Coalescence of Saffman-Taylor fingers: A new global instability

We study the stability of a parallel array of Saffman-Taylor fingers in the limit of infinite viscosity contrast. We discover a modulatory instability which prevents the system from remaining in steady-state motion. We discuss how this instability signals the beginning of the coalescence of the finger array to the final single-finger steady-state configuration. Finally, we speculate on the importance of this global instability for the understanding of patterns in diffusion-limited growth.