Numerical determination of turbulent fractal dimensions

Abstract

This paper focuses on the fractal dimension of a line embedded in a homogeneous turbulent field. Based on an intuitive picture motivated by fractal theory, the introduction provides a physical approach for analysing the fractal dimension. The analysis is first applied to the case of an isotropic turbulent field which is suddenly subjected to steady rotation. It is shown that for a non-rotating field the fractal dimension D′ of the line increases with time. When expressed as a function of t/td, where td is the time of decay, the fractal dimension depends on both the Reynolds number and the rotation rate. However, using a suitable combination of linear (rotation rate Ω) and non-linear (td) mechanisms to define a characteristic time t*=td(1 + αtdΩ), the dependence of the fractal dimension on rotation rate can be absorbed for Rossby numbers Ro>1.54. The fractal dimension of a line immersed in periodic channel flow is also considered and the role of a no-slip wall is analysed. It shows that the fractal dimension increases rapidly from unity on the solid surface, and that this sharp and substantial increase occurs with 15 wall units. In the cases considered, this region corresponds to zones where the rms value of the velocity fluctuation is maximum. © 1996 American Institut of Physics.