Abstract
A mass source wave-maker method is generalized as the two-wave-source wave-maker method to generate bichromatic waves in the numerical model, whose governing equations are Navier–Stokes equations with the continuity equation. The Fluent software is taken as the calculation platform. In the numerical model, the waves at both the left and right ends of the numerical wave flume are absorbed with the momentum sources added in Navier–Stokes equations. The numerical simulation of bichromatic waves propagation with different frequencies in uniform deep, intermediate, and shallow water has been conducted. The numerical solutions are compared with the theoretical solutions obtained on the basis of Stokes waves theory. The frequency spectrum analyses of the results are conducted and discussed, and the differences between the weakly nonlinear theoretical solutions and the fully nonlinear numerical results are investigated in detail. It is found that the numerical model can effectively simulate the nonlinear effect of bichromatic waves in water with different depths, and the theoretical solutions only adapt the deep and intermediate water. The results indicate that the present numerical model is valuable in the aspect of practical application.
Highlights
Nonlinear problem is one of the important subjects of gravity surface waves
To simulate a more realistic wave field, the traditional mass source wave-maker method is revised as the two wave sources wave-maker method to generate the bichromatic waves in the numerical wave flume whose governing equations are the incompressible N–S. equations with the continuity equation. e VOF method is used in the numerical model, where the Fluent software is taken as the calculation platform. e present numerical model is completely nonlinear since its governing equations are incompressible N–S. equations with the continuity equation. e present numerical model is used to study the interactions of bichromatic waves, the numerical results are compared with theoretical solutions, and the differences between the numerical results and the theoretical results are analyzed in detail
Due to the difference of wavelengths between the two incident waves of case C2 being large, the effect of the relatively short wave is equivalent to adding a disturbance to the relatively long wave. e wave profile shown in Figure 3 confirms this. e wave heights of the numerical solutions are slightly smaller than those of the theoretical numerical solutions. is is because the wave energy can be more effectively redistributed in the numerical solutions between different orders of harmonics due to the nonlinearity
Summary
Nonlinear problem is one of the important subjects of gravity surface waves. Phillips [1] made a pioneering work for the study of wave interaction dynamics in the random gravity wave fields with finite amplitude by analyzing the third-order interaction of waves. Hong [8] derived a fourth-order approximate theoretical solution of the nonlinear interaction of surface gravity waves in water with uniform depth based on the Stokes finite amplitude wave theory by the application of the perturbation method. With the nonlinear Boussinesq-type equations used as the governing equations, different numerical models are provided by Madsen and Sørensen [9] and Zhang et al.[10] to solve the nonlinear interaction problems. To simulate a more realistic wave field, the traditional mass source wave-maker method is revised as the two wave sources wave-maker method to generate the bichromatic waves in the numerical wave flume whose governing equations are the incompressible N–S. equations with the continuity equation. E present numerical model is used to study the interactions of bichromatic waves, the numerical results are compared with theoretical solutions, and the differences between the numerical results and the theoretical results are analyzed in detail To simulate a more realistic wave field, the traditional mass source wave-maker method is revised as the two wave sources wave-maker method to generate the bichromatic waves in the numerical wave flume whose governing equations are the incompressible N–S. equations with the continuity equation. e VOF method is used in the numerical model, where the Fluent software is taken as the calculation platform. e present numerical model is completely nonlinear since its governing equations are incompressible N–S. equations with the continuity equation. e present numerical model is used to study the interactions of bichromatic waves, the numerical results are compared with theoretical solutions, and the differences between the numerical results and the theoretical results are analyzed in detail
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