Transitions between systems of satellite vortices in a rotating fluid

Abstract

We investigate experimentally the transitions between systems of two and three satellite vortices found within a shallow layer of water above a rotating disk at the bottom of an open stationary cylindrical tank. We found that these systems of two and three satellite vortices are associated with two fundamental multipolar modes, namely, the quadrupole and hexapole, respectively. The forward and backward transitions between the two systems of satellite vortices, which occur at critical disk speeds, involve growth and decay of the fundamental modes as well as the excitation of their common harmonic (the dodecapole) and symmetric radial oscillations.