A multifractal model for the momentum transfer process in wall-bounded flows.

The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation , where is the filtering length scale. According to the multifractal formalism, and in the log-region, where is the friction Reynolds number, is a real number, is an outer length scale and is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at = 4200.