Abstract
On the influence of wave reflection on shoaling and breaking solitary Waves
Highlights
Model equations for free surface water waves propagating in a horizontal channel of uniform depth have been widely studied for many years
A coupled BBM system of equations is studied in the situation of water waves propagating over a decreasing fluid depth
A Fourier collocation method coupled with a 4-stage Runge–Kutta time integration scheme is employed to approximate solutions of the BBM system
Summary
Model equations for free surface water waves propagating in a horizontal channel of uniform depth have been widely studied for many years. Boussinesq models incorporate the lowest-order effects of nonlinearity and frequency dispersion as corrections to the linear long wave equation. These models are widely used for describing the propagation of non-linear shallow water waves near coastal regions. The more realistic situation of an uneven bottom profile is fundamental to studies of ocean wave dynamics in coastal regions. Wave shoaling is the effect by which surface waves propagating shorewards experience a decrease in the water depth. The study of shoaling waves is of importance in the nearshore areas and in the design of coastal structures.
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