# non dimensionalisation eddy viscosity, mixing length and turbulent shear stress

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 January 30, 2019, 09:20 non dimensionalisation eddy viscosity, mixing length and turbulent shear stress #1 New Member   Join Date: Jan 2019 Posts: 7 Rep Power: 5 The velocity profile is defined as law of the wall is defined as , where ; and . How would one then non dimensionalize the eddy viscosity and turbulent sheer stress as a function of ?

 January 30, 2019, 09:23 #2 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 4,927 Rep Power: 58 You can non-dimensionalize anything anyway you want. The question is what you are going to do with these quantities later? Then you want to choose a non-dimensionalization that makes sense. For example, the friction velocity isn't just a random non-dimensionalization of shear stress, but it is used because that's the characteristic velocity in the perturbatino when you do asymptotic analysis (i.e. u+ = y+ which happens only you scale u and y using u*).

January 30, 2019, 09:29
#3
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 Originally Posted by LuckyTran You can non-dimensionalize anything anyway you want. The question is what you are going to do with these quantities later?
I want to explicitly define these in terms of . Then I want to relate each of these properties to after which these will be evaluated in the limit . Eventually I want to prove that in the overlap region the turbulent properties are independent of viscosity.

January 30, 2019, 10:44
#4
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Filippo Maria Denaro
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Quote:
 Originally Posted by Lmath The velocity profile is defined as law of the wall is defined as , where ; and . How would one then non dimensionalize the eddy viscosity and turbulent sheer stress as a function of ?

Actually, the eddy viscosity function is naturally non-dimensional when is computed from a non-dimensional expression. Just use the correct velocity and pressure reference quantities to work directly in terms of u+ and Re_tau.

You can find in Sec.5 of this paper how to select the variables
https://www.researchgate.net/publica...ection_methods

 January 30, 2019, 12:22 #5 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 1,847 Blog Entries: 29 Rep Power: 36 Typically, , for some function . For example, at high , it typically holds that . In contrast, for small , it typically holds that . Of course, we're talking about equilibrium boundary layers here.

 Tags eddy viscosity, turbulence, viscous flow