Determining the Essential Elements of Hydrodynamic Erosion of Granular Beds

Major Goals: The erosion of earth materials by shear flows is common in nature, and has numerous applications including geomorphology, agriculture, and climate science [1-3]. Large sums of money are spent every year to control or mitigate erosion, with varying degrees of success. In some cases, such as controlling silting in dams and reservoirs, erosion may be desirable to remove deposited sediment. On the other hand, the prevention of erosion is crucial in places where bodies of water, landmasses, and human development meet. Despite its importance, modeling erosion remains a difficult problem due to its tremendous complexity [4,5]. Strongly erosive flows are typically turbulent, leading to highly stochastic shear stress imparted to the earth material. The grains that make up the bed typically have highly nonspherical shapes and variable sizes or material properties. Commonly used riverbed erosion models typically do not include these complexities and instead employ dimensional analysis [6]. Previous studies have suggested that the onset of erosion (i.e., the conditions under which a static bed will begin to erode) is controlled by two nondimensional parameters: ? and Re_*. The Shields number ? is the ratio of the shear stress ? imparted to the surface layer of the bed by the flow to the (reduced) weight of the bed particles ((?_g-?_f)gD), where ?_g is the density of the bed grains, ?_f is the density of the fluid, g is the acceleration due to gravity, and D is the diameter of the grains. The shear Reynolds number ? Re?_* is the ratio of the inertial forces in the flow (where u_*^2=?/?_f is the known as the friction velocity) to viscous damping, where ? is the kinematic viscosity of the fluid. Based on a compilation of empirical data from field and laboratory measurements, the onset of erosion is given by a curve, known as the Shields curve, in the parameter space spanned by these two nondimensional parameters [7].