Mohammad R. Jalali and Mohammad M. Jalali
Nonlinear Modelling of Sloshing Waves and Solitary Waves in Shallow Basins
229 - 237
2018
12
3
International Journal of Aerospace and Mechanical Engineering
https://publications.waset.org/pdf/10008925
https://publications.waset.org/vol/135
World Academy of Science, Engineering and Technology
The earliest theories of sloshing waves and solitary waves based on potential theory idealisations and irrotational flow have been extended to be applicable to more realistic domains. To this end, the computational fluid dynamics (CFD) methods are widely used. Threedimensional CFD methods such as NavierStokes solvers with volume of fluid treatment of the free surface and NavierStokes solvers with mappings of the free surface inherently impose high computational expense; therefore, considerable effort has gone into developing depthaveraged approaches. Examples of such approaches include Green&ndash;Naghdi (GN) equations. In Cartesian system, GN velocity profile depends on horizontal directions, xdirection and ydirection. The effect of vertical direction (zdirection) is also taken into consideration by applying weighting function in approximation. GN theory considers the effect of vertical acceleration and the consequent nonhydrostatic pressure. Moreover, in GN theory, the flow is rotational. The present study illustrates the application of GN equations to propagation of sloshing waves and solitary waves. For this purpose, GN equations solver is verified for the benchmark tests of Gaussian hump sloshing and solitary wave propagation in shallow basins. Analysis of the free surface sloshing of even harmonic components of an initial Gaussian hump demonstrates that the GN model gives predictions in satisfactory agreement with the linear analytical solutions. Discrepancies between the GN predictions and the linear analytical solutions arise from the effect of wave nonlinearities arising from the wave amplitude itself and wavewave interactions. Numerically predicted solitary wave propagation indicates that the GN model produces simulations in good agreement with the analytical solution of the linearised wave theory. Comparison between the GN model numerical prediction and the result from perturbation analysis confirms that nonlinear interaction between solitary wave and a solid wall is satisfactorilly modelled. Moreover, solitary wave propagation at an angle to the xaxis and the interaction of solitary waves with each other are conducted to validate the developed model.
Open Science Index 135, 2018