In equation 4.8 of Turbulent Flow by Pope (2000), it is explained that the isotropic part of the stress tensor can be absorbed into the modified pressure and hence doesn't effect the mean momentum transfer. Is there a physical explanation of why isotropic components don't transfer mean momentum?
Thanks.
The pressure gradient in the momentum can be written also as Div (Ip), therefore you can see that any additional isotropic term in the form Div (If) (such as the terms coming from the turbulence model) is absorbed in Div [I(p+f)]=Div(Ip')= Grad p'. That is, you end up to compute a modified pressure function.
https://www.sciencedirect.com/search?qs=isotropic%20part%20of%20Reynolds%20stress%20tensor%20not%20transfer%20momentum&show=25&sortBy=relevance
The pressure gradient in the momentum can be written also as Div (Ip), therefore you can see that any additional isotropic term in the form Div (If) (such as the terms coming from the turbulence model) is absorbed in Div [I(p+f)]=Div(Ip')= Grad p'. That is, you end up to compute a modified pressure function.
I also have the same question why only anisotropic part of residual stress tensor can be associated with strain tensor in linear eddy-viscosity model.
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