A Dynamic Model of Gully Erosion

Abstract

The main causes of gully formation are anthropogenic: the clearing of native forests, tilling of fallow lands and associated change of the hydrological conditions in the rainfall-runoff system. Gully formation is very intensive during the period of initiation, when morphological characteristics (length, depth, width, area, and volume) are far from stable. About 80 per cent of a gully’s length, 60 per cent of its area and 35 per cent of its volume are formed in only 5 per cent of its lifetime. This stage of development can be described by a dynamic model to predict rapid changes of gully morphology.

The dynamic gully model is based on the solution of the equations of mass conservation and gully bed and wall deformation. An analysis of experimental results shows that the rate of soil particle detachment is linearly correlated with the product of bed shear stress and mean flow velocity. Basic equations were written in the form of a transport equation and solved with the use of an explicit predictor-corrector scheme of the Lax-Wendroff type. The side walls of gullies become practically straight after rapid sliding following its incision. A straight stable slope model was used for prediction of gully-side wall inclination.

This dynamic gully erosion model has been verified with data on gully morphology and dynamics from the Yamal peninsula (Russia) and New South Wales (Australia).