Analysis of three-dimensional transition mechanisms in the near wake behind a circular cylinder

The transition to three-dimensionality in the near wake behind a circular cylinder is studied numerically. Two modes of instability are considered for the Reynolds numbers 220 (mode A) and 300 (mode B). In the linear approximation the evolution of three-dimensional perturbations in a fluid particle can be described through the action of four mechanisms: (I) stretching of the vortex lines of perturbations by the base flow; (II) shear deformations of the vortex lines of the base flow by perturbations; (Ill) viscous diffusion of perturbations; (IV) solid-state rotation of fluid particles. The fields of each mechanism are determined by the results of a numerical solution of the three-dimensional Navier-Stokes equations. An analysis of the influence of these mechanisms is carried out and the regions of growth and decay of the three-dimensional vortex structures are identified. The main destabilizing effect is related to the stretching of vortex lines of perturbations (I) and shear deformations of the base flow vorticity (II). Viscous diffusion (III) stabilizes the flow and solid-state rotation (IV) does not influence the amplitude of perturbation in a fluid particle. For mode A there are two stages of perturbations growth: inside the elliptic part of the forming vortex and in the hyperbolic region of the braid shear layer, where the forming vortex is separated from the cylinder. At both stages the growth of three-dimensional vortex structures is mostly related to mechanism (I), however, a significant impact of mechanism (II) on this process is observed at the first stage. The most intensive growth occurs at the second stage. Perturbations of mode B are growing outside elliptic regions and are determined by mechanism (1), the shear deformations (II) have mainly a stabilizing effect. The length of perturbation enhancement time interval was estimated: it is twice as large for mode A as for mode B. (C) 2018 Elsevier Masson SAS. All rights reserved.