Impact of the climate variations in nonlinear topographies on some vast oceans

Mustafah Abou-Dina; Amel Alaidrous; Mustafah Abou-Dina; Amel Alaidrous

doi:10.3934/math.2024873

AIMS Mathematics

2024, Volume 9, Issue 7: 17932-17954. doi: 10.3934/math.2024873

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Impact of the climate variations in nonlinear topographies on some vast oceans

Mustafah Abou-Dina ¹,
Amel Alaidrous ^{2
,
,}

1.
Department of Mathematics, Faculty of Science, Cairo University, Giza 12631, Egypt
2.
Department of Mathematics, Faculty of Sciences, Umm Al-Qura University, P.O. Box 4454, Makkah21955, Saudi Arabia

Received: 16 March 2024 Revised: 26 April 2024 Accepted: 29 April 2024 Published: 27 May 2024
MSC : 31B10, 34G20, 37N10, 37N30

We study the non-linear transient gravity waves inside vast oceans with general topographies. These waves are generated following climate variations simulated by an external pressure acting on the ocean's surface. We use a perturbation method for the study. The present approach necessitates a mild slope of the topography. Quadratic solutions are obtained from nonlinear theory technique and illustrated. The reliability of the nonlinear (quadratic) solution is examined by a comparison between the trace of the bottom and the lowest streamline. The proposed model is shown to be strongly efficient in simulating the considered phenomenon, especially if the slope of the topography is not sharp. The features of the phenomenon under consideration are revealed and discussed mathematically and physically according to the nonlinear theory technique.
- climate variations,
- potential flow,
- nonlinear gravity waves,
- linear theory,
- nonlinear theory,
- irregular topography,
- integral transform
Citation: Mustafah Abou-Dina, Amel Alaidrous. Impact of the climate variations in nonlinear topographies on some vast oceans[J]. AIMS Mathematics, 2024, 9(7): 17932-17954. doi: 10.3934/math.2024873

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Abstract

We study the non-linear transient gravity waves inside vast oceans with general topographies. These waves are generated following climate variations simulated by an external pressure acting on the ocean's surface. We use a perturbation method for the study. The present approach necessitates a mild slope of the topography. Quadratic solutions are obtained from nonlinear theory technique and illustrated. The reliability of the nonlinear (quadratic) solution is examined by a comparison between the trace of the bottom and the lowest streamline. The proposed model is shown to be strongly efficient in simulating the considered phenomenon, especially if the slope of the topography is not sharp. The features of the phenomenon under consideration are revealed and discussed mathematically and physically according to the nonlinear theory technique.

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