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We describe the downstream flow developing at the corner of a partially immersed flat plate, placed perpendicular to a uniform stream. As the flow converges toward the plate centerline, a steady wave, which remains attached to the corner of the plate, develops downstream. Both the amplitude and slope of the wave increase with the downstream distance until the wave either gently spills or plunges depending on the flow conditions. We show that this "corner wave'' can be used as a prototypical flow to study the breaking process of two-dimensional deep-water surface waves allowing for the application of a variety of measurement techniques to characterize their evolution. We propose a criterion, based on the Froude number, to determine the transition from spilling to plunging for two-dimensional surface gravity waves consistent with a large set of experimental observations obtained in this flow configuration.