  We investigate erosion patterns observed in a horizontal granular bed
resulting from seepage of water motivated by observation of beach rills and
channel growth in larger scale landforms. Our experimental apparatus consists
of a wide rectangular box filled with glass beads with a narrow opening in one
of the side walls from which eroded grains can exit. Quantitative data on the
shape of the pattern and erosion dynamics are obtained with a laser-aided
topography technique. We show that the spatial distribution of the source of
groundwater can significantly impact the shape of observed patterns. An
elongated channel is observed to grow upstream when groundwater is injected at
a boundary adjacent to a reservoir held at constant height. An amphitheater
(semi-circular) shape is observed when uniform rainfall infiltrates the
granular bed to maintain a water table. Bifurcations are observed as the
channels grow in response to the ground water. We further find that the
channels grow by discrete avalanches as the height of the granular bed is
increased above the capillary rise, causing the deeper channels to have rougher
fronts. The spatio-temporal distribution of avalanches increase with bed height
when partial saturation of the bed leads to cohesion between grains. However,
the overall shape of the channels is observed to remain unaffected indicating
that seepage erosion is robust to perturbation of the erosion front.
