Dipole-Wall collision

Dipole-Wall collisionThis 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).

 

 

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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  (u_0, v_0) :

u_0 = - {1}/{2} delim{|}{{eta}_e}{|} (y-y_1) e^{-(r_1{/}r_0)^2}  + {1}/{2} delim{|}{{eta}_e}{|} (y-y_2) e^{-(r_2{/}r_0)^2},

v_0 = + {1}/{2} delim{|}{{eta}_e}{|} (x-x_1) e^{-(r_1{/}r_0)^2}  - {1}/{2} delim{|}{{eta}_e}{|} (x-x_2) e^{-(r_2{/}r_0)^2},

Here, the distance to the vortex centers is defined as

 r_i = sqrt{(x-x_i)^2+(y-y_i)^2}.

The parameter  r_0 labels the radius of a vortex, and  {eta}_e 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)

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