Abstract:
A new analytical solution is derived for tide-driven groundwater waves in coastal aquifers using
higher-order Boussinesq equation. The homotopy perturbation solution is derived using a virtual perturbation
approach without any pre-defined physical parameters. The secular term removal is performed using a combination
of parameter expansion and auxiliary term. This approach is unique compared with existing perturbation
solutions. The present first-order solution compares well with the previous analytical solutions and a 2D
FEFLOW solution for a steep beach slope. This is due to the fact that the higher-order Boussinesq equation
captures the streamlines better than ordinary Boussinesq equation based on Dupuit’s assumption. The slope of
the beach emerges as an implicit physical parameter from the solution process