Fully developed turbulent flow indeed consists of a hierarchy of eddies or scales of various disorders. Due to the complexity of turbulence, the turbulent flow structure has not been completely understood. Thus, abundant empirical observations have been made about fractality in hydrodynamic turbulence. In this study, the fractal scaling of velocity components (u′, v′) and Reynolds shear stress (u′v′) for fully developed flow in an open channel were studied for Reynolds number in the range of 29,000–85,000. An efficient algorithm was developed to construct Fractal Interpolation Functions (FIF). The algorithm was used to simulate more than 200,000 time series of u′, v′, and u′v′ that were measured in a laboratory flume. The algorithm was also used to compute fractal dimension. The fractal dimensions of the turbulent data were accurately obtained by applying only as few as 500 data points. It was found that the fractal dimension of u′, v′, and u′v′ were 1.615, 1.657, and 1.559, respectively. The relationships between the fractal dimension and Froude number (Fr) and Reynolds number (Re) were also investigated. It was found that the fractal dimension of turbulent data and Re and Fr were reasonably correlated. Moreover, the fractal dimension of Reynolds shear stress in bursting events (outward interaction, ejection, inward interaction, and sweep) was calculated and compared with each other. There were some differences among the fractal dimension of Reynolds shear stress for four quadrants of bursting process. The fractal dimension of u′v′ in sweep and ejection events were more than the fractal dimension of the overall Reynolds shear stress.

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