Counter-rotation in an orbitally shaken glass of beer

Swirling a glass of wine induces a rotating gravity wave along with a mean flow rotating in the direction of the applied swirl. Surprisingly, when the liquid is covered by a floating cohesive material, for instance a thin layer of foam in a glass of beer, the mean rotation at the surface can reverse. This intriguing counter-rotation can also be observed with coffee cream, tea scum, cohesive powder, provided that the wave amplitude is small and the surface covering fraction is large. Here we show that the mechanism for counter-rotation is a fluid analog of the rolling without slipping motion of a planetary gear train: for sufficiently large density, the covered surface behaves as a rigid raft transported by the rotating sloshing wave, and friction with the near-wall low-velocity fluid produces a negative torque which can overcome the positive Stokes drift rotation induced by the wave.