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Filtered equations in WRF LES


Hi everyone,

I am currently working on LES models implemented in WRF. I found few articles presenting and studying these models [1], [2]. In these articles, filtered incompressible Navier-Stokes equations in Cartesian coordinates are presented to make the sfs stress tensor appear. However, WRF is a compressible code and equation are written in (x, y, eta, t) referential frame (not Cartesian). Skamarock et al. [3] only give the final equations for the different turbulent modeling option.

Then I have few questions :
- Is there a document explaining how WRF equations are filtered ?
- What approximations are made here ?
- Does the compressible WRF equations need a Favre/Hesselberg averaging for the prognostic variables ?
- Since there are 2nd order terms in F_Ucor (coriolis and curvature terms), shouldn't there be also an sfs stress tensor associated with these terms ?

[1] : Simon, Jason S., Bowen Zhou, Jeffrey D. Mirocha, et Fotini Katopodes Chow. « Explicit Filtering and Reconstruction to Reduce Grid Dependence in Convective Boundary Layer Simulations Using WRF-LES ». Monthly Weather Review 147, no 5 (1st May 2019): 1805‑21.

[2] : Kirkil, Gokhan, Jeff Mirocha, Elie Bou-Zeid, Fotini Katopodes Chow, et Branko Kosović. « Implementation and Evaluation of Dynamic Subfilter-Scale Stress Models for Large-Eddy Simulation Using WRF ». Monthly Weather Review 140, no 1 (1st January 2012): 266‑84.

[3] : Skamarock, C., B. Klemp, Jimy Dudhia, O. Gill, Zhiquan Liu, Judith Berner, Wei Wang, et al. « A Description of the Advanced Research WRF Model Version 4.1 », 2019. A Description of the Advanced Research WRF Model Version 4.3 | OpenSky.
HI Mattieu,

Those are some pretty specific questions that might be best answered by contacting one of the scientists above directly. For example, BIll Skamarock or Branko Kosovic at NCAR or even Fotini (Tina) Katopodes Chow at UC Berkeley. Another might be Margaret (Peggy) LeMone who is Senior Scientist Emerita with NCAR. I believe all of these individuals would have valuable insight for your questions regarding the filtered equations in WRF for LES. Of course, hopefully someone on the forum will offer a good answer quickly since a major point of this site is to keep the actual senior scientists from getting their valuable time consumed by community emails asking WRF-related specific questions (that could easily be answered here). This is just one where you might actually benefit from a direct contact but I'll leave this to you and the forum moderators to conclude.