Numerical Calculation of the Formation and Persistence, or Collapse, of Vortex Pairs in Counter-Current Parallel Channel Flows

A numerical investigation has been performed for the time-dependent motion of a constant property, Newtonian fluid in a counter-current shearing flows configuration. In the geometry of interest, two initially separated streams are made to flow counter to each other through a pair of stacked parallel channels of approximately square cross-section. The streams are then made to shear at a common free interface between the two channels. This problem consists of a very simple Cartesian geometry with well posed initial and boundary conditions. However, for the conditions explored the resulting physics are highly non-linear and complex. Starting from rest, the opposing streams in the free interface region initially display the characteristics of a two-dimensional saddle point flow when observed along the spanwise z-direction. Soon thereafter, depending on the shapes of the velocity profiles imposed at the channel inlet planes, two pairs of transversely aligned vortices appear that can be stable or unstable. If the inlet plane velocity profiles are symmetric each of the two channel vortex pairs counter-rotates and they are stable over long periods of time. If, however, the inlet velocity profiles are asymmetric, two opposed antisymmetric co-rotating vortices dominate the flow. The pair of vortices orbit around each other while being stretched by the background saddle-like flow. They ultimately merge and collapse in a burst of chaotic three-dimensional unsteady motion. In this case, the cycle repeats with an average frequency which appears to depend on the Reynolds number. Aside from their fundamental nature, the phenomena observed have potential applications for the controlled mixing of fluid streams at relatively low Reynolds number.