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Systematic study of the existing statistical data from direct numericalsimulations (DNS) lead to a logical and important classification of genericturbulent boundary layers (TBL), namely Type A,B and C TBL, based on thedistribution patterns of time averaged wall shear stress. Among these threetypes, Type A and B TBLs are investigated in terms of its universal statisticallaws of velocity and temperature with independency on both Reynolds (Re) andPrandtl (Pr) numbers. With reference to the analysis by von Karman indeveloping the conventional law of the wall for Type A TBL, the current studyfirst physically distinguishes the time averaged local velocity scale from theensemble averaged velocity scale, and properly defines the TBL temperaturescale based on wall heat flux, similar to the well known frictional velocityscale based on wall shear stress. The unified law of the wall formulations arethen derived for the inner layer of Type A and B thermal TBLs using thesescales. The formulations are constructed by introducing the general damping andenhancing functions in inner layer, and further, these functions are extendedto logarithmic coordinate based on the multiscale characteristics of TBLvelocity profiles. The validations of the law are conducted both by the DNSguided near wall integration of Type B TBL governing equations, which uncoveredthe Re and Pr independency mechanisms of the law. The research advances thecurrent understandings of the conventional TBL theory and develop the completeanalytical forms of law of the wall for Type A and B TBLs, including innerlayer, transition layer, logarithmic layer and wake layer.

Unified Flow and Thermal Law-of-the-wall for Type-A and B Turbulent Boundary Layers