In this paper, long interfacial waves of finite amplitude in uniform basic flows are considered with the assumption that the aspect ratio between wavelength and water depth is small. A new model is derived using the v...In this paper, long interfacial waves of finite amplitude in uniform basic flows are considered with the assumption that the aspect ratio between wavelength and water depth is small. A new model is derived using the velocities at arbitrary distances from the still water level as the velocity variables instead of the commonly used depth-averaged velocities. This significantly improves the dispersion properties and makes them applicable to a wider range of water depths. Since its derivation requires no assumption on wave amplitude, the model thus can be used to describe waves with arbitrary amplitude.展开更多
This paper is mainly concerned with modeling nonlinear internal waves in the ocean of great depth.The ocean is assumed to be composed of three homogeneous fluid layers of different densities in a stable stratified con...This paper is mainly concerned with modeling nonlinear internal waves in the ocean of great depth.The ocean is assumed to be composed of three homogeneous fluid layers of different densities in a stable stratified configuration.Based on the Ablowitz-Fokas-Musslimani formulation for irrotational flows,strongly nonlinear and weakly nonlinear models are developed for the“shallow-shallow-deep”and“deep-shallow-deep”scenarios.Internal solitary waves are computed using numerical iteration schemes,and their global bifurcation diagrams are obtained by a numerical continuation method and compared for different models.For the“shallow-shallow-deep”case,both mode-1 and mode-2 internal solitary waves can be found,and a pulse broad-ening phenomenon resulting in conjugate flows is observed in the mode-2 branch.While in the“deep-shallow-deep”situation,only mode-2 solitary waves can be obtained.The existence and stability of mode-2 internal solitary waves are confirmed by solving the primitive equations based on the MITgcm model.展开更多
基金Supported by the Knowledge Innovation Programs of the Chinese Academy of Sciences (Nos. KZCX2-YW-201 and KZCX1-YW-12)Natural Science Fund of the Educational Department, Inner Mongolia (No.NJzy08005)the Science Fund for Young Scholars of Inner Mongolia University (No. ND0801)
文摘In this paper, long interfacial waves of finite amplitude in uniform basic flows are considered with the assumption that the aspect ratio between wavelength and water depth is small. A new model is derived using the velocities at arbitrary distances from the still water level as the velocity variables instead of the commonly used depth-averaged velocities. This significantly improves the dispersion properties and makes them applicable to a wider range of water depths. Since its derivation requires no assumption on wave amplitude, the model thus can be used to describe waves with arbitrary amplitude.
基金supported by the National Natural Science Foundation of China(Grant Nos.11911530171,11772341,and 42006016)the Key Program of National Natural Science Foundation of China(Grant Nos.12132018,and 91958206)the Natural Science Foundation of Shandong Province(Grant No.ZR2020QD063).
文摘This paper is mainly concerned with modeling nonlinear internal waves in the ocean of great depth.The ocean is assumed to be composed of three homogeneous fluid layers of different densities in a stable stratified configuration.Based on the Ablowitz-Fokas-Musslimani formulation for irrotational flows,strongly nonlinear and weakly nonlinear models are developed for the“shallow-shallow-deep”and“deep-shallow-deep”scenarios.Internal solitary waves are computed using numerical iteration schemes,and their global bifurcation diagrams are obtained by a numerical continuation method and compared for different models.For the“shallow-shallow-deep”case,both mode-1 and mode-2 internal solitary waves can be found,and a pulse broad-ening phenomenon resulting in conjugate flows is observed in the mode-2 branch.While in the“deep-shallow-deep”situation,only mode-2 solitary waves can be obtained.The existence and stability of mode-2 internal solitary waves are confirmed by solving the primitive equations based on the MITgcm model.
