2020/05/27 by А. А. Чесноков, Alexander Chesnokov, Chesnokov, Alexander +3
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Aquatic and Environmental Studies #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.2005.13173
arxiv created 2020/05/27 · openalex publication_date 2020/05/27 · arxiv updated 2020/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive a new hyperbolic model describing the propagation of internal waves in a stratified shallow water with a non-hydrostatic pressure distribution. The construction of the hyperbolic model is based on the use of additional `instantaneous' variables. This allows one to reduce the dispersive multi-layer Green--Naghdi model to a first-order system of evolution equations. The main attention is paid to the study of three-layer flows over uneven bottom in the Boussinesq approximation with the additional assumption of hydrostatic pressure in the intermediate layer. The hyperbolicity conditions of the obtained equations of three-layer flows are formulated and solutions in the class of travelling waves are studied. Based on the proposed hyperbolic and dispersive models, numerical calculations of the generation and propagation of internal solitary waves are carried out and their comparison with experimental data is given. Within the framework of the proposed three-layer hyperbolic model, a numerical study of the propagation and interaction of symmetric and non-symmetric soliton-like waves is performed.