THEORETICAL PERIOD AND AMPLITUDE OF LOCALLY FORCED PRECURSOR SOLITON GENERATION IN SINGLE-LAYER FLOW

Period and amplitude of precursor solitons over a localized topography are studied in a rectangular channel at near-resonance. A relation be tween asymptotic mean level and hydraulic fall H determined based on a n averaged fKdV equation in phase frame, where the asymptotic mean lev els in upstream and depressed water region are determined theoreticall y by the solution of the hydraulic falls. The period and amplitude of the precursor solitons are found by using the asymptotic mean levels a nd the mass and energy conservation theorems. The analytic results sho w that the period and amplitude of the precursor solitons theoreticall y depend on the hydraulic falls and the velocity of the topography onl y. The results from the joint theoretical, experimental and numerical studies are in good agreement. At the resonant points, two general rel ations on the generating amplitude A(0) and period tau(0) of the precu rsor solitons are obtained; (\) A(0) = 2H and (parallel to) tau(0) = 1 6 root 6H(-3/2)/9.