Vortex Dynamo in an Obliquely Rotating Stratified Nanofluid by Small-Scale Non-Helical Forces

  • Michael I. Kopp Institute for Single Cristals, Nat. Academy of Science Ukraine, Kharkov, Ukraine https://orcid.org/0000-0001-7457-3272
  • Anatoly V. Tur Universite Toulouse, CNRS, Institute of Research for Astrophysics and Planetology, Toulouse, France https://orcid.org/0000-0002-3889-8130
  • Volodymyr V. Yanovsky Institute for Single Cristals, Nat. Academy of Science Ukraine, Kharkov, Ukraine; V.N. Karazin Kharkiv National University, Kharkiv, Ukraine https://orcid.org/0000-0003-0461-749X
Keywords: stratified nanofluid, large-scale instability, Coriolis force, multiscale asymptotic expansions, alpha-effect, localized vortex structures


In this work, a large-scale instability of the hydrodynamic -effect in an obliquely rotating stratified nanofluid taking into account the effects of Brownian diffusion and particle flux under the influence of a temperature gradient (thermophoresis)  is obtained. The instability is caused by the action of an external small-scale non-spiral force, which excites small-scale velocity oscillations with zero helicity and a low Reynolds number. Nonlinear equations for large-scale motions are obtained using the method of multiscale asymptotic expansions by a small parameter (Reynolds number). A linear large-scale instability of hydrodynamic -effect is investigated depending on the parameters of rotation , temperature stratification , and concentration of nanoparticles . A new effect of the generation of large-scale vortex structures in nanofluid at  is associated with an increase in the concentration of nanoparticles is obtained. The maximum instability increment  is reached  at inclination angles  for the Prandtl numbers  , and for the Prandtl numbers   at  inclination angles   . It has been found that the frequency changing of the parametric impact will make it possible to control and track the generation of large-scale vortex structures. It is shown that circularly polarized Beltrami vortices appear in nanofluid as the result of new large-scale instability development. In this paper, the saturation regime of large-scale instability in an obliquely rotating stratified nanofluid with an external small-scale non-spiral force is investigated. In the stationary regime was obtained a dynamic system of equations for large-scale perturbations of the velocity field. Numerical solutions of this system of equations are obtained, which show the existence of localized vortex structures in the form of nonlinear Beltrami waves and kinks. The velocity  profile of kink tends to be constant at large Z values.


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S.K. Das, S. U.S Choi, W.Yu, and T. Pradeep, Nanofluids: science and technology, (Hoboken, New Jersey, Wiley-Interscience, 2008), pp. 397.

Dhananjay Yadav, G.S. Agrawal, and R. Bhargava, International Journal of Engineering Science, 49, 1171-1184 (2011), https://doi.org/10.1016/j.ijengsci.2011.07.002

Shilpi Agarwal, and B.S. Bhadauria, Continuum Mech. Thermodyn., 26, 437-445 (2014), https://doi.org/10.1007/s00161-013-0309-6

R. Chand, G.C. Rana, and S. K. Kango, FME Transactions, 43, 62-69 (2015), https://scindeks.ceon.rs/article.aspx?artid=1451-20921501062C

B.L. Smorodin, S.M. Ishutov, and B.I. Myznikova, Microgravity Science and Technology, 30, 95-102 (2018), https://doi.org/10.1007/s12217-017-9582-5

M.I. Kopp, A.V. Tur, and V.V. Yanovsky, https://arxiv.org/abs/1706.00223v1

U. Frisch, Z.S. She, and P.L. Sulem, Physica D, 28, 382-392 (1987), https://doi.org/10.1016/0167-2789(87)90026-1

M.I. Kopp, A.V. Tur, and V.V Yanovsky, Open Journal of Fluid Dynamics, 05(04), 311-321 (2015), https://doi.org/10.4236/ojfd.2015.54032

G. Rüdiger, Astron. Nachr. 299(4), 217-222 (1978), https://doi.org/10.1002/asna.19782990408.

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How to Cite
Kopp, M., Tur, A., & Yanovsky, V. (2021). Vortex Dynamo in an Obliquely Rotating Stratified Nanofluid by Small-Scale Non-Helical Forces. East European Journal of Physics, (2), 51-72. https://doi.org/10.26565/2312-4334-2021-2-02