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FRACTAL GEOMETRY AND MIXING TRANSITION IN TURBULENT MIXING LAYER

Mamoru Tanahashi
Department of Mechanical and Aerospace Engineering Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan

Yifei Wang
Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8850, Japan

Takeharu Fujisawa
Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8850, Japan

Makoto Sato
Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8850, Japan

Kazuya Chinda
Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8850, Japan

Toshio Miyauchi
Dept. Mechanical and Aerospace Eng., Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan; Organization for the Strategic Coordination of Research and Intellectual Properties Meiji University 1-1-1 Higashimita, Tama-ku, Kawasaki, Kanagawa, Japan

Abstract

Direct numerical simulations (DNSs) of turbulent mixing layer with non-reactive and reactive scalar transports have been conducted to investigate the mixing transition mechanism and fractal geometry of scalar surfaces in turbulence. DNS of non-reactive scalar up to Reω.o = 1900 with moderate Schmidt number (Sc) show that fractal dimension of scalar surfaces in the fully-developed turbulent state is independent to Reynolds number and coincides with the theoretical expectation of Mandelbrot (1975) (~2.5). The inner cutoff is 8 times Kolmogorov length both in the transitional and fully-developed state, and coincides with the most expected diameter of coherent fine scale eddy in turbulence. The mixing transition is characterized by the drastic increase of difference between the outer and inner cutoffs (Reλ ~ 100). DNS of reactive scalars show that fractal dimension decreases to 2.40 ~ 2.45 due to the chemical reaction. The inner cutoff is not affected by the chemical reaction and agrees with that of non-reactive scalars with moderate Sc number. To investigate Schmidt number effects, DNS of non-reactive scalar up to Sc = 6.0 has been conducted for moderate Reynolds number. For high Sc, two fractal dimensions can be defined. The first fractal dimension coincides with that of moderate Sc, whereas the second one shows larger values around 2.7. The inner cutoff of the second fractal reaches to about 8 times of Batchelor length scale for high Sc.