Intermediate Scaling of Turbulent Momentum and Heat Transfer in a Transitional Rough Channel

Abstract

The properties of the mean momentum and thermal balance in fully developed turbulent channel flow on transitional rough surface have been explored by method of matched asymptotic expansions. Available high quality data support a dynamically relevant three-layer description that is a departure from two-layer traditional description of turbulent wall flows. The scaling properties of the intermediate layer are determined. The analysis shows the existence of an intermediate layer, with its own characteristic of mesolayer scaling, between the traditional inner and outer layers. Our predictions of the peak values of the Reynolds shear stress and Reynolds heat flux and their locations in the intermediate layer are well supported by the experimental and direct numerical simulation (DNS) data. The inflectional surface roughness data in a turbulent channel flow provide strong support to our proposed universal log law in the intermediate layer, that is, explicitly independent transitional surface roughness. There is no universality of scalings in traditional variables and different expressions are needed for various types of roughness, as suggested, for example, with inflectional type roughness, Colebrook–Moody monotonic roughness, etc. In traditional variables, the roughness scale for inflectional roughness is supported very well by experimental and DNS data. The higher order effects are also presented, which show the implications of the low Reynolds-number flows, where the intermediate layer provides the uniformly valid solutions in terms of generalized logarithmic laws for the velocity and the temperature distributions.