Steady free-surface flow past an uneven channel bottom

Abstract

New free-surface flows past a semi-infinite ‘step’ in the bottom of a channel are considered. Surface tension is neglected but gravity is included in the dynamic boundary condition. Fully nonlinear solutions are computed by boundary integral equation methods. Additional weakly nonlinear solutions are derived analytically. A thorough analysis of the weakly nonlinear problem provides a systematic approach to identify all the possible types of solutions and the number of independent parameters.gravity is included in the dynamic boundary condition. Fully nonlinear solutions are computed by boundary integral equation methods. Additional weakly nonlinear solutions are derived analytically. A thorough analysis of the weakly nonlinear problem provides a systematic approach to identify all the possible types of solutions and the number of independent parameters.