Valleys that form around a stream head often develop characteristic finger-like elevation contours. We study the processes involved in the formation of these valleys and introduce a theoretical model that indicates how shape may inform the underlying processes. We consider valley growth as the advance of a moving boundary travelling forward purely through linearly diffusive erosion, and we obtain a solution for the valley shape in three dimensions. Our solution compares well to the shape of slowly growing groundwater-fed valleys found in Bristol, Florida. Our results identify a new feature in the formation of groundwater-fed valleys: a spatially variable diffusivity that can be modelled by a fixed-height moving boundary.
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