On the transition between Kelvin’s equilibria*

In earlier studies we have showed experimentally that the polygonal patterns observed in a rotating shallow water layer in confined cylinder are Kelvin’s equilibria [PRL 100, 174503 (2008)]. We have also reported that the transition of m into (m + 1) equilibria involves a beat-wave resonance that mediates energy transfer between the background flow and the vortex core [PRE 83, 056319 (2011)].  Here, we revisit this transition between relative equilibria involving two and three satellite vortices. This transition is investigated forward and backward, using particle image velocimetry (PIV).  The evolution of the satellite vortices is depicted and analyzed.