Critical flow in rockbed streams with estimated values for Manningʹs n

Substitution of the equation of critical flow into the Manning equation applied along a homogeneous flow panel enables values of Manningʹs roughness, n, slope, s, and depth, d, to be isolated with respect to the other two variables. Total energy losses indexed by Manningʹs n (which include boundary roughness), must increase as slope and depth increase if flow is to remain critical (Fr = 1), and it must increase beyond the bounding surface described by the equation n = 0.32 s0.5d0.167 if flow is to revert to subcritical. Field observations that portions of the channel flow remain critical within a fluid-bounded channel as stage rises allows the deduction that the increased roughness required to maintain criticality must come principally from increased shearing and vorticity with respect to adjacent subcritical lower-velocity water, and from the initiation of bedload transport (other conditions permitting). At a sufficiently high stage, roughness at channel margins and depth reduction may increase roughness enough for flow to revert to subcritical even as reach slope remains constant. On other occasions, however, flow may become supercritical with rising stage. When the critical flow assumption can be used in central portions of the flow, it enables a range of standard hydraulic quantities to be calculated directly (velocity, shear stress and power). Application of the equation of critical flow to data from well-known catastrophic flows provides surprisingly good estimates of Manningʹs n for these flows. The relation s = gn2d−0.33 is suggested as a boundary to define the lower limit of slope for ‘steep’ natural channels, i.e., channels in which central flow is critical or supercritical.