Transcritical Flow Over a Bump using Forced Korteweg-de Vries Equation

Abstract

The flow of water over an obstacle is a fundamental problem in fluid mechanics. Transcritical flow means the wave phenomenon near the exact criticality. The transcritical flow cannot be handled by linear solutions as the energy is unable to propagate away from the obstacle. Thus, it is important to carry out a study to identify suitable model to analyse the transcritical flow. The aim of this study is to analyse the transcritical flow over a bump as localized obstacles where the bump consequently generates upstream and downstream flows. Nonlinear shallow water forced Korteweg-de Vries (fKdV) model is used to analyse the flow over the bump. This theoretical model, containing forcing functions represents bottom topography is considered as the simplified model to describe water flows over a bump. The effect of water dispersion over the forcing region is investigated using the fKdV model. Homotopy Analysis Method (HAM) is used to solve this theoretical fKdV model. The HAM solution which is chosen with a special choice of }-value describes the physical flow of waves and the significance of dispersion over abump is elaborated.