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 -ray theory 3

hydrodynamic fundamental, small amplitude wave

fluid mechanics

water-wave-Kelvin-Wedge

water wave -ray theory 2

hydrodynamic fundamental, small amplitude wave

fluid mechanics

water-wave-Kelvin-Wedge

water wave -ray theory 1

hydrodynamic fundamental, three conservation equations

fluid mechanics

water-wave-Kelvin-Wedge