Bedrock Channel Evolution

3D Bedrock Channel Evolution with Smoothed Particle Hydrodynamics Coupled to a Finite Element Earth

An enduring obstacle to reliable modeling of the short and long-term evolution of the stream channel-hillslope ensemble has been the difficulty of estimating stresses generated by stream hydrodynamics. To capture the influence of complex three-dimensional (3D) flows on bedrock channel evolution, we derive the contribution of hydrodynamic stresses to the stress state of the underlying bedrock through a Smoothed Particle Hydrodynamics (SPH) approximation of the Navier-Stokes equations as calculated by the DualSPHysics code (Crespo et al., 2015). Capturing the 3D component of complex flows with SPH provides a more complete description of the stream channel-hillslope ensemble than traditional 1D shear stress derived from hydraulic estimates. Coupling the SPH flow solutions to the stress-strain formulation of the Failure Earth Response Model (FERM) (Koons et al., 2013) provides three-dimensional erosion as a function of the strength-stress ratio of each point in the computational domain. From the coupling of SPH and FERM we gain a 3D physics-based erosion scheme and a two-way link between complex flows and hillslope dynamics in a finite element framework. This novel approach robustly approximates the geomorphic response of bedrock channels with complex geometries and lithologies.