Leapfrogging of 2 smoke rings (same speed) at low Reynolds number

Two smoke rings are driven by given pressure drops from left to right, while at other times the external forces for driving the flow are almost in equilibrium. The second "puff" reaches and almost penetrates the first one which also accelerates during this game: both chase each other! The main problem with visualizing this dynamic behaviour is due to the dominant diffusive terms. While "absolute" quantities as pressure, streamfunction and velocity plots do not show the physical movement, only tracing of concentration may provide some helpful illustration. However, due to the strong diffusion, we had to rescale the concentration in each step which explains the "funny colors" and the "funny structure" of the smoke rings. For this kind of flow simulation, definitively a particle tracing is the best visualization tool!!!

• Distribution of temperature/concentration via Boussinesq model
  
  

  Visualization via tracing of concentration, starting from the small hole in the interior wall which separates both semi-circles. We show two shaded results with different color maps (2 MB and 2.5 MB) and with isolines (5.1 MB).
  

  
  
  

• Pressure
  
  

  Visualization via shaded pressure plots (first with adaptive range 1.2 MB and second with fixed range 1.1 MB) and via isolines (third, 3.5 MB).
  

  
  
  

• Streamfunction
  
  

  Visualization via shaded streamline plots (first with adaptive range 1.3 MB and second with fixed range 1.2 MB) and via isolines (third, 7.4 MB).
  

  
  
  

• Velocity
  
  

  Visualization via vector plots (vectors, 8.4 MB)