The two-layer fluid system and the continuous density system are based on two typical simplified stratification conditions to support the propagation of the internal solitary waves(ISWs).The aim of this study is to es...The two-layer fluid system and the continuous density system are based on two typical simplified stratification conditions to support the propagation of the internal solitary waves(ISWs).The aim of this study is to establish several extension methods of the classical ISW models across the stratification systems in an attempt to find a simple ISW structure that can propagate more stably,and to determine whether the stable ISW structure in the two typical stratification systems can be expressed in terms of a consistent nonlinear model.For the constructed ISW structures,the propagation stability has been investigated by taking the Euler equations as the evolution equations.The results show that the ISW structure constructed from the Miyata-Choi-Camassa(MCC)model undergoes two stages of instability and the re-stable ISW has a larger available potential energy and a smaller kinetic energy than the initialized condition.This illustrates the limitation of the weakly dispersive assumption in the MCC model.In contrast,the ISW structure constructed from the Dubreil-Jacotin-Long(DJL)model for the two-layer fluid system is generally stable,due to the fact that the Boussinesq approximation introduced in the derivation of the DJL model will be automatically satisfied in this system.The initial condition interpolated from the DJL model with a thin pycnocline thickness can be regarded as an appropriate ISW structure for the two-layer system and is even more stable than that initialized by the MCC model.In addition,the effect of the Boussinesq approximation is also included in the discussion.The approximation can be considered equivalent to a weakly dispersive assumption and should not be ignored for the ISW problem in the continuous density system.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.52231011,52071056)This work was supported by the Liaoning Revitalization Talents Program(XLYC2007109)+1 种基金Dalian Science and Technology Innovation Fund(Grant No.2020JJ25CY012)the Marine S&T Fund of Shandong Province for Pilot National Laboratory for Marine Science and Technology(Qingdao)(Grant No.2021QNLM020003-5).
文摘The two-layer fluid system and the continuous density system are based on two typical simplified stratification conditions to support the propagation of the internal solitary waves(ISWs).The aim of this study is to establish several extension methods of the classical ISW models across the stratification systems in an attempt to find a simple ISW structure that can propagate more stably,and to determine whether the stable ISW structure in the two typical stratification systems can be expressed in terms of a consistent nonlinear model.For the constructed ISW structures,the propagation stability has been investigated by taking the Euler equations as the evolution equations.The results show that the ISW structure constructed from the Miyata-Choi-Camassa(MCC)model undergoes two stages of instability and the re-stable ISW has a larger available potential energy and a smaller kinetic energy than the initialized condition.This illustrates the limitation of the weakly dispersive assumption in the MCC model.In contrast,the ISW structure constructed from the Dubreil-Jacotin-Long(DJL)model for the two-layer fluid system is generally stable,due to the fact that the Boussinesq approximation introduced in the derivation of the DJL model will be automatically satisfied in this system.The initial condition interpolated from the DJL model with a thin pycnocline thickness can be regarded as an appropriate ISW structure for the two-layer system and is even more stable than that initialized by the MCC model.In addition,the effect of the Boussinesq approximation is also included in the discussion.The approximation can be considered equivalent to a weakly dispersive assumption and should not be ignored for the ISW problem in the continuous density system.
