Fractal Feature of Sets of Isoconcentration Points of a Plume and the Effect of the Distortion of Flow due to a Sphere on It

Abstract

This paper gives a detailed investigation of the fractal feature of sets of isoconcentration points taken from data on an axisymmetric point source plume which is evolved in grid-generated turbulence and distorted by a sphere. The following points are clarified in this paper : (1) The fractal dimensions of sets of isoconcentration points, D_f1, are valued at approximately 0.3, and are likely to be independent of the threshold level of a wide range of concentration : (2) Although there is no clear range of the -5/3 power law in the spectra of the turbulence and the concentration fluctuation, sets of isoconcentration points appear to be fractal-like, and the fractal dimension is close to the value of 0.36±0.05, found in high Reynolds number flows : (3) The distortion of flow due to a sphere has almost no effect on the magnitude of the fractal dimension of a set of isoconcentration points, but merely gives rise to the change of the boxsize range within which the fractality holds.