Nonlinear Vortex Structures Driven by Small-Scale Non-helical Forces in Obliquely Rotating Stratified Fluids
Keywords:equations of hydrodynamics in the Boussinesq approximation, Coriolis force, multiscale asymptotic expansions, small-scale nonhelical turbulence, a-effect
We study a new type of large-scale instability in obliquely rotating stratifi ed fl uids with small-scale nonhelical turbulence. The small-scale turbulence is generated by the external force with zero helicity and low Reynolds number. The theory uses the method of multiscale asymptotic expansions. The nonlinear equations for large-scale motions are obtained in the third order of perturbation theory. We consider a linear instability and stationary nonlinear modes. Solutions in the form of nonlinear Beltrami waves and localized vortex structures such as kinks of a new type are obtained.
A.S. Monin. Theoretical Fundamentals of Geophysical Hydrodynamics (Gidrometeoizdat, 1988) (in Russian).
O.G. Onishchenko, O.A. Pokhotelov, N.M. Astafi eva. Generation of large-scale vortices and zonal winds in atmopheric planets. Physics-Uspekhi 178, 605 (2008).
B.Y. Shmerlin, M.V. Kalashnik. Convective instability of Rayleigh in the presence of phase transitions of the humidity. The formation of the large-scale eddies and cloud structures. Physics-Uspekhi 183, 497 (2013).
V.I. Petviashvili, O.A. Pokhotelov. Solitary Vortices in Plasma and Atmosphere (Energoatomizdat, 1989) (in Russian).
G.D. Aburjania. Self-Organization of Nonlinear Vortex Structures and Vortex Turbulence in Dispersive Media (Komkniga, 2006) (in Russian).
A.V. Kolesnichenko, M.Ya. Marov. Turbulence and Self-Organization. Problems of Modeling Space and Natural Media (BINOM, 2009) (in Russian