Groove oscillation of the doublon structure in the phase-field model

A doublon is a unique pattern found in crystal growth. It is a pair of symmetry broken fingers. We perform numerical simulations in a channel with the phase-field model to study the doublon more in detail. Two small seeds of crystal with different sizes are set on the left side of the channel as an initial condition. The groove between the two fingers exhibits damping oscillation in a fairly wide range of parameters. We find that the groove oscillation does not attenuate in a narrow parameter range. In this paper, we report the details of the groove oscillation.