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
With the aid of numerical method, both flow field and its accompanied loss mechanism within the rotating cavity are investigated in detail in the 1^(st) part of the two parts paper. For ease of comparison, rotating ca...With the aid of numerical method, both flow field and its accompanied loss mechanism within the rotating cavity are investigated in detail in the 1^(st) part of the two parts paper. For ease of comparison, rotating cavity is further classified as the rotor-stator cavity case and the rotor-rotor cavity case. Results indicate that flow within both kinds of the cavity act as the inviscid flow except that the flow near walls, neighboring the lower G region and in the vicinity of the rotating orifices. In the regions except such inviscid-flow-dominate domains, the theoretical core rotation factor can be safely used to predict the swirl ratio within the cavity. When detailed flow pattern is considered, Ekman-type flow exists near periphery of the surface's boundary layer where viscous effect is non-negligible. However, due to the complex profile of the simulated cavity case, vortices structure is varied within the cavity. By comparison, swirl ratio can be used to predict the magnitude of loss. Due to the relatively evident rotating effects of the rotor-rotor cavity, swirl ratio even increases to 1.4 in the current model, which means that flow is moving faster than the surrounding disc. Further investigation finds that this kind of highly rotating flow is accompanied with serious undesirable pressure loss. Parenthetically, unlike its counterpart, swirl ratio above 1.0 doesn't happen when fluid passes through the rotor-stator cavity. So it is suggested that rotor-rotor flow cavity with the superimposed inward throughflow should be avoided in the engine design or certain measurements should be provided when such structure design is unavoidable. Simulation done in the current paper is meaningful since these dimensional parameters are typical in the design of state-of-art. Relatively lower range of Re_φ and C_w is not considered in the current two parts paper.展开更多
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.
基金the National Natural Science Foundation of China for sponsoring the research described in the current paper(No.51406204)
文摘With the aid of numerical method, both flow field and its accompanied loss mechanism within the rotating cavity are investigated in detail in the 1^(st) part of the two parts paper. For ease of comparison, rotating cavity is further classified as the rotor-stator cavity case and the rotor-rotor cavity case. Results indicate that flow within both kinds of the cavity act as the inviscid flow except that the flow near walls, neighboring the lower G region and in the vicinity of the rotating orifices. In the regions except such inviscid-flow-dominate domains, the theoretical core rotation factor can be safely used to predict the swirl ratio within the cavity. When detailed flow pattern is considered, Ekman-type flow exists near periphery of the surface's boundary layer where viscous effect is non-negligible. However, due to the complex profile of the simulated cavity case, vortices structure is varied within the cavity. By comparison, swirl ratio can be used to predict the magnitude of loss. Due to the relatively evident rotating effects of the rotor-rotor cavity, swirl ratio even increases to 1.4 in the current model, which means that flow is moving faster than the surrounding disc. Further investigation finds that this kind of highly rotating flow is accompanied with serious undesirable pressure loss. Parenthetically, unlike its counterpart, swirl ratio above 1.0 doesn't happen when fluid passes through the rotor-stator cavity. So it is suggested that rotor-rotor flow cavity with the superimposed inward throughflow should be avoided in the engine design or certain measurements should be provided when such structure design is unavoidable. Simulation done in the current paper is meaningful since these dimensional parameters are typical in the design of state-of-art. Relatively lower range of Re_φ and C_w is not considered in the current two parts paper.
