引入强分层近似对含密度跃层情况下的大幅内孤立波计算误差研究

At present,studies on large-amplitude internal solitary waves mostly adopt strong stratification models,such as the twoand three-layer Miyata–Choi–Camassa(MCC)internal wave models,which omit the pycnocline or treat it as another fluid layer with a constant density.Because the pycnocline exists in real oceans and cannot be omitted sometimes,the computational error of a large-amplitude internal solitary wave within the pycnocline introduced by the strong stratification approximation is unclear.In this study,the two-and three-layer MCC internal wave models are used to calculate the wave profile and wave speed of large-amplitude internal solitary waves.By comparing these results with the results provided by the Dubreil–Jacotin–Long(DJL)equation,which accurately describes large-amplitude internal solitary waves in a continuous density stratification,the computational errors of large-amplitude internal solitary waves at different pycnocline depths introduced by the strong stratification approximation are assessed.Although the pycnocline thicknesses are relatively large(accounting for 8%–10%of the total water depth),the error is much smaller under the three-layer approximation than under the two-layer approximation.

Discussion on the extended form of internal solitary wave models between two typical stratification systems

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.