Fractal-Markovian scaling of turbulent bursting process in open channel flow

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.