Analytical Approach of Long Waves Dynamics in an Estuary (Case Study in Karang Mumus River Estuary)

Abstract

A mathematical model is developed for describing a propagating long wave in an estuary. Wave dynamics in an estuary will employ the Saint Venant equation in the form of a nonlinear partial differential equation (PDE), which consists of equations of mass conservation and momentum conservation. Waves propagate in an estuary usually generated by tides entering a gentle slope channel. The analytical approach is used to solve this non-linear PDE approach using a perturbation method. This paper considers only a zero order. A cross-differentiation between conservation of mass and conservation of momentum equations result in the Bessel differential equation. The solution of zero order gives decreasing amplitude of the long wave to the end of the estuary.