On steady columnar vortices under local compression

Numerical simulations are presented of the long time behaviour of viscous columnar vortices subject to non-uniform axial stretching. The relevant result is that the vortices reach a steady state even when the axial average of the strain is zero, such that they are being compressed during half of their extent. The structure of the flow is analysed and shown to range from local Burgers equilibrium to massive separation. For an intermediate range of Reynolds numbers the vortices are more or less uniform and compact, and it is suggested that this condition is related to the strong vortices observed in turbulent flows. The reason for the survival of the vortices under compression is traced to induced axial pressure gradients and to the viscous cancellation of outgoing vorticity. Theoretical analyses of the linear Burgers’ regime and of the onset of separation are presented and compared to the numerical experiments. The results are related to the observation of intermittency in turbulence, and shown to be consistent both with the observed scaling of vortex diameter, and with the lack of intermittency of the velocity signal.