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We describe a PDE model of bedrock abrasion by impact of moving particles andshow that by assuming unidirectional impacts the modification of a geometricalPDE due to Bloore exhibits circular arcs as solitary profiles. We demonstratethe existence and stability of these stationary, travelling shapes by numericalexperiments based on finite difference approximations. Our simulations showthat, depending on initial profile shape and other parameters, these circularprofiles may evolve via long transients which, in a geological setting, mayappear as non-circular stationary profiles.

Circular, stationary profiles emerging in unidirectional abrasion