Energy formulations of head cut dynamics

This study employs the principles of energy conservation to establish the framework for the development of the dynamical equations of head cut as a part of a continuum mechanical analysis of soil erosion induced by surface flow. The dynamics of head cut are controlled by several physically distinct processes, notable among which are surface seal formation, its failure and the redistribution of flow energy into kinetic and dissipation energies of water and soil. Thus, an erosive energy release rate function is introduced in the global energy equation, which is shown to depend on physical parameters governing the dynamics of the process region. The energy release rates are decomposed into line integrals representing motions associated with the translation, rotation, self-similar expansion and the distortion of the head cut cavity. From these considerations, approximate analytical expressions are derived which establish criteria for the initiation and the steady state head cut velocity. The results at this stage of development are preliminary and need testing and validation with data under controlled experimental conditions.