Waltzing {\it Volvox\/}: Orbiting Bound States of Flagellated Multicellular Algae

The spherical colonial alga {\it Volvox} swims by means of flagella on thousands of surface somatic cells. This geometry and its large size makes it a model organism for the fluid dynamics of multicellularity. Remarkably, when two nearby colonies swim close to a solid surface, they are attracted together and can form a stable bound state in which they continuously waltz around each other. A surface-mediated hydrodynamic attraction between colonies combined with the rotational motion of bottom-heavy {\it Volvox} are shown to explain the stability and dynamics of the bound state. This phenomenon is suggested to underlie observed clustering of colonies at surfaces.