Numerical Simulations of Nonlinear Waves

A special issue of Fluids (ISSN 2311-5521). This special issue belongs to the section "Mathematical and Computational Fluid Mechanics".

Deadline for manuscript submissions: closed (15 May 2023) | Viewed by 2810

Special Issue Editor


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Guest Editor
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Interests: wave turbulence theory; internal waves in the ocean; Fermi–Pasta–Ulam–Tsingou chains; nonlinear waves
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Special Issue Information

Dear Colleagues,

Nonlinear waves are widely present in both nature and in artificial systems. Examples of such waves are surface gravity waves, surface capillary waves, internal waves in the ocean and atmosphere, Rossby waves in the ocean, and plasma waves. The most famaous example of a model system for such waves is the celebrated Fermi–Pasta–Ulam-–Tsingou chain introduced in the fifties in Los Alamos Lab to study the heat propagation in crystals.

The first numerical simulation of nonlinear waves was the numerical experiments conducted by Fermi, Pasta, Ulam, and Tsingou on their chain in Los Alamos. Numerical experiments of nonlinear waves are carried out ever since. We went a long way since then, with multiples CPUs, multiple cores, GPUs, and even quantum computers. 

In modern times, numerical experiments are even seen as a legitimate replacement for real-life experiments.

This Special Issue will provide an opportunity to share modern cutting-edge research on modelling nonlinear waves on modern computers to gain insights into the nonlinear wave propagation and interactions.

The deadline for submission is 15 May 2023.

Prof. Dr. Yuri Lvov
Guest Editor

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Keywords

  • nonlinear waves
  • surface gravity waves
  • surface capillary waves
  • internal waves in the ocean
  • internal waves in the atmosphere
  • Rossby waves in the ocean
  • plasma waves
  • numerical simulation
  • numerical experiments

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Published Papers (2 papers)

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Research

15 pages, 4712 KiB  
Article
Numerical Study on Collisions of Solitons of Surface Waves in Finite Water Depth
by Bo Liao, Guohai Dong, Yuxiang Ma and Xiaozhou Ma
Fluids 2023, 8(4), 125; https://doi.org/10.3390/fluids8040125 - 3 Apr 2023
Cited by 1 | Viewed by 1292
Abstract
Head-on collisions between two solitary waves in the framework of the nonlinear Schrödinger (NLS) equation were investigated using the Fourier spectral method. When solitary waves undergo collision, the peak value of surface elevation (hereafter referred to as ζmax) exhibits fluctuations with [...] Read more.
Head-on collisions between two solitary waves in the framework of the nonlinear Schrödinger (NLS) equation were investigated using the Fourier spectral method. When solitary waves undergo collision, the peak value of surface elevation (hereafter referred to as ζmax) exhibits fluctuations with increasing relative water depths k0h (where k0 is the wave number and h is the water depth). ζmax is approximately equal to the sum of the peak values of the two solitary waves with smaller wave steepness ε0 (ε0 = k0a0, a0 is the free background amplitude parameter), and it exhibits fluctuations for ε0 > 0.10. Similar results have been observed in the study of head-on collisions for four solitary waves. These results show that the water depth and wave steepness play important roles in the collision of solitary waves, and the effects of the interactions of intense wave groups are important in studies of the mechanisms and manifestations of freak oceanic waves. Full article
(This article belongs to the Special Issue Numerical Simulations of Nonlinear Waves)
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11 pages, 1258 KiB  
Article
Time-Dependent Numerical Modelling of Acoustic Cavitation in Liquid Metal Driven by Electromagnetic Induction
by Georgi Djambazov
Fluids 2023, 8(3), 79; https://doi.org/10.3390/fluids8030079 - 22 Feb 2023
Viewed by 1110
Abstract
The numerically simulated method of using electromagnetic field from an alternating current is a patented method to create in liquid metal, under the conditions of resonance, acoustic waves of sufficient strength to cause cavitation and implosion of gas bubbles, leading to beneficial degassing [...] Read more.
The numerically simulated method of using electromagnetic field from an alternating current is a patented method to create in liquid metal, under the conditions of resonance, acoustic waves of sufficient strength to cause cavitation and implosion of gas bubbles, leading to beneficial degassing and grain refinement. The modelling stages of electromagnetics are described below along with acoustics in liquids, bubble dynamics, and their interactions. Sample results are presented for a cylindrical container with liquid aluminium surrounded by an induction coil. The possibility of establishing acoustic resonance and sustaining the bubble oscillation at a useful level is demonstrated. Limitations of the time-dependent approach to this multi-physics modelling problem are also discussed. Full article
(This article belongs to the Special Issue Numerical Simulations of Nonlinear Waves)
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