Abstract
The multifractal measure enables an examination of the characteristics of a quantity distributed over a domain. This study examined the multifractal properties of turbulent intensities obtained from jet discharge experiments, where three types of nozzle geometries were examined in terms of the velocity fields and turbulent characteristics using particle image velocimetry. Depending on the nozzle geometry, the experimental results showed that the distribution of turbulent intensities and resulting dilution exhibited different behaviors. The experiment also showed that the transversal velocity profiles are similar to each other regardless of the outfall nozzle shapes and demonstrates the traditional similarity assumption at the same time. The multifractal exponents of the turbulent intensities were obtained with Box Count Method in a two-dimensional space. The results showed that the turbulent intensities obtained in two-dimensional space have a common multifractal spectrum, which was not the case for the velocity or shear stress observed in the same space. Although the transversal velocity profiles are similar, the multifractal exponent clearly shows a difference depending on the outfall geometries. In particular, the minimum value of the Lipschitz–Hölder exponent (α min) and the entropy dimension (α 1) tends to increase as turbulent intensity and dilution increase. These results suggest that the multifractal properties can be utilized potentially to categorize and evaluate the discharge outfall capabilities in terms of the resulting dilution.
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Acknowledgments
This study was supported by Basic Science Research Program by the National Research Foundation of Korea (NRF) from the Ministry of Science, ICT and Future Planning (NRF-2013R1A1A1058964) and the Ministry of Education (2012R1A1A2007807).
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Seo, Y., Lyu, S. Multifractal characteristics of the jet turbulent intensity depending on the outfall nozzle geometry. Stoch Environ Res Risk Assess 30, 653–664 (2016). https://doi.org/10.1007/s00477-015-1127-0
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DOI: https://doi.org/10.1007/s00477-015-1127-0