KOPP M. Generation of nonlinear structures in hydrodynamic media under the influence of external fields

Українська версія

Thesis for the degree of Doctor of Science (DSc)

State registration number

0526U000034

Thesis Registration Form

0526U000034.pdf

Applicant for

Mykhailo Y. KOPP

Specialization

01.04.02 - Теоретична фізика

Date of defense

07-04-2026

Specialized Academic Board

Д 64.845.02

National Science Center "Kharkiv Institute of Physics and Technology"

Essay

Kopp M.I. Generation of nonlinear structures in hydrodynamic media under the influence of external fields. – A qualification scientific work in manuscript form. Dissertation for the degree of Doctor of Physical and Mathematical Sciences in the specialty 01.04.02 “Theoretical Physics” (Natural Sciences, E5 – Physics and Astronomy (0533)). – Institute for Single Crystals of the National Academy of Sciences of Ukraine, Kharkiv, 2025. The dissertation develops a nonlinear self-consistent theory of vortex and magnetic dynamos within a dynamic approach, wherein small-scale turbulence is generated as a result of parametric excitation by an external small-scale force. The advantage of the dynamic approach over the statistical one lies in the simpler construction of a self-consistent nonlinear dynamo theory based on the asymptotic method of multiscale expansions. Closed-form equations for nonlinear vortex and magnetic dynamos are obtained for rotating, stratified, viscous, and nanofluid media. At the linear stage, the generation of large-scale vortex and magnetic structures occurs due to instabilities of the α-effect type. At the nonlinear stage of large-scale instability, stationary localized structures are obtained in the form of nonlinear waves, kinks, and spiral kinks. Within a modified Boussinesq model, the influence of inhomogeneous rotation and external magnetic fields (both axial and helical) on the threshold and convective instability in thin layers of hydrodynamic media is studied for the first time. It is shown that a negative inhomogeneous rotation profile lowers the threshold for magnetic convection, i.e., it has a destabilizing effect. A positive profile of inhomogeneous azimuthal magnetic field also exhibits a destabilizing effect. Six- and eight-dimensional dynamical systems are constructed to reproduce the chaotic evolution of the magnetic field and the formation of strange attractors in inhomogeneously rotating media. Thermomagnetic (TM) effects contributing to the self-generation of magnetic fields in such environments are analyzed. It is shown that TM instability arises in the presence of collinear gradients of temperature and specific thermoelectromotive force (thermo-e.m.f.). Taking TM effects into account lowers the threshold for the development of convective instability for any rotation profile, thus also having a destabilizing impact. TM dynamo models are proposed and their chaotic behavior is examined. A nonlinear theory of TM instability is developed for a temperature-stratified thin layer of electron fluid (plasma). Estimates of induced magnetic fields may be applicable to neutron stars in the early stages of their evolution. It is established that in strongly magnetized, inhomogeneous plasma with collinear density and temperature gradients, TM instability can develop even under short-wavelength perturbations. It is demonstrated that modulation of gravity, temperature, external magnetic field, and angular rotation speed enables control over the intensity of heat and mass transfer. The theory of bio-thermal convection in nanofluids containing gyrotactic microorganisms is developed, accounting for Brownian and thermophoretic diffusion. It is shown that increasing the concentration of microorganisms enhances magnetic convection, while the spherical shape of the cells promotes the development of thermal instability. Key words: multiscale asymptotic expansions, small-scale turbulence, Coriolis force, α-effect, nonlinear waves, kinks, chaotic structures, helical magnetic field, magnetorotational instability, Rayleigh-Benard convection, weakly nonlinear theory, thermomagnetic instability, chaotic behavior, biothermal convection, fully ionized plasma.

Official opponents

Bohdan I. Lev
Anatolii A. Turkin
Dmytro O. Kharchenko

Research papers

1. M.I. Kopp, A.V. Tur, V.V. Yanovsky. The Large scale instability in rotating fluid with small scale force, Open Journal of Fluid Dynamics, 2015, v.5, p. 128-138. arXiv:1504.06953v1 [physics.flu-dyn].

2. M.I. Kopp, A.V. Tur, V.V. Yanovsky. Nonlinear Vortex Structures in Obliquely Rotating Fluid, Open Journal of Fluid Dynamics, 2015, v.5, p.311-321.

