Numerical analysis of the weakly nonlinear Boussinesq system with a freely moving body on the bottom

TL;DR

This paper develops a finite difference numerical scheme to analyze the effects of a moving bottom object on wave behavior within the weakly nonlinear Boussinesq system, highlighting energy dissipation and wave amplitude loss.

Contribution

It introduces an accurate numerical method for coupled fluid-solid interaction in the Boussinesq system, accounting for nonlinear effects and energy dissipation due to a moving bottom object.

Findings

Wave amplitude decreases with a moving bottom object.

Friction influences wave transformation and energy dissipation.

Hydrodynamic damping effects similar to dead-water phenomenon observed.

Abstract

In this study, the numerical analysis of a specific fluid-solid interaction problem is detailed. The weakly nonlinear Boussinesq system is considered with the addition of a solid object lying on the flat bottom, allowed to move horizontally under the pressure forces created by the waves. We present an accurate finite difference scheme for this physical model, finely tuned to preserve important features of the original coupled system: nonlinear effects for the waves, energy dissipation due to the frictional movement of the solid. The moving bottom case is compared with a system where the same object is fixed to the bottom in order to observe the qualitative and quantitative differences in wave transformation. In particular a loss of wave amplitude is observed. The influence of the friction on the whole system is also measured, indicating differences for small and large coefficients of friction. Overall, hydrodynamic damping effects reminiscent to the dead-water phenomenon can be established.