Derivation and rogue waves of the fractional nonlinear Schrödinger equation for the Rossby waves

Geng, Jingxuan; Fu, Lei; Dong, Huanhe; Ren, Yanwei

doi:10.1063/5.0176812

Chaos: An Interdisciplinary Journal of Nonlinear Science

2023

DOI: 10.1063/5.0176812

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Derivation and rogue waves of the fractional nonlinear Schrödinger equation for the Rossby waves

Jingxuan Geng,

Lei Fu,

Huanhe Dong

et al.

Abstract: The Cartesian coordinate system is not sufficient to study wave propagation on the coastline or in the sea where the terrain is extremely complicated, so it is necessary to study it in an unconventional coordinate system, fractals. In this paper, from the governing equations of fluid, the fractional nonlinear Schrödinger equation is derived to describe the evolution of Rossby waves in fractal by using multi-scale analysis and perturbation method. Based on the equation, the rogue-wave solution is obtained by th… Show more

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2024

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Cited by 3 publications

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On the dynamics of nonlinear Rossby solitary waves via the Ostrovsky hierarchy

Zhang,

Yang

et al. 2024

Physics of Fluids

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The impact mechanisms of large-scale atmospheric and ocean dynamics on weather and climate change have long been a focus of attention. In this paper, based on the generalized β-plane approximation with turbulence dissipation and forcing terms, we derived the Ostrovsky equation describing the evolution of Rossby wave amplitudes using multiscale and perturbation expansion methods. This is the first derivation of the Ostrovsky equation from the quasi-geostrophic potential vorticity conservation equation. A detailed analysis was conducted on the evolution of Rossby waves under the influence of multiple physical factors. We investigated the evolution of flow fields and Rossby wave amplitudes under conditions of weak shear in the background flow and discussed the effects of physical factors such as Rossby parameter β0 and turbulence dissipation on the evolution of dipole blocking and Rossby wave amplitudes. The results indicate that an increase in the Rossby parameter slows down the evolution of dipole blocking and amplitudes, while an increase in turbulence dissipation and background flow shear accelerates these evolutions. Additionally, we conducted comparative analyses on the evolution of relative vorticity and perturbed relative vorticity, further enriching the theoretical achievements in atmospheric dynamics.

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On the dynamics of nonlinear Rossby solitary waves via the Ostrovsky hierarchy

Zhang,

Yang

et al. 2024

Physics of Fluids

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Rossby waves with barotropic–baroclinic coherent structures and dynamics for the (2 + 1)-dimensional coupled cylindrical KP equations with variable coefficients

Yin,

Du,

Wang

et al. 2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Starting from the classical quasi-geostrophic potential vorticity equation with equal depth two-layer fluid, the coupled cylindrical Kadomtsev–Petviashvili (KP) equations with variable coefficients for Rossby waves are studied. To be more general, the phase velocity is considered an indefinite integral about time and improves the analysis procedure. So the variable coefficients are obtained and some previous studies are reasonably explained. The cylindrical wave theory is therewith utilized to reduce the coupled cylindrical KP equations with variable coefficients, and based on the modified Hirota bilinear method, the lump solutions and interaction solutions are found. Through numerical simulations, the Rossby lump waves on both sides of the y axis move closer to the center, and their amplitude gradually decreases and tends to flatten with the generalized Rossby parameter growth. In the Rossby waves flow field, the dipole structures propagate to the east and lead to the appearance of the compress phenomenon during barotropic–baroclinic interaction. It is possibly useful for further theoretical research on atmospheric phenomena.

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High-accuracy solution for fractional solitary wave dynamics in finite water depth with linear shear flow, wind, and dissipation effects

Zhou,

2024

Physics of Fluids

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In this paper, a fractional nonlinear Schrödinger equation has been initially derived for capturing the dynamics of gravity waves in finite water depth, accounting for factors such as wind, dissipation, and shear currents. A comprehensive framework is established to enhance the model's representation of gravity wave behavior. We employ a high-order iterative method, specifically the homotopy iterative technique, along with a non-uniform collocation approach integrated into the Haar wavelet method, resulting in a novel computational method characterized by high precision and efficiency. The robustness and reliability of the proposed approach are validated through convergence analysis and comparisons with analytical solutions. Furthermore, the results indicate that the nonlinear and dispersive effects caused by the fractional orders lead to changes in the propagation characteristics of gravity waves. The impacts of the damping coefficient related to wind action and dissipative effects on the temporal evolution of solitary waves are also discussed. The construction of the fractional model holds far-reaching significance for researching the nonlinear propagation of gravity waves in actual ocean water waves. Additionally, an outstanding computational technique for solving fractional nonlinear evolution equations in diverse applications has been developed.

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Derivation and rogue waves of the fractional nonlinear Schrödinger equation for the Rossby waves

Cited by 3 publications

References 42 publications

On the dynamics of nonlinear Rossby solitary waves via the Ostrovsky hierarchy

On the dynamics of nonlinear Rossby solitary waves via the Ostrovsky hierarchy

Rossby waves with barotropic–baroclinic coherent structures and dynamics for the (2 + 1)-dimensional coupled cylindrical KP equations with variable coefficients

High-accuracy solution for fractional solitary wave dynamics in finite water depth with linear shear flow, wind, and dissipation effects

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