scholarly journals Faster and Slower Soliton Phase Shift: Oceanic Waves Affected by Earth Rotation

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3223
Author(s):  
Mostafa M. A. Khater ◽  
Aliaa Mahfooz Alabdali
Keyword(s):  
Phase Shift ◽  
Gravity Waves ◽  
Earth Rotation ◽  
Kdv Equation ◽  
Rotational Symmetry ◽  
Computational Scheme ◽  
New Technique ◽  
Kdv Equations ◽  
Adomian Decomposition ◽  
Inertia Gravity Waves

This research paper investigates the accuracy of a novel computational scheme (Khater II method) by applying this new technique to the fractional nonlinear Ostrovsky (FNO) equation. The accuracy of the obtained solutions was verified by employing the Adomian decomposition (AD) and El Kalla (EK) methods. The AD and EK methods are considered as two of the most accurate semi-analytical schemes. The FNO model is a modified version of the well-known Korteweg–de Vries (KdV) equation that considers the effects of rotational symmetry in space. However, in the KdV model, solutions to the KdV equations substitute this effect with radiating inertia gravity waves, and thus this impact is ignored. The analytical, semi-analytical, and accuracy between solutions are represented in some distinct plots. Additionally, the paper’s novelty and its contributions are demonstrated by comparing the obtained solutions with previously published results.

Diverse solitary and Jacobian solutions in a continually laminated fluid with respect to shear flows through the Ostrovsky equation

2021 ◽  
pp. 2150220
Author(s):  
Mostafa M. A. Khater
Keyword(s):  
Gravity Waves ◽  
Kdv Equation ◽  
Computational Schemes ◽  
Solitary Solutions ◽  
Dominant Feature ◽  
Contour Plots ◽  
Ostrovsky Equation ◽  
Lump Wave ◽  
Published Research ◽  
Inertia Gravity Waves

In this paper, the generalized Jacobi elliptical functional (JEF) and modified Khater (MK) methods are employed to find the soliton, breather, kink, periodic kink, and lump wave solutions of the Ostrovsky equation. This model is considered as a mathematical modification model of the Korteweg-de Vries (KdV) equation with respect to the effects of background rotation. The solitary solutions of the well-known mathematical model (KdV equation) usually decay and are replaced by radiating inertia gravity waves. The obtained solitary solutions emerge the localized wave packet as a persistent and dominant feature. Many distinct solutions are obtained through the employed computational schemes. Moreover, some solutions are sketched in 2D, 3D, and contour plots. The effective and powerful of the two used computational schemes are tested. Furthermore, the accuracy of the obtained solutions is examined through a comparison between them and that had been obtained in previously published research.

scholarly journals On Semi-Analytical Solutions for Linearized Dispersive KdV Equations

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1769
Author(s):  
Appanah Rao Appadu ◽  
Abey Sherif Kelil
Keyword(s):  
Decomposition Method ◽  
Kdv Equation ◽  
Bernstein Polynomials ◽  
Adomian Decomposition Method ◽  
Test Problems ◽  
Transform Method ◽  
Kdv Equations ◽  
Adomian Decomposition ◽  
Adomian Method ◽  
Relative Errors

The most well-known equations both in the theory of nonlinearity and dispersion, KdV equations, have received tremendous attention over the years and have been used as model equations for the advancement of the theory of solitons. In this paper, some semi-analytic methods are applied to solve linearized dispersive KdV equations with homogeneous and inhomogeneous source terms. These methods are the Laplace-Adomian decomposition method (LADM), Homotopy perturbation method (HPM), Bernstein-Laplace-Adomian Method (BALDM), and Reduced Differential Transform Method (RDTM). Three numerical experiments are considered. As the main contribution, we proposed a new scheme, known as BALDM, which involves Bernstein polynomials, Laplace transform and Adomian decomposition method to solve inhomogeneous linearized dispersive KdV equations. Besides, some modifications of HPM are also considered to solve certain inhomogeneous KdV equations by first constructing a newly modified homotopy on the source term and secondly by modifying Laplace’s transform with HPM to build HPTM. Both modifications of HPM numerically confirm the efficiency and validity of the methods for some test problems of dispersive KdV-like equations. We also applied LADM and RDTM to both homogeneous as well as inhomogeneous KdV equations to compare the obtained results and extended to higher dimensions. As a result, RDTM is applied to a 3D-dispersive KdV equation. The proposed iterative schemes determined the approximate solution without any discretization, linearization, or restrictive assumptions. The performance of the four methods is gauged over short and long propagation times and we compute absolute and relative errors at a given time for some spatial nodes.

Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid

2020 ◽  
Vol 35 (6) ◽  
pp. 355-366
Author(s):  
Vladimir V. Shashkin ◽  
Gordey S. Goyman
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Shallow Water Equations ◽  
Time Integration ◽  
Standard Test ◽  
Integration Scheme ◽  
Test Problems ◽  
Cubed Sphere ◽  
Lagrangian Scheme ◽  
Inertia Gravity Waves

AbstractThis paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models. The developed scheme is as good as the conventional semi-implicit semi-Lagrangian scheme in accuracy of slowly varying flow component reproduction and significantly better in the reproduction of the fast inertia-gravity waves. The accuracy of inertia-gravity waves reproduction is close to that of the explicit time-integration scheme. The computational efficiency of the proposed exponential semi-Lagrangian scheme is somewhat lower than the efficiency of semi-implicit semi-Lagrangian scheme, but significantly higher than the efficiency of explicit, semi-implicit, and exponential Eulerian schemes.

scholarly journals Solitons in the Close Binary Systems

1998 ◽  
Vol 11 (1) ◽  
pp. 398-398
Author(s):  
Kenji Tanabe
Keyword(s):  
Gravity Waves ◽  
Binary Systems ◽  
Kdv Equation ◽  
Frame Of Reference ◽  
Close Binary ◽  
Flare Activity ◽  
Lagrangian Point ◽  
Nls Equation ◽  
Close Binary Systems ◽  
The Earth

Propagation of the surface waves of the lobe-filing components of close binary systems is investigated theoretically. Such waves are considered to be analogous to the gravity waves of water on the earth. As a result, the equations of the surface wave in the rotating frame of reference are reduced to the so-called Kortewegde Vries (KdV) equation and non-linear Schroedinger (NLS) equation according to its ”depth”. Each of these equations is known to have the solution of soliton. When this soliton is sent to the other component of the binary system through the Lagrangian point, it can give rise to the flare activity observed in some kinds of close binary systems.

Spontaneous-adjustment emission of inertia-gravity waves by unsteady vortical motion in the hurricane core

2010 ◽  
Vol 136 (647) ◽  
pp. 537-548 ◽  
Author(s):  
E. A. Hendricks ◽  
W. H. Schubert ◽  
S. R. Fulton ◽  
B. D. McNoldy
Keyword(s):  
Gravity Waves ◽  
Vortical Motion ◽  
Inertia Gravity Waves

Nonholonomic deformation of coupled and supersymmetric KdV equations and Euler–Poincaré–Suslov method

2015 ◽  
Vol 27 (04) ◽  
pp. 1550011 ◽  
Author(s):  
Partha Guha
Keyword(s):  
Kdv Equation ◽  
Infinite Dimensional ◽  
Kdv Equations ◽  
Finite Dimensional ◽  
Euler Top ◽  
Two Component ◽  
Finite Dimensional Case ◽  
Coupled Kdv Equations ◽  
The Right ◽  
Supersymmetric Kdv Equation

Recently, Kupershmidt [38] presented a Lie algebraic derivation of a new sixth-order wave equation, which was proposed by Karasu-Kalkani et al. [31]. In this paper, we demonstrate that Kupershmidt's method can be interpreted as an infinite-dimensional analogue of the Euler–Poincaré–Suslov (EPS) formulation. In a finite-dimensional case, we modify Kupershmidt's deformation of the Euler top equation to obtain the standard EPS construction on SO(3). We extend Kupershmidt's infinite-dimensional construction to construct a nonholonomic deformation of a wide class of coupled KdV equations, where all these equations follow from the Euler–Poincaré–Suslov flows of the right invariant L2 metric on the semidirect product group [Formula: see text], where Diff (S1) is the group of orientation preserving diffeomorphisms on a circle. We generalize our construction to the two-component Camassa–Holm equation. We also give a derivation of a nonholonomic deformation of the N = 1 supersymmetric KdV equation, dubbed as sKdV6 equation and this method can be interpreted as an infinite-dimensional supersymmetric analogue of the Euler–Poincaré–Suslov (EPS) method.

scholarly journals Intraseasonal Modulation of the Surface Cooling in the Gulf of Guinea

2013 ◽  
Vol 43 (2) ◽  
pp. 382-401 ◽  
Author(s):  
Julien Jouanno ◽  
Frédéric Marin ◽  
Yves du Penhoat ◽  
Jean-Marc Molines
Keyword(s):  
Mixed Layer ◽  
Gravity Waves ◽  
Heat Budget ◽  
Vertical Shear ◽  
Upper Ocean ◽  
Equatorial Waves ◽  
Gulf Of Guinea ◽  
The Core ◽  
Mixed Layer Heat Budget ◽  
Inertia Gravity Waves

Abstract A regional numerical model of the tropical Atlantic Ocean and observations are analyzed to investigate the intraseasonal fluctuations of the sea surface temperature at the equator in the Gulf of Guinea. Results indicate that the seasonal cooling in this region is significantly shaped by short-duration cooling events caused by wind-forced equatorial waves: mixed Rossby–gravity waves within the 12–20-day period band, inertia–gravity waves with periods below 11 days, and equatorially trapped Kelvin waves with periods between 25 and 40 days. In these different ranges of frequencies, it is shown that the wave-induced horizontal oscillations of the northern front of the mean cold tongue dominate the variations of mixed layer temperature near the equator. But the model mixed layer heat budget also shows that the equatorial waves make a significant contribution to the mixed layer heat budget through modulation of the turbulent cooling, especially above the core of the Equatorial Undercurrent (EUC). The turbulent cooling variability is found to be mainly controlled by the intraseasonal modulation of the vertical shear in the upper ocean. This mechanism is maximum during periods of seasonal cooling, especially in boreal summer, when the surface South Equatorial Current is strongest and between 2°S and the equator, where the presence of the EUC provides a background vertical shear in the upper ocean. It applies for the three types of intraseasonal waves. Inertia–gravity waves also modulate the turbulent heat flux at the equator through vertical displacement of the core of the EUC in response to equatorial divergence and convergence.

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