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Traveling Waves, Impulses and Laminar-turbulent Transitions in Fluid Dynamics Equations

Submission Deadline: 01 December 2025 (closed) View: 902 Submit to Special Issue

Guest Editors

Prof. Dr. Nikolai A. Magnitskii

Email: nikmagn@gmail.com

Affiliation:  Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia 

Homepage:

Research Interests: differential and integral equations; nonlinear dynamical systems; theory of control; theory of chaos; artificial neural networks; mathematical modeling;  theory of ether 


Dr. Nikolay M. Evstigneev 

Email: evstigneevnm@gmail.com

Affiliation:  Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia

Homepage:  

Research Interests: differential equations; nonlinear dynamical systems, theory of chaos, fluid dynamics


Summary

The issue is supposed to publish articles devoted to both theoretical and numerical aspects of nonlinear, bifurcation and chaotic analysis of partial differential equations of fluid dynamics. The issue invites for publication original and review articles on the theory of nonlinear dynamics and space-time chaos in fluid  dynamics equations and the application of numerical methods for the analysis of nonlinear problems in fluid dynamics. Papers on control and numerical modeling in nonlinear systems of fluid dynamics are also welcome. The deadline for submitting articles to the journal is May 01, 2025.


Keywords

Nonlinear differential equations of fluid dynamics, bifurcations, chaotic dynamics, laminar-turbulent transitions, irregular attractors

Published Papers


  • Open Access

    REVIEW

    Solitons-Like Coherent Structures in Shear Flows

    Ning Hu, Cunbiao Lee
    FDMP-Fluid Dynamics & Materials Processing, Vol.21, No.10, pp. 2389-2417, 2025, DOI:10.32604/fdmp.2025.067248
    (This article belongs to the Special Issue: Traveling Waves, Impulses and Laminar-turbulent Transitions in Fluid Dynamics Equations)
    Abstract The formation, evolution, and dynamics of flow structures in wall-bounded turbulence have long been central themes in fluid-mechanics research. Over the past three decades, Soliton-like Coherent Structures (SCSs) have emerged as a ubiquitous and unifying feature across a wide range of shear flows, including K-type, O-type, N-type, and bypass transitional boundary layers, as well as fully developed turbulent boundary layers, mixing layers, and pipe flows. This paper presents a systematic review of the fundamental properties of SCSs and highlights their fundamental role in multiple transition scenarios. The analysis further explores the connection between SCSs and… More >

    Graphic Abstract

    Solitons-Like Coherent Structures in Shear Flows

  • Open Access

    ARTICLE

    Wave Propagation and Chaotic Behavior in Conservative and Dissipative Sawada–Kotera Models

    Nikolai A. Magnitskii
    FDMP-Fluid Dynamics & Materials Processing, Vol.21, No.7, pp. 1529-1544, 2025, DOI:10.32604/fdmp.2025.067021
    (This article belongs to the Special Issue: Traveling Waves, Impulses and Laminar-turbulent Transitions in Fluid Dynamics Equations)
    Abstract This paper presents both analytical and numerical studies of the conservative Sawada–Kotera equation and its dissipative generalization, equations known for their soliton solutions and rich chaotic dynamics. These models offer valuable insights into nonlinear wave propagation, with applications in fluid dynamics and materials science, including systems such as liquid crystals and ferrofluids. It is shown that the conservative Sawada–Kotera equation supports traveling wave solutions corresponding to elliptic limit cycles, as well as two- and three-dimensional invariant tori surrounding these cycles in the associated ordinary differential equation (ODE) system. For the dissipative generalized Sawada–Kotera equation, chaotic More >

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