Periodic Vortices in a Stagnation Point Flow

Streamlines of a periodic array of vortices when viewed along
the axis of the diverging flow in a 2-D stagnation point flow.


Area of Interest

 

In this work we are looking at a recently discovered family of solutions of the full incompressible steady-state Navier-Stokes equation. These solutions represent flows that consist of a periodic linear array of vortices whose axes are aligned with the diverging flow direction in a 2-D stagnation point flow of the form u=(0,Ay,-Az). This stagnation point flow has the property that perturbations to it that are independent of the y-coordinate can satisfy the full Navier-Stokes equation. There is a large range of solutions that depend on the strength of the background flow and the behaviour of the vorticity as z goes to infinity. Some of these are illustrated in some animated gif files:

In each of the above the left image gives the streamlines of the flow when observed down the y axis, the middle image gives the vorticity and the right image the perturbation streamfunction.

 

The discovery of these solutions was due to our desire to find a flow that mimiced certain aspects of the turbulent mixing of gases (i.e. converging flows with mixing due to vortices) for the purposes of shedding light on the behaviour of laminar flames in such an environment. The properties of these vortices has given insights into the mechanisms for the onset of streamwise vortices that develop between the transverse Kelvin-Helmholtz vortices that grow in a shear layer.

 

 


Schematic diagram showing the thin streamwise vortices growing between the transverse vortices that develop in a shear layer due to the Kelvin-Helmholtz instability.

 

Papers

  • O.S. Kerr & J.W. Dold (1994) Periodic Steady Vortices in a Stagnation Point Flow, J. Fluid Mech., 276, 307-325.
  • O.S. Kerr(1999) Periodic Steady Vortices in a Stagnation Point Flow II (submitted for publication)

Principal Researchers