Spectral Collocation Model for Solitary Wave Attenuation and Mass Transport over Viscous Mud

Abstract

In this paper, wave attenuation and mass transport of a water-mud system due to a solitary wave on the free surface is modeled by using the Chebyshev-Chebyshev collocation spectral method for spatial discretization and a fourth-order multistage scheme for time integration. The governing equations are formulated in Lagrangian coordinates and perturbation equations for shallow water waves are derived. An iteration-by-subdomain technique is introduced to tackle the interface in the two-layer system. The numerical model is tested against available analytical solutions and good agreement has been found. Numerical simulations of the water-mud system with different layer thicknesses suggest that the accuracy of the existing boundary layer theory for fluid-mud interaction is limited when the mud layer is thin because the assumption of irrotational core may not be valid. Although the paper is focused on solitary waves and Newtonian fluid-mud, the methodology can be extended to oscillatory, nonlinear water waves over a non-Newtonian mud bottom.