Time-Series Analysis of Intermittent Velocity Fluctuations in Turbulent Boundary Layers*

Classical turbulence theory is modified under the inhomogeneities produced by the presence of a wall.  In this regard, we propose a new time series model for the streamwise velocity fluctuations in the inertial sub-layer of turbulent boundary layers. The new model employs tempered fractional calculus and seamlessly extends the classical 5/3 spectral model of Kolmogorov in the inertial subrange to the whole spectrum from large to small scales. Moreover, the proposed time-series model allows the quantification of data uncertainties in the underlying stochastic cascade of turbulent kinetic energy. The model is tested using well-resolved streamwise velocity measurements up to friction Reynolds numbers of about 20,000.  The physics of the energy cascade are briefly described within the context of the determined model parameters.