Hello!

Can Turbulent Viscosity be a Tensor ??? As we know it is a flow property. I would appreciate if some can offer comments on it. Thanks in advance, Murthy

In general the effect of turbulence on the mean-flow is not a scalar but a tensor called the Reynolds stresses. However, when you introduce the concept of a turbulent viscosity you assume or approximate the Reynolds stresses with a scalar eddy viscosity. So I'd say that by definition the turbulent viscosity is a scalar and not a tensor, although in reality the effect of turbulence on the mean flow needs a tensor to be fully described.

I am not sure what you mean by flow property, turbulent viscosity is an invention for modelling purposes.

As Jonas says, the turbulent viscosity is usually a scalar quantity when it is used in a model for the the Reynolds stresses.

However, when used as a model for the triple correlations appearing in the Reynolds stress transport equations the most common models (there are quite a few) use effective coefficients with the dimensions of a second order tensor.

Thanq both Jonas Larsson & Andy for your valuable comments.

As you know reynolds stress is analogous to molecular shear stress but proportionality constant (mol visc) doesn't vary with flow, where in case of Reynolds stresses proportionality constant(eddy viscosity) is a function of flow.

Now my query is, Having accurate distribution of all Reynolds stresses and all strain rate tensors in a given flow field, calculate turbulent viscosity, would it be a tensor ?? Mathematically turbulent viscosity has to be either a scalar or a tensor. I Hope my query makes sense.

looking forward for your both comments.

regards Murthy

I am not sure your query makes sense because turbulent viscosity is defined by the model it appears in. If the model chosen for the turbulent quantity uses a scalar turbulent viscosity then it is a scalar, if it defines a second order tensor then it is a second order tensor, etc... Different models for the same turbulent quantity will have different turbulent viscosities.

Here is a reference where the SGS term is modeled as a second order tensor

"Dynamic one-equation nonviscosity LES model" Pomraning E. and Rutland, J. AIAA Journal vol. 40, No. 4, April 2002

Thanks a lot Andy for your reply. I will soon get all Reynolds components and respective strain rates. I would calculate turbulent viscosity and let you know back. By the way i may take a little more time to do all these stuff.

Kind Regards, Murthy

Thanq agg. I will go through it Murthy

For any turbulence model using the Boussinesq assumption the eddy viscosity is a scalar quantity regardless of how we calculate it in the particular model.

I think you had it slightly mixed up. The Reynolds stresses are proportional to the eddy viscosity times the mean strain rate tensor.

even a scalar is also a zero order tensor. If it is a isotropic property, then it a scalar, otherwise it vector. (which is a first order tensor). Generally, in two equation models it is scalar and flow property.

vishnu

Thanq Vishnu for your enthusiasm. Turbulent viscosity cann't be vector, it is either a scalar or second order Tensor. A agree with you it's a isotropic property in case of Two-Equation models as same eddy viscosity is used for all Reynolds Stress components.But what if i use different formulation for Eddy viscosity to close different Reynolds Stresses.

Regards Murthy

then it becomes a vector if it is anisotropic otherwise again it is scalar. (i.e first order tensor, i.e each direction and it represents NU_T=nu_t_x I+nu_t_y J+nu_t_y K). and in each momentum equation correspoding "nu_t" will come. if u know plz tell me. In RSTM we will directly calculate reynold stress without going to the eddy viscosity formulation. But i dont know any methods (models) which give different "nu_t" in corresponding direction.

Can i get your mail i.d i can communicate to that only Murthy

vishnu.kavuluru@gmail.com

Turbulent viscosity is defined by the model it appears in.Different models for the same turbulent quantity will have different turbulent viscosities.However,the turbulent viscosity is usually a scalar quantity when it is used in a model for the the Reynolds stresses(not exclude a tensor in some model).When used as a model for the triple correlations appearing in the Reynolds stress transport equations the most common models (there are quite a few) use effective coefficients with the dimensions of a second order tensor(sometimes twain).

I think you could refer to one or two textbooks on turbulent.