Identifying coherent structures and vortex clusters in Taylor-Couette turbulence

Abstract

The nature of the underlying structures in Taylor-Couette (TC) flow, the flow between two co-axial and independently rotating cylinders is investigated by two methods. First, the quadrant analysis technique for identifying structures with intense radial-azimuthal stresses (also referred to as ‘Q’s) of Lozano-Durán et al., (J. Fluid Mech. 694, 100-130) is used to identify the main structures responsible for the transport of angular velocity. Second, the vortex clusters are identified based on the analysis by del Álamo et al., (J. Fluid. Mech., 561, 329-358). In order to test these criteria, two different radius ratios η = r_i/r_o are considered, where r_i and r_o are the radii of inner and outer cylinder, respectively: (i) η = 0.5 and (ii) η = 0.909, which correspond to high and low curvature geometries, respectively and have different underlying structures. The Taylor rolls, i.e. the large-scale coherent structures, are effectively captured as ‘Q’s for the low curvature setup and it is observed that curvature plays a dominant role in influencing the size and volumes of these ‘Q’s. On the other hand, the vortex clusters are smaller in size when compared to the ‘Q’ structures. These vortex clusters are found to be taller in the case of η = 0.909, while the distribution of the lengths of these clusters is almost homogenous for both radius ratios.