On the two-layer high-level Green-Naghdi model in a general form

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(h_(2)/λ■1,h_(1)/λ■1).However,for the cases of the deep configuration(h_(2)/λ■1,h_(1)/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.