A Multi-scale Numerical Model for Breaking Waves Using The Lattice Boltzmann Method (LBM)

Wave breaking is a crucial oceanic process that facilitates momentum, heat, and gas exchange between the atmosphere and the sea. For example, oceans absorb air through bubble entrainment and dissolution. However, predicting breaking waves is challenging due to the wide range of physical scales involved, from kilometers to millimeters. No experimental setup fully captures these multi-scale, three-dimensional interactions, making numerical modeling essential. This research develops a hybrid numerical model to bridge these scales. A third-order Stokes wave model first simulates the liquid phase before breaking. Then, the phase-field Lattice Boltzmann model (LBM) captures air-water interactions. This approach allows accurate representation of both phases and their interface while addressing the conflicting resolution requirements of large wavelengths and small air bubbles. The in-house numerical model is three-dimensional and multi-scale, utilizing the Message-Passing Interface (MPI) library to enhance computational efficiency across large domains. Parallel computing enables high-resolution simulations that would otherwise be impractical. The model's accuracy and consistency have been validated by comparing its results with existing numerical studies across multiple test cases. By bridging the gap between different physical scales, this model offers a powerful tool for studying breaking waves and their role in air-sea interactions. Its multi-scale capability provides insights that could improve climate modeling, ocean engineering, and environmental predictions.