Shock Capturing Shallow Water Model for Long Waves Generated by a Moving Atmospheric Pressure

Abstract

The shock capturing numerical model based on nonlinear shallow water equations is developed to predict run-up as well as edge waves generated by a moving atmospheric pressure disturbance across a straight shoreline on a sloping beach. The HLL approximate Riemann solver with the fifth order accurate WENO scheme is used to compute numerical flux in spatial discretization, which yields better results in comparison with TVD-MUSCL type schemes. Numerical experiments are conducted for wave propagation by a moving atmospheric pressure disturbance normally approaching the coastline. When the atmospheric pressure disturbance suddenly acts on the water surface, both free and forced waves are generated and amplified due to shoaling and Proudman resonance. The maximum run-up is presented using different moving speeds for an atmospheric pressure. While wave run-up and run-down are repeated at the shoreline, edge waves are generated and propagate in the alongshore direction due to wave refraction.