A coupled phase-field and volume-of-fluid method for accurate representation of limiting water wave deformation

A coupled phase-field and volume-of-fluid method is developed to study the sensitive behavior of water waves during breaking. The THINC model is employed to solve the volume-of-fluid function over the entire domain covered by a relatively coarse grid while the phase-field model based on Allen-Cahn equation is applied over the fine grid. A special algorithm that takes into account the sharpness of the diffuse-interface is introduced to correlate the order parameter obtained on the fine grid and the volume-of-fluid function obtained on the coarse grid. The coupled model is then applied to the study of water waves generated by moving pressures on the free surface. The deformation process of the wave crest during the initial stage of breaking is discussed in details. It is shown that there is a significant variation of the free nappe developed at the front side of the wave crest as the wave steepness differs. It is of a plunging type at large wave steepness while of a spilling type at small wave steepness. The numerical results also indicate that breaking occurs later and the duration of breaking is shorter for waves of smaller steepness and vice versa. Neglecting the capillary effect leads to wave breaking with a sharper nappe and a more dynamic plunging process. The surface tension also has an effect to prevent the formation of a free nappe at the front side of the wave crest in some cases.