Symmetry of periodic structures in a 3D mixing cavity flow

Symmetry concepts are applied to analyze three-dimensional time-periodic mixing Stokes flows in a cubic domain. Usage of simple map algebra, developed by Franjione et al. [Phys. Fluids A 11, 1772–1783 (1989); Philos. Trans. R. Soc. London, Ser. A 338, 301–323 (1992)], allows us to reveal the symmetry in the arrangement of periodic points in such a flow. Symmetries reveal essential features of the underlying physics, and with manipulation of symmetries mixing protocols can be made efficient over the entire flow domain.