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

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.

The role of coherent vortices near the turbulent/non-turbulent interface in a planar jet

“…In turbulent flows, the regions of concentrated vorticity consist of either (i) vortical tube-like structures (vortex tubes) or in (ii) structures exhibiting a sheetlike shape (vortex sheets) [20]. Whereas in the tube-like structures, vorticity and strain are comparable, the sheet-like structures are dominated by vorticity with relatively low levels of strain.…”

Amplification of enstrophy in the far field of an axisymmetric turbulent jet

“…Andreotti (1997) showed that the tendency for the vorticity vector to align with the intermediate strain-rate eigenvector is a result of the crossover of the eigenvalues. This led to the development of an alternative reordering of the eigenvalues in which the eigenvalue with the corresponding eigenvector that is most closely aligned with the vorticity vector is denoted σ z , with the largest of the two remaining eigenvalues denoted σ + and the smallest one denoted as σ − (Andreotti 1997;Nomura & Post 1998;Horiuti 2001). However, in the current study, the eigenvalues would have more physical meaning when arranged by magnitude as it would be clear that the corresponding eigenvector would be compressive, extensive or alternate.…”

Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence

“…The majority of identification methods (local and non-local) are devoted to educing those types of structures. Traditionally, more attention has been paid to tube-like structures, but recently considerable interest has put forward the eduction of sheet-like structures (see, for example, Tanaka & Kida 1993;Horiuti 2001). Local methods targeted at educing tubes and sheets, based on physical principles, resort often to visualization of the regions of joined classified points to assess the geometrical character of those regions.…”