Define incipient motion condition

Incipient motion

Incipient motion is the condition at which the hydrodynamic forces (drag and lift) acting on a bed particle are just equal to the forces resisting its movement (submerged weight and friction). It is the threshold between a stable bed and a moving bed: if the flow increases even slightly, the particle starts to move.

It is described by:

• the critical (threshold) shear stress $\tau_c$: the bed shear stress at which motion starts; or
• the critical velocity $V_c$ at which motion starts.

Quantitatively, for non-cohesive grains, $\tau_c$ is obtained from the Shields diagram, $\tau_c = \tau_*(\gamma_s - \gamma)d$. Motion occurs when the actual bed shear stress $\tau_0 = \gamma R S_0$ exceeds $\tau_c$.

Mobile boundary (alluvial) channel

A mobile boundary channel is an open channel whose bed and banks consist of loose granular material (sand, gravel, silt) that can be eroded, transported and deposited by the flowing water itself. The boundary is therefore deformable: the shape, slope and bed forms of the channel adjust to the flow and sediment load. Natural rivers, and unlined earth canals in sandy soil, are examples.

An alluvial channel is a channel formed in alluvium, that is, in its own deposited sediment. Its geometry is partly determined by the flow, unlike a rigid boundary channel (concrete or rock lined) whose boundary does not change.