# Smagorinsky Sub-Grid Turbulence Model vs. Deardorff

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 July 29, 2015, 00:14 Smagorinsky Sub-Grid Turbulence Model vs. Deardorff #1 New Member   Join Date: Jul 2015 Posts: 5 Rep Power: 2 I was wondering if anyone could give me some details about what the primary difference between the typical Smagorinsky SGS turbulence model and the Deardorff SGS turbulence model is. Specifically the Deardorff model outlined in Deardorff (1980) found here. For some background information, I am a graduate student in mechanical engineering using CM1 to study some high intensity wind phenomenon (CM1 is a three-dimensional, non-hydrostatic, non-linear, time-dependent numerical model designed for idealized studies of atmospheric phenomena). I am trying to get a good understanding of the sub-grid turbulence modelling used for this code, as it is a large requirement for my master's work. I have read countless papers on this turbulence modelling, I just feel like someone who is very knowledgeable on this subject would be able to explain it in a more simple and logical way. Here's some links to CM1, and the relevant turbulence models that it uses : http://www2.mmm.ucar.edu/people/bryan/cm1/ http://www2.mmm.ucar.edu/people/brya..._equations.pdf http://link.springer.com/article/10.1007%2FBF00119502 Any help would be great.

July 29, 2015, 03:11
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Filippo Maria Denaro
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 Originally Posted by oksero I was wondering if anyone could give me some details about what the primary difference between the typical Smagorinsky SGS turbulence model and the Deardorff SGS turbulence model is. Specifically the Deardorff model outlined in Deardorff (1980) found here. For some background information, I am a graduate student in mechanical engineering using CM1 to study some high intensity wind phenomenon (CM1 is a three-dimensional, non-hydrostatic, non-linear, time-dependent numerical model designed for idealized studies of atmospheric phenomena). I am trying to get a good understanding of the sub-grid turbulence modelling used for this code, as it is a large requirement for my master's work. I have read countless papers on this turbulence modelling, I just feel like someone who is very knowledgeable on this subject would be able to explain it in a more simple and logical way. Here's some links to CM1, and the relevant turbulence models that it uses : http://www2.mmm.ucar.edu/people/bryan/cm1/ http://www2.mmm.ucar.edu/people/brya..._equations.pdf http://link.springer.com/article/10.1007%2FBF00119502 Any help would be great.

I think that the answer is detailed in the books dedicated to LES/turbulence. I suggest a reading of specialized book if you want to have a strong background in this field

You can search for books of Sagaut, Pope, Lesieur, etc.

July 29, 2015, 09:39
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 Originally Posted by FMDenaro I think that the answer is detailed in the books dedicated to LES/turbulence. I suggest a reading of specialized book if you want to have a strong background in this field You can search for books of Sagaut, Pope, Lesieur, etc.
Do you, or anyone reading this, have any recommendations for books that deal specifically with these two models (Deardorff (1980) TKE SGS and Smagorinsky SGS)?

July 29, 2015, 10:40
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Filippo Maria Denaro
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 Originally Posted by oksero Do you, or anyone reading this, have any recommendations for books that deal specifically with these two models (Deardorff (1980) TKE SGS and Smagorinsky SGS)?

Again, I suggest reading the topic in detailed book...

Smagorinsky has the idea that the eddy viscosity ni_SGS depends on a unique characteristic lenght that is related to the minimum computational grid that describes a vortical, turbulent structure. This is justified by the assumption of homogeneity and isotropy of the motion of unresolved structure below this lenght. Smagorinsky expressses the closure in terms of the single function ni_SGS = f(v_bar;delta) that is inserted in the filtered momentum equation.

Deardoff in 1980 considered a planetary flow, if I remember with stratification effects. The key is that both a supplementary unknown and a supplementary equation (TKE) are introduced. Stratification enters in the scale lenght. A paper of Lilly on PoF also considered such issue.

In my opinion, you have two different models by a conceptual point of view.

July 29, 2015, 10:43
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 Originally Posted by FMDenaro Again, I suggest reading the topic in detailed book... Smagorinsky has the idea that the eddy viscosity ni_SGS depends on a unique characteristic lenght that is related to the minimum computational grid that describes a vortical, turbulent structure. This is justified by the assumption of homogeneity and isotropy of the motion of unresolved structure below this lenght. Smagorinsky expressses the closure in terms of the single function ni_SGS = f(v_bar;delta) that is inserted in the filtered momentum equation. Deardoff in 1980 considered a planetary flow, if I remember with stratification effects. The key is that both a supplementary unknown and a supplementary equation (TKE) are introduced. Stratification enters in the scale lenght. A paper of Lilly on PoF also considered such issue. In my opinion, you have two different models by a conceptual point of view.
Thank you. That was an excellent description of each model. I suppose I am trying to find some guidance on which specific books would go into some more detail on each model.

 Tags deardorff, sgs, smagorinsky, turbulence

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