Earth, Atmospheric and Planetary Sciences
> Massachusetts Institute of Technology
> 54-1622
> Cambridge, MA  02139
> 
> email: xruan at mit.edu
> web:   http://www.mit.edu/~xruan
> 
> 
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