Abstract
The traditional high-level Green-Naghdi(HLGN)model,which uses the polynomial as the shape function to approximate the variation of the horizontal-and vertical-velocity components along the vertical direction for each-fluid layer,can accurately describe the large-amplitude internal waves in a two-layer system for the shallow configuration(h2/λ<<1,h,/λ<<1).However,for the cases of the deep confiiguration(h2/λ<<1,h1/λ=O(1)),higher-order polynomial is needed to approximate the variation of the velocity components along the vertical direction for the lower-fluid layer.This,however,introduces additional unknowns,leading to a significant increase in computational time.This paper,for the first time,derives a general form of the HLGN model for a two-layer fluid system,where the general form of the shape function is used during the derivation.After obtaining the general form of the two-layer HLGN equations,corresponding solutions can be obtained by determining the reasonable shape function.Large-amplitude internal solitary waves in a deep configuration are studied by use of two different HLGN models.Comparison of the two HLGN models shows that the polynomial as the shape function for the upper-fluid layer and the production of exponential and polynomial as the shape function for the lower-fluid layer is a good choice.By comparing with Euler's solutions and the laboratory measurements,the accuracy of the two-layer HLGN model is verified.
基金项目
National Natural Science Foundation of China(12202114)
National Natural Science Foundation of China(52261135547)
Fundamental Research Funds for the Central Universities(3072022FSC0101)
China Postdoctoral Science Foundation(2022M710932)
Ph.D.Student Research and Innovation Fund(BCJJ2023103)
High-End Foreign Expert Recruitment Program()
Heilongjiang Touyan Innovation Team Program()
NETL
NSTL
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