Generic Equations for Long Gravity Waves in Incompressible Fluid with Finite Amplitude
We present the derivation of generic equations describing the long gravity waves in incompressible fluid with a decaying effect. We show that in this theory, the only restriction to the surface deviation is connected to the stability condition for the waves. Derivation of these generic equations is...
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MDPI AG
2025-01-01
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| author | Vladimir I. Kruglov |
| author_facet | Vladimir I. Kruglov |
| author_sort | Vladimir I. Kruglov |
| collection | DOAJ |
| description | We present the derivation of generic equations describing the long gravity waves in incompressible fluid with a decaying effect. We show that in this theory, the only restriction to the surface deviation is connected to the stability condition for the waves. Derivation of these generic equations is based on Euler equations for inviscid incompressible fluid and the definition of dynamic pressure which leads to a correct dispersion equation for gravity waves. These derived generic equations for the velocity of fluid and the surface deviation describe the propagation of long gravity waves in incompressible fluid with finite amplitude. We also find the necessary and sufficient conditions for generic equations with dissipation of energy or a decaying effect. The developed approach can significantly improve the accuracy of theory for long gravity waves in incompressible fluid. We also find the quasi-periodic and solitary wave solutions for generic equations with a decaying effect. |
| format | Article |
| id | doaj-art-9d168cc702224da4813dd8025f7d54ea |
| institution | DOAJ |
| issn | 2673-9909 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj-art-9d168cc702224da4813dd8025f7d54ea2025-08-20T02:42:45ZengMDPI AGAppliedMath2673-99092025-01-0151510.3390/appliedmath5010005Generic Equations for Long Gravity Waves in Incompressible Fluid with Finite AmplitudeVladimir I. Kruglov0Centre for Engineering Quantum Systems, School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, AustraliaWe present the derivation of generic equations describing the long gravity waves in incompressible fluid with a decaying effect. We show that in this theory, the only restriction to the surface deviation is connected to the stability condition for the waves. Derivation of these generic equations is based on Euler equations for inviscid incompressible fluid and the definition of dynamic pressure which leads to a correct dispersion equation for gravity waves. These derived generic equations for the velocity of fluid and the surface deviation describe the propagation of long gravity waves in incompressible fluid with finite amplitude. We also find the necessary and sufficient conditions for generic equations with dissipation of energy or a decaying effect. The developed approach can significantly improve the accuracy of theory for long gravity waves in incompressible fluid. We also find the quasi-periodic and solitary wave solutions for generic equations with a decaying effect.https://www.mdpi.com/2673-9909/5/1/5long gravity wavesquasi-periodic and solitary wavesdecaying effect |
| spellingShingle | Vladimir I. Kruglov Generic Equations for Long Gravity Waves in Incompressible Fluid with Finite Amplitude AppliedMath long gravity waves quasi-periodic and solitary waves decaying effect |
| title | Generic Equations for Long Gravity Waves in Incompressible Fluid with Finite Amplitude |
| title_full | Generic Equations for Long Gravity Waves in Incompressible Fluid with Finite Amplitude |
| title_fullStr | Generic Equations for Long Gravity Waves in Incompressible Fluid with Finite Amplitude |
| title_full_unstemmed | Generic Equations for Long Gravity Waves in Incompressible Fluid with Finite Amplitude |
| title_short | Generic Equations for Long Gravity Waves in Incompressible Fluid with Finite Amplitude |
| title_sort | generic equations for long gravity waves in incompressible fluid with finite amplitude |
| topic | long gravity waves quasi-periodic and solitary waves decaying effect |
| url | https://www.mdpi.com/2673-9909/5/1/5 |
| work_keys_str_mv | AT vladimirikruglov genericequationsforlonggravitywavesinincompressiblefluidwithfiniteamplitude |