A simple approximation for the drift rates of rotating polygons on a free fluid surface

We report on laboratory experiments investigating the dynamics of a free fluid surface in a cylindrical tank with a rotating bottom plate. The shear instability in the system creates polygonal structures, which propagate around the domain, along the fixed vertical sidewalls. We analyze the wavelengths and drift rates of these patterns, which are known from previous literature to be created by a complex interplay between centrifugal effects and gravity wave propagation in this unique geometry. We find that with an empirical correction factor, the drift rates of the polygonal vortices can be approximated fairly well by a surprisingly simple formula derived from the dispersion relation of linear gravity waves using easily observable parameters.

Automated summary

We conducted laboratory experiments to study the dynamics of a free fluid surface in a cylindrical tank with a rotating bottom plate. The shear instability in the system generated polygonal structures that propagated along the fixed vertical sidewalls. By analyzing the wavelengths and drift rates of these patterns, we found that the drift rates of the polygonal vortices can be well approximated by a simple formula derived from the dispersion relation of linear gravity waves using easily observable parameters, with an empirical correction factor.