No abstract

Abstract. Solitary wave runup on a non-plane beach is studied analytically and numerically. For the theoretical approach, nonlinear shallow-water theory is applied to obtain the analytical solution for the simplified bottom geometry, such as an inclined channel whose cross-slope shape is parabolic. It generalizes Carrier-Greenspan approach for long wave runup on the inclined plane beach that is currently used now. For the numerical study, the Reynolds Averaged Navier-Stokes (RANS) system is applied to study soliton runup on an inclined beach and the detailed characteristics of the wave processes (water displacement, velocity field, turbulent kinetic energy, energy dissipation) are analyzed. In this study, it is theoretically and numerically proved that the existence of a parabolic cross-slope channel on the plane beach causes runup intensification, which is often observed in post-tsunami field surveys.

SUMMARYA new finite element method is presented to solve one-dimensional depth-integrated equations for fully non-linear and weakly dispersive waves. For spatial integration, the Petrov -Galerkin weighted residual method is used. The weak forms of the governing equations are arranged in such a way that the shape functions can be piecewise linear, while the weighting functions are piecewise cubic with C 2 -continuity. For the time integration an implicit predictor-corrector iterative scheme is employed. Within the framework of linear theory, the accuracy of the scheme is discussed by considering the truncation error at a node. The leading truncation error is fourth-order in terms of element size. Numerical stability of the scheme is also investigated. If the Courant number is less than 0.5, the scheme is unconditionally stable. By increasing the number of iterations and/or decreasing the element size, the stability characteristics are improved significantly. Both Dirichlet boundary condition (for incident waves) and Neumann boundary condition (for a reflecting wall) are implemented. Several examples are presented to demonstrate the range of applicabilities and the accuracy of the model.

No abstract

No abstract