Numerical study on cnoidal wave run-up around a vertical circular cylinder: Fid-Bau Portal

Numerical study on cnoidal wave run-up around a vertical circular cylinder

Zhang, Jun-sheng / Teng, Bin

Highlights•The full reflection condition is exactly satisfied at curved wall boundaries in the present FEM model of Boussinesq equations.•The effects of the related parameters on the run-up of cnoidal waves around a cylinder were fully examined.•Cnoidal waves with the same normalized profile still produce different run-up owing to the difference in H/d.•The nonlinearity of a cnoidal wave train almost makes a constant contribution to the 2nd-order run-up for different cylinders.•The variations of the maximum run-up with the wavelength for cnoidal waves are completely distinct from those for Stokes waves.

AbstractA finite element model of Boussinesq-type equations was set up, and a direct numerical method is proposed so that the full reflection boundary condition is exactly satisfied at a curved wall surface. The accuracy of the model was verified in tests. The present model was used to further examine cnoidal wave propagation and run-up around the cylinder. The results showed that the Ursell number is a nonlinear parameter that indicates the normalized profile of cnoidal waves and has a significant effect on the wave run-up. Cnoidal waves with the same Ursell number have the same normalized profile, but a difference in the relative wave height can still cause differences in the wave run-up between these waves. The maximum dimensionless run-up was predicted under various conditions. Cnoidal waves hold entirely distinct properties from Stokes waves under the influence of the water depth, and the nonlinearity of cnoidal waves enhances rather than weakens with increasing wavelength. Thus, the variations in the maximum run-up with the wavelength for cnoidal waves are completely different from those for Stokes waves, and there are even significant differences in the variation between different cnoidal waves.