Mesolayer theory for turbulent flows

Turbulent shear flows in pipes are investigated theoretically using a 3-layer model. The intermediate-layer (IL) theory of Long and Chen (1981) is modified to follow the suggestion of Afzal (1982), that IL velocity is of the order of Uc: a composite-expansion formulation is obtained for IL and inner layer and matched with the outer defect layer. It is shown that, with properly selected Uc, a classical logarithmic region always exists. The IL plays only a minor role for 2-layer-model lower-order computations but becomes significant in first-order 3-layer theory, where the IL reference velocity is half that at the pipe axis, and the velocity distribution follows a half-defect law.