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

The Equations for Water Waves

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

gravity wave and capillary wave

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

water wave - stationary phase -final

Asymptotic expansion of analytic functions and contour integral

water wave - stationary phase -2

asymptotic expansions for integrals

water wave - stationary phase -1

asymptotic expansions and Abel's lemma

water wave -ray theory 3

hydrodynamic fundamental, small amplitude wave

water wave -ray theory 2

hydrodynamic fundamental, small amplitude wave

water wave -ray theory 1

hydrodynamic fundamental, three conservation equations