Steady waves in water of constant finite depth

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

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 variational approach in water waves

This post primarily introduces The Variational Approach and demonstrates how to employ the method to derive the Euler-Lagrange equations for the water wave equations

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

water wave - stationary phase -final

Asymptotic expansion of analytic functions and contour integral

fluid mechanics

water-wave-Kelvin-Wedge

water wave - stationary phase -2

asymptotic expansions for integrals

fluid mechanics

water-wave-Kelvin-Wedge

water wave - stationary phase -1

asymptotic expansions and Abel's lemma

fluid mechanics

water-wave-Kelvin-Wedge

water wave -the depth slowly vary for water wave -4

hydrodynamic fundamental, small amplitude wave

fluid mechanics

water-wave-Kelvin-Wedge

water wave -ray theory 3

hydrodynamic fundamental, small amplitude wave

fluid mechanics

water-wave-Kelvin-Wedge