Direction selection of metachronal waves in hydrodynamic coordination of cilia

Large arrays of active cilia coordinate their beat cycles into metachronal waves. These waves can travel in different directions with respect to the cilium's beat direction and the resulting direction of fluid propulsion. Hydrodynamic interactions provide a mechanism for the individual cilia to coordinate their beat cycles. Using an analytical framework that connects the properties of the individual cilia to the emergent wave behavior, I show how the forcing pattern of the beat cycle breaks the symmetry to select a wave direction. Previously, it was found that the second harmonic in the beat pattern is the dominant term for coordination. Here, I show that the first harmonic in the beat pattern enters the coordination dynamics at higher order and demonstrate the important role the higher order terms play in determining the direction of emerging metachronal waves.