Periodic steady vortices in a stagnation-point flow

A stagnation point flow of the form U = (0, Ay, - Az) is unstable to three-dimensional disturbances. It has been shown that the vorticity components of such a disturbance that are perpendicular to the direction of the diverging flow will decay, and that the parallel component of vorticity can grow. We augment these findings by showing that fully nonlinear steady-state deviations from this flow exist that consist of a periodic distribution of counter-rotating vortices whose axes lie parallel to the direction of the diverging flow. These solutions have two independent parameters: the dimensionless strength of the converging flow, and the intensity of the vortices. We examine the structure of these vortices in the asymptotic limits of large strain rate of the converging flow, and of large amplitude of the vortices.