1. Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, New Jersey 08854-8058, USA
2. Present address: Schering-Plough Research Institute, Kenilworth, New Jersey 07033, USA.

Correspondence to: Benjamin J. Glasser¹ Correspondence and requests for materials should be addressed to B.J.G. (e-mail: Email: bglasser@sol.rutgers.edu).

Unstable waves have been long studied in fluid shear layers^{1, 2, 3}. These waves affect transport in the atmosphere and oceans, in addition to slipstream stability behind ships, aeroplanes and heat-transfer devices. Corresponding instabilities in granular flows have not been previously documented⁴, despite the importance of these flows in geophysical and industrial systems^{5, 6, 7}. Here we report that breaking waves can form at the interface between two streams of identical grains flowing on an inclined plane downstream of a splitter plate. Changes in either the shear rate or the angle of incline cause such waves to appear abruptly. We analyse a granular flow model that agrees qualitatively with our experimental data; the model suggests that the waves result from competition between shear and extensional strains in the flowing granular bed. We propose a dimensionless shear number that governs the transition between steady and wavy flows.