3. Яновський В.В., Тур А.В., Копп М.Й. Квазідвовимірні великомасштабні вихрові та магнітні структури в магнітній гідродинаміці. Проблеми теоретичної фізики. Наукові праці. Випуск 4. Харків: ХНУ імені В.М. Каразіна, 2020, 412-506 с.

4. M.I. Kopp, A.V. Tur, V.V. Yanovsky. Nonlinear Dynamo in a Rotating Electrically Conducting Fluid, East European Journal of Physics, 2017, v.4(1), p. 4-27. (SJR квартиль Q4).

5. M.I. Kopp, A.V. Tur, V.V. Yanovsky. Instabilities in the non-uniformly rotating medium with temperature stratification in the external uniform magnetic field, 2019, East European Journal of Physics, v.1, p. 4-33. (SJR квартиль Q4).

6. M.I. Kopp, A.V. Tur, K.N. Kulik, V.V. Yanovsky. Nonlinear dynamo in obliquely rotating stratified electroconductive fluid in a uniform magnetic field, East European Journal of Physics, 2020, v.1, p. 5-36. arXiv:1807.01986v1 [physics.flu-dyn]. (SJR квартиль Q4).

7. M.I. Kopp, A.V. Tur, V.V. Yanovsky. Weakly nonlinear magnetic convection in a nonuniformly rotating electrically conductive medium under the action of modulation of external fields, East European Journal of Physics, 2020, v.2, p. 5-37. arXiv:1911.05368v1 [physics.plasm-ph]. (SJR квартиль Q4).

8. M.I. Kopp, A.V. Tur, V.V. Yanovsky. Magnetic convection in a nonuniformly rotating electrically conductive medium in an external spiral magnetic field, Fluid Dynamics Research, 2021, v. 53, 015509. arXiv:1905.05472v1 [physics.plasm-ph]. (SJR квартиль Q2).

9. M.I. Kopp, K.N. Kulik, A.V. Tur, V.V. Yanovsky. Generation of magnetic fields by thermomagnetic effects in a nonuniformly rotating layer of an electrically conductive fluid, Journal of Physical Studies, 2021, v. 25, No. 2, 2401. arXiv:2104.11068v1 [physics.flu-dyn]. (SJR квартиль Q4).

10. M.I. Kopp, A.V. Tur, V.V. Yanovsky. Nonlinear Vortex Structures Driven by Small-Scale Nonhelical Forces in Obliquely Rotating Stratified Fluids, Ukrainian Journal of Physics, 2021, v. 66, No. 6, p. 478-488. arXiv:1706.00223 [physics.flu-dyn]. (SJR квартиль Q3).

11. M.I. Kopp, A.V. Tur, V.V. Yanovsky. Hydrodynamic α-effect in a rotating stratified moist atmosphere driven by small-scale nonhelical force, Geophysical and Astrophysical Fluid Dynamics, 2021, v. 115, No. 5-6, p. 551-576. (SJR квартиль Q2).

12. M.I. Kopp, A.V. Tur, V.V. Yanovsky. Vortex Dynamo in an Obliquelly Rotating Sratified Nanofluid by Small-Scale Non-Helical Forces, East European Journal of Physics, 2021, v.2, p.51-72. (SJR квартиль Q4).

13. M.I. Kopp, A.V. Tur, V.V. Yanovsky. Spontaneous generation of magnetic fields in thin layers of stratified plasma, Physics of Plasmas, 2022, v. 29, 042115. (SJR квартиль Q1).

14. Michael Kopp, Andrii Kopp. A New 6D Chaotic Generator: Computer Modelling and Circuit Design, International Journal of Engineering and Technology Innovation, 2022, v. 12, no. 4, p. 288-307. (SJR квартиль Q3).

15. M.I. Kopp, V.V. Yanovsky. Influence of the Hall current on the convective and magnetorotational instability in a thin layer of an electrically conductive nanofluid, Physics of Fluids, 2022, v. 34, 064107. (SJR квартиль Q1).

16. M.I. Kopp, V.V. Yanovsky. Thermal convection in a rotating porous medium layer saturated by a nanofluid under a helical magnetic field, Journal of Applied Physics, 2022, v. 132, 084302. (SJR квартиль Q2).

17. M.I. Kopp, A.V. Tur, V.V. Yanovsky. Thermomagnetic instabilities in a nonuniformly rotating electrically conductive fluid, Journal of Physical Studies, 2022, v. 26, No. 4, 4401. (SJR квартиль Q4).

18. M.I. Kopp, V.V. Yanovsky, U. S. Mahabaleshwar. A Bio-Thermal Convection in a Porous Medium Saturated by Nanofluid Containing Gyrotactic Microorganisms Under an External Magnetic Field, East European Journal of Physics, 2022, v.4, p.23-47. (SJR квартиль Q4).

19. M.I. Kopp, V.V. Yanovsky. Darcy-Brinkman bio-thermal convection in a porous rotating layer saturated by Newtonian fluid containing gyrotactic microorganisms, Ukrainian Journal of Physics, 2023, v. 68, No. 1, p. 30-37. (SJR квартиль Q3).

20. M.I. Kopp, A.V. Tur, V.V. Yanovsky. Chaotic Dynamics of Magnetic Fields Generated by Thermomagnetic Instability in a Nonuniformly Rotating Electrically Conductive Fluid, Journal of Physical Studies, 2023, v. 27, No. 2, 2403. (SJR квартиль Q3).

21. M. Kopp, A. Kopp. A New 8D Lorenz-like Hyperchaotic System: Computer Modelling, Circuit Design and Arduino Uno Board Implementation, Journal of Telecommunication, Electronic and Computer Engineering, 2023, v. 15, No. 2, p. 37-46.

22. M.I. Kopp, V.V. Yanovsky. Vortex dynamo in rotating media, East European Journal of Physics, 2023, v.2, p. 7-50. (SJR квартиль Q4).

23. M.I. Kopp, V.V. Yanovsky. Investigating the effect of gravity modulation on weakly nonlinear magnetoconvection in a nonuniformly rotating nanofluid layer, East European Journal of Physics, 2023, v.3, p. 207-222. (SJR квартиль Q4).

24. M.I. Kopp, V.V. Yanovsky. Effect of gravity modulation on weakly nonlinear bio-thermal convection in a porous medium layer. Journal of Applied Physics, 2023, v. 134, 104702. (SJR квартиль Q2).

25. M.I. Kopp, V.V. Yanovsky. Gravity modulation and its impact on weakly nonlinear bio-thermal convection in a porous layer under rotation: a Ginzburg-Landau model approach, Journal of Porous Media, v. 27(9), 2024, p. 1-17. (SJR квартиль Q3).

26. M.I. Kopp, V.V. Yanovsky. Weakly Nonlinear Bio-Thermal Convection in a Porous Media Layer Under Rotation, Gravity Modulation, and Heat Source, East European Journal of Physics, 2024, v. 1, p. 175-191. (SJR квартиль Q3).

27. M.I. Kopp, V.V. Yanovsky. The Effect of Throughflow and Gravitational Modulation on Weakly Nonlinear Bio-Thermal Convection in a Porous Medium Layer, Ukrainian Journal of Physics, 2024, v. 69(2), p. 82-95. (SJR квартиль Q4).

28. M.I. Kopp, V.V. Yanovsky. Thermal modulation effects on weakly nonlinear bio-thermal convection with thermotactic microorganisms in a liquid layer, Journal of Physical Studies, 2024, v. 28(3), 3401. (SJR квартиль Q4).

29. M.I. Kopp, V.V. Yanovsky. Generation of large-scale magnetic-vortex structures in stratified magnetized plasma by a small-scale force, Physics of Plasmas, 2024, v. 31, 082301. (SJR квартиль Q2).

30. M.I. Kopp, V.V. Yanovsky. Features of generation of spontaneous magnetic fields in fully ionized plasma, Problems of Atomic Science and Technology, 2024, №6(154), p. 25-30. (SJR квартиль Q3).

31. Michael Kopp, Inna Samuilik. A New 6D Two-wing Hyperhaotic System: Dynamical Analysis, Circuit Design, and Synchronization, Chaos Theory and Applications, 2024, v. 6(4), p. 273-283. (SJR квартиль Q1).

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