Numerical Simulation of Overtopping of Cnoidal Waves on a Porous Breakwater Using the Boussinesq Equations: Comparison with Solutions of the Navier-Stokes Equations

摘要

We approximately obtain heights of cnoidal waves overtopping on a porous breakwater using both the one-layer Boussinesq equations (Vu et al.,2018) and the two-layer Boussinesq equations (Huynh et al.,2017).For cnoidal waves overtopping on a porous breakwater,we find through numerical experiments that the heights of cnoidal waves overtopping on a low-crested breakwater (obtained by the Navier-Stokes equations) are smaller than the heights of waves passing through a high-crested breakwater (obtained by the one-layer Boussinesq equations) and larger than the heights of waves passing through a submerged breakwater (obtained by the two-layer Boussinesq equations).As the cnoidal wave nonlinearity becomes smaller or the porous breakwater width becomes narrower,the heights of transmitting waves obtained by the one-layer and two-layer Boussinesq equations become closer to the height of overtopping waves obtained by the Navier-Stokes equations.