On the two-layer high-level Green-Naghdi model in a general form Full article
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Journal of Hydrodynamics
ISSN: 1001-6058 |
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| Output data | Year: 2024, Volume: 36, Number: 1, Pages: 78-86 Pages count : 9 DOI: 10.1007/s42241-024-0012-z | ||||
| Tags | High-level Green-Naghdi (HLGN) model, general form, internal waves, deep configuration | ||||
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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 ( 2 h / 1 = , 1 h / 1 = ). However,
for the cases of the deep configuration ( 2 h / 1 = , 1 h 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.
Cite:
Zhao B-b.
, Zhang T-y.
, Wang Z.
, Duan W-y.
, Chesnokov A.
, Shmakova N.
On the two-layer high-level Green-Naghdi model in a general form
Journal of Hydrodynamics. 2024. V.36. N1. P.78-86. DOI: 10.1007/s42241-024-0012-z WOS Scopus РИНЦ OpenAlex
On the two-layer high-level Green-Naghdi model in a general form
Journal of Hydrodynamics. 2024. V.36. N1. P.78-86. DOI: 10.1007/s42241-024-0012-z WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jan 7, 2024 |
| Accepted: | Mar 17, 2024 |
| Published print: | Apr 11, 2024 |
Identifiers:
| Web of science: | WOS:001204694900005 |
| Scopus: | 2-s2.0-85190457056 |
| Elibrary: | 66841795 |
| OpenAlex: | W4394810465 |