wave on a running stream part-1

Consider the effect of a pressure source located within the interval $[−a,a]$ acting on a free surface and with a flow velocity of U, examine the relationships between $\phi$ and $\eta$.

fluid mechanics

water-wave-Kelvin-Wedge

The Equations for Water Waves

incompressible flow momentum equation and Surface of water waves and boundary condition and Variational Formulation

fluid mechanics

water-wave-Kelvin-Wedge

gravity wave and capillary wave

dispersion relation and solutions of the water wave equation incorporating surface tension

fluid mechanics

water-wave-Kelvin-Wedge