Dynamics of Benjamin-Ono Solitons in a Two-Layer Ocean with a Shear Flow
Article
Article Title | Dynamics of Benjamin-Ono Solitons in a Two-Layer Ocean with a Shear Flow |
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ERA Journal ID | 213646 |
Article Category | Article |
Authors | Negi, Pawan, Sahoo, Trilochan, Singh, Niharika and Stepanyants, Yury |
Journal Title | Mathematics |
Journal Citation | 11 (15) |
Article Number | 3399 |
Number of Pages | 15 |
Year | 2023 |
Publisher | MDPI AG |
Place of Publication | Switzerland |
ISSN | 2227-7390 |
Digital Object Identifier (DOI) | https://doi.org/10.3390/math11153399 |
Web Address (URL) | https://www.mdpi.com/journal/mathematics |
Abstract | The results of a theoretical study on Benjamin–Ono (BO) soliton evolution are presented in a simple model of a two-layer ocean with a shear flow and viscosity. The upper layer is assumed to move with a constant speed relative to the lower layer with a tangential discontinuity in the flow profile. It is shown that in the long-wave approximation, such a model can be appropriate. If the flow is supercritical, i.e., its speed (U) exceeds the speed of long linear waves (c1), then BO solitons experience “explosive-type” enhancement due to viscosity, such that their amplitudes increase to infinity in a finite time. In the subcritical regime, when U < c_1, BO solitons experience very slow decay due to viscosity. Soliton amplitude decays with time as A ~ t^{1/2} or A ~ t^{1/3}, depending on whether both layers are weakly viscous (the former case) or only the lower layer is viscous (the latter case). Estimates of "explosion time" are presented for real oceanic parameters. |
Keywords | ocean waves; viscous fluid; stratified ocean; explosive instability; soliton; Benjamin–Ono equation |
Contains Sensitive Content | Does not contain sensitive content |
ANZSRC Field of Research 2020 | 490105. Dynamical systems in applications |
Byline Affiliations | Indian Institute of Technology Kharagpur, India |
Indian Institute of Technology Kharagpur, India | |
UniSQ College (Pathways) | |
School of Mathematics, Physics and Computing | |
Nizhny Novgorod State Technical University, Russia |
https://research.usq.edu.au/item/z00zx/dynamics-of-benjamin-ono-solitons-in-a-two-layer-ocean-with-a-shear-flow
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