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The turbulent coherent structure of flow in open channel is a chaotic and stochastic process in nature. The coherence structure of the flow or bursting process consists of a series of eddies with a variety of different length scales and it is very important for the entrainment of sediment particles from the bed. In this study, a fractal-Markovian process is applied to the measured turbulent data in open channel. The turbulent data was measured in an experimental flume using three-dimensional acoustic Doppler velocity meter (ADV). A fractal interpolation function (FIF) algorithm was used to simulate more than 500,000 time series data of measured instantaneous velocity fluctuations and Reynolds shear stress. The fractal interpolation functions (FIF) enables to simulate and construct time series of u ′, v ′, and u ′ v ′ for any particular movement and state in the Markov process. The fractal dimension of the bursting events is calculated for 16 particular movements with the transition probability of the events based on 1st order Markov process. It was found that the average fractal dimensions of the streamwise flow velocity ( u ′) are; 1.73, 1.74, 1.71 and 1.74 with the transition probability of 60.82%, 63.77%, 59.23% and 62.09% for the 1–1, 2–2, 3–3 and 4–4 movements, respectively. It was also found that the fractal dimensions of Reynold stress u ′ v ′ for quadrants 1, 2, 3 and 4 are 1.623, 1.623, 1.625 and 1.618, respectively.

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.