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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Main Author: Vladimir I. Kruglov
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:AppliedMath
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Online Access:https://www.mdpi.com/2673-9909/5/1/5
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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.
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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