A nonlocal theory of sediment transport on hillslopes

Sediment disentrainment and the concept of local versus nonlocal transport on hillslopes

[1] A local formulation of the sediment flux on a hillslope describes the flux as a unique function of local hillslope conditions at any contour position x, whereas a nonlocal formulation must take into account nonlocal (upslope or downslope) conditions that influence the flux at x. Local formulations are reasonable when particle motions involve small length scales associated with localized bio...

Sediment transport by runoff on debris-mantled dryland hillslopes

Evidence for nonlinear, diffusive sediment transport on hillslopes and implications for landscape morphology

Steep, soil-mantled hillslopes evolve through the downslope movement of soil, driven largely by slope-dependent transport processes. Most landscape evolution models represent hillslope transport by linear diffusion, in which rates of sediment transport are proportional to slope, such that equilibrium hillslopes should have constant curvature between divides and channels. On many soil-mantled hi...

A nonlocal theory of sediment buffering and bedrock channel evolution

[1] Bedrock erosion in mountain river channels ultimately sets the erosion rate of the surrounding hillslopes and the rate of sediment supply to the channels. The supply of coarse bed sediment acts as a dampening effect on further erosion by depositing an alluvial cover that temporarily obscures the bedrock. For landscapes where the residence time of the alluvial bed cover is comparable to the ...

Transport theory with nonlocal corrections

A kinetic equation which combines the quasiparticle drift of Landau’s equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider’s equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second order quantum virial corrections and are proven to be consistent wi...