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A higher-order σ-coordinate non-hydrostatic model for nonlinear surface waves |
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| Authors: | Chih-Chieh Young Jan-Tai Kuo |
| Institution: | a Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC b Department of Civil and Environmental Engineering, 1269D Engineering Hall, University of Wisconsin, Madison, WI 53706-1691, USA c Department of Civil and Disaster Prevention Engineering, National United University, Miao-Li 36003, Taiwan, ROC |
| Abstract: | A higher-order non-hydrostatic model in a σ-coordinate system is developed. The model uses an implicit finite difference scheme on a staggered grid to simultaneously solve the unsteady Navier-Stokes equations (NSE) with the free-surface boundary conditions. An integral method is applied to resolve the top-layer non-hydrostatic pressure, allowing for accurately resolving free-surface wave propagation. In contrast to the previous work, a higher-order spatial discretization is utilized to approximate the large horizontal pressure gradient due to steep surface waves or rapidly varying topographies. An efficient direct solver is developed to solve the resulting block hepta-diagonal matrix system. Accuracy of the new model is validated by linear and nonlinear standing waves and progressive waves. The model is then used to examine freak (extreme) waves. Features of downshifting focusing location and wave asymmetry characteristics are predicted on the temporal and spatial domains of a freak wave. |
| Keywords: | σ-coordinate Non-hydrostatic pressure Free-surface waves Freak waves |
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