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Investigation of the fractal structure of jets and plumes

This paper is a description of an experimental study of round, turbulent jets and plumes, investigating the effects of buoyancy on the fractal structure. The jets and plumes are formed by injecting fluid from a small source, with diameter, d, of 0.508 mm, into a stationary body of water contained in a tall tank of dimensions 1.75 m high by 0.6 m by 0.6 m. For both jets and plumes the Reynolds number at the source was in the range 800 to 1800, and the flow was observed in the far field at distances 250d to 550d. In the case of the plumes momentum still dominated near the source so that the flow was fully turbulent before buoyancy forces had a significant effect. The source fluid was dyed with fluorescein, and the flow was illuminated by a ‘thick’ sheet of light (thick in the sense of many Kolmogorov scales) effectively giving a projection rather than a true two–dimensional slice. The fractal dimensions of contours of concentration on this projection were measured, with care taken to normalize with respect to the local intensity and lengthscales. There were no significant differences in the results for jets and plumes, so the smaller scales of motion seem unaffected by the presence of buoyancy forces, The fractal dimension was found and to be a function of threshold intensity, with an apparent minimum of 1.23. This may be an artefact of the noise level, however, and an estimated value for the zero–intensity threshold of 1.16 may be important, though the use of a single value for the fractal dimension is questionable. The implications of the results for measurements where no account has been taken of local scales is discussed.