# Dipole-Wall collision

This two-dimensional turbulent flow illustrates the interaction between a vortex and a no-slip wall. From the initial condition, a pair of counter-rotating vortices is self-propelled to the right. The system is confined in a square box with no-slip wall. At the contact with the right wall, additional vortices detach from the boundary layer, break apart the original vortex pair to form two secondary pairs. These describe a circular path to bounce against the wall a few more times.

Although only two-dimensional, this problem is challenging because it requires a high resolution of the boundary layer in order to yield accurate results. A detailed description of the problem and solutions obtained with other numerical tools are provided Clerx&Bruneau (2005).

## Simulation setup

The simulation is contained in a 2-by-2 square domain. The initial state is defined by two counter-rotating vortices, with the following velocity :

Here, the distance to the vortex centers is defined as

The parameter labels the radius of a vortex, and its core vorticity.

## Numerical Parameters

Reynolds number | 5000 |

Core vorticity | 320 |

Vortex radius | 0.1 |

Center of first vortex | (0,0.1) |

Center of second vortex | (0,-0.1) |