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Patterns of parallel submarine gullies with regular transverse spacing are observed at continental margins. These gullies are thought to be formed by turbidity currents. In this study, the existing model is extended to more general cases in which the slope profile is arbitrary and the entrainment of fresh seawater cannot be neglected. A linear stability analysis is performed with the use of the layer-averaged momentum and continuity equations of turbidity currents, a dispersion equation of suspended sediment, and the Exner equation extended for the seabed subject to erosion and deposition due to turbidity currents. The analysis shows that the dominant spacing of submarine gullies on slopes with arbitrary shapes is of the order of 800-1600 times the Richardson-critical layer thickness of turbidity currents.

The formation of submarine gullies on continental shelves with arbitrary shapes by turbidity currents