By means of direct numerical simulations of a passive scalar with an imposed linear and steady mean gradient in isotropic turbulence, the micro scales of the scalar field has been studied for a wide range of Schmidt numbers. The Schmidt number is the ratio of the kinematic viscosity of the fluid to the diffusivity of the scalar and has an important influence on the micro structure of the scalar field. The figure shows the instantaneous scalar field on a two-dimensional plane through the computational domain for a Schmidt number of 25. In this particular case the smallest length scale of the scalar field, the so-called Batchelor scale, is about 5 times smaller than the Kolmogorov length scale. At this high Schmidt number we observe very thin, elongated structures with cross-sections that indicate sheet-like structures in the scalar field. Many of the elongated structures are more or less straight but at some places they are twisted and folded or even rolled up. The typical spiral scalar structures, as observed in the figure, appear only when the Schmidt number is larger than one. They are formed by scalar sheets wrapping around turbulent vortices.

Contributors: Dr. Geert Brethouwer, Department of Mechanics, KTH, Stockholm, Sweden, and Prof. F. Nieuwstadt, laboratory of Aero and Hydronamics, Delft University of Technology, The Netherlands

Reference:

G. Brethouwer (2000) Mixing of passive and reactive scalars in turbulent flows: A numerical study. Ph.D. dissertation, Delft University of Technology, The Netherlands.