# What is linear eddy viscosity

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 January 12, 2018, 09:00 What is linear eddy viscosity #1 New Member   toboto Join Date: Jun 2016 Posts: 20 Rep Power: 10 Dear all, I was reading about turbulence modeling (a topic which I am not expert in) and I was puzzled by the discussion about linear vs. nonlinear eddy viscosity. Most references (including CFD-online wiki) say that in linear eddy viscosity models the Reynolds stresses are linearly related to mean strains via the turbulent, or eddy, viscosity. But from my basic understanding, eddy viscosity is dependent on turbulence variable (e.g. k & epsilon) which in turn depend on the flow field. So, eddy viscosity actually depends on the flow field. This is similar to non-Newtonian viscosity (correct me if I am wrong) So, how can linear eddy viscosity model exist?

January 12, 2018, 10:04
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Filippo Maria Denaro
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Quote:
 Originally Posted by toboto Dear all, I was reading about turbulence modeling (a topic which I am not expert in) and I was puzzled by the discussion about linear vs. nonlinear eddy viscosity. Most references (including CFD-online wiki) say that in linear eddy viscosity models the Reynolds stresses are linearly related to mean strains via the turbulent, or eddy, viscosity. But from my basic understanding, eddy viscosity is dependent on turbulence variable (e.g. k & epsilon) which in turn depend on the flow field. So, eddy viscosity actually depends on the flow field. This is similar to non-Newtonian viscosity (correct me if I am wrong) So, how can linear eddy viscosity model exist?

You are right about the ambiguity in the nomenclature. The eddy viscosity is a function of the resolved velocity even in the linear relation. The nomenclature mimics the linear relation used for newtonian fluid. Actually, we could say that appears linear in the functional relation, not mathematically.
Check also in the books of Pope and Wilcox.

January 12, 2018, 18:30
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Lucky
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 Originally Posted by toboto But from my basic understanding, eddy viscosity is dependent on turbulence variable (e.g. k & epsilon) which in turn depend on the flow field. So, eddy viscosity actually depends on the flow field.
Assume that you magically know the eddy viscosity (say via a hotline to God). For demonstrative purposes, forget that we will call it eddy viscosity or that it is a flow property. Then the linear eddy viscosity relates the reynolds stresses to the strain (i.e. the linear functional relation between the two). This is all that the (linear) eddy viscosity model claims. No one says (yet) how the heck you can find this eddy viscosity yet. Of course other models do not have this simple linear proportionality relation but more complex ones.

How to find this linear coefficient which we call eddy viscosity is another matter.

 Tags linear eddy viscosity, turbulence modeling

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