Mathematical properties of the kinematic cascade

A kinematic cascade is defined as a sequence of n discrete overland flow planes or channel segments in which the kinematic wave equations are used to describe the unsteady flow. Each plane or channel is characterized by a length, lk, width, wk, and a roughness-slope factor, αk. Outflow from the kth plane, along with the parameters for planes k and (k + 1), estalishes the upstream boundary condition for plane (k + 1). Such a model has been used in a number of recent hydrologic studies. Nondimensional equations are presented for the kth element in a kinematic cascade. Properties of the solutions for a kinematic cascade with pulsed lateral inputs are examined. Kinematic shock waves develop whenever the following criterion is met: Wk−1Wk·αk−1αk>1 . These shock waves represent discontinuities in the flow field and produce vertical segments in the outflow hydrographs. The magnitude of the shock and its effect on the outflow hydrograph can be appreciable for realistic parameter values.