Mean profiles for a passive scalar in wall-bounded flows from symmetry analysis

Abstract

Based on the symmetry properties of the equations for a passive scalar in turbulent wall-bounded flows we derive the symmetry invariant mean profiles of the scalar. In a unifying framework we classify all of the coexisting profiles in terms of their invariance properties and derive analytical expressions for the different scaling laws of the mean profiles for velocity and passive scalars at Prandtl numbers of order unity. In addition to the well-known logarithmic law also algebraic and exponential profiles are found. The results are supported by extensive numerical simulations in channel and Couette flows as well as experiments on thermal boundary layers.

Keywords:

• Boundary layers
• Symmetry analysis
• Passive scalars