Shear Stress Models

Satisfaction

  • In analogy with the coefficient of viscosity for laminar flow, J. Boussinesq introduced a mixing coefficient  for the Reynolds stress term, defined as
  • Using  the shearing stresses can be written as 
such that the equation
may be written as
(33.13)

The term Î½t is known as eddy viscosity and the model is known as eddy viscosity model .
  • Unfortunately the value of Î½t is not known. The term Î½ is a property of the fluid whereas Î½t is attributed to random fluctuations and is not a property of the fluid. However, it is necessary to find out empirical relations between Î½t, and the mean velocity. The following section discusses relation between the aforesaid apparent or eddy viscosity and the mean velocity components