Erosion of unconsolidated beds by turbidity currents

Turbidity currents are gravity flows of fluids with suspended, denser sediment, which remains aloft due to turbulence generated by the current motion itself. To remain active, turbidity currents must have an ability to entrain material from their base to counteract the sedimentation of particles from the current to the base. A number of decades ago, Bagnold, Engelund, and Fredsøe proposed a physical picture for erosion as a function of the overall velocity of the turbidity current (bed stress). Recently, it has been argued that the high-velocity form of this law is critical in determining the overall mechanics of turbidity currents, particularly their predeliction to erode or deposit sediment in different locations. This letter reexamines the Bagnold-Engelund-Fredsøe picture, and determines the corresponding erosion law in a way that is consistent with turbidity current mechanics, and has a high-velocity plateau that determines the qualitative features of turbidity current deposition and erosion. I also address the differential role of fluid and grain stress transmission in determining erosion; provided the grain stress transmission is less effective than the fluid stress transmission in eroding sediment, there will continue to be a high-velocity plateau in the erosion rate.

Figure 1

The granular base underneath a turbidity current is a jammed solid (below A), which transitions to a creeping flow (between A and B) and ultimately a bedload and suspended load flow (above B). The inset displays the fluid-mediated (${\tau }_F$) and grain-mediated (${\tau }_G$) components of the overall stress. The stress across A is primarily transmitted by granular interactions, while that across B is transmitted both by fluid forces and by granular collisions. Note that the fluid component of the stress at B (${\tau }_B$) is less than the total stress.

Figure 2

The “bare” erosion rate $\mathcal{E}/v_s$, from Eq. (16), vs the tractive stress $Z$, as determined from Eq. (22), for ${\varphi }_0<0.25$. As hypothesized by Garcia and Parker [5], a clear saturation is evident at larger values of tractive stress.