Assumptions

The derivation of the near-wall relations for turbulent flows depends on several assumptions presented in this section. It is assumed that the flow close to the wall is in the x direction.

Fully developed flow

This means that all streamwise derivatives vanish, i.e. , and that the flow is parallel to the wall.

Constant shear layer flow

This is equivalent to requiring that there is no pressure gradient or other momentum source term.

Boussinesq or eddy viscosity assumption

This states that the Reynolds stress can be expressed as the product of an effective eddy viscosity and the mean flow strain rate. Combining the Boussinesq approximation to equation above gives: