Weakly dispersive hydraulic flows in a contraction - Nonlinear stability analysis

The nonlinear stability of steady weakly dispersive hydraulic solutions of the forced Korteweg de-Vries equation is investigated here. For numerical convenience the solutions are considered as periodic pairs consisting of an upward and downward jump. Two types of instability are found to occur. For largely symmetric problems, a solitary wave type instability dominates which features subexponential growth prior to saturation. For asymmetric solutions, the downward jump is destabilized by a hydraulic instability in which superexponential growth occurs prior to saturation. A qualitative description of both instability processes is presented using wave kinematics.