A classification method for vortex sheet and tube structures in turbulent flows

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Abstract
A new classification method for structures in turbulent flow is proposed and applied to the analysis of homogeneous isotropic turbulence. The criteria for the classification of the structures into three groups, namely, the group of structures similar to the core region of the Burgers’ vortex tube in which vorticity is predominant, that of the structures similar to the curved sheet in the circumference of the tube core in which strain is predominant, and that of the flat sheets similar to the Burgers’ vortex layer in which vorticity and strain are comparably large, were considered. This method was developed based on the eigenvalue solutions of the λ2 method [Jeong and Hussain, J. Fluid Mech. 285, 69 (1995)] on the basis of the principal strain eigenvectors, which were reordered according to the degrees of alignment with the vorticity vector. Assessment of the proposed method was carried out in fully developed homogeneous isotropic turbulence and in the process of rolling up of the vortex layer in ABC flow. It was shown that the spiral vortex sheet emanating from the tube core, which was generated during the rolling up of the layer, can be accurately educed using the proposed method, and its performance was markedly better than that of eduction obtained using the second-order invariant of the velocity gradient tensor Q. The process of formation of a vortex tube was investigated using the proposed method. In the analysis of turbulence statistics, it was shown that the characteristic differences of the three regions for contributions of strain and vorticity were correctly educed using the proposed method, and that the flat sheet region is primarily responsible for the generation of turbulence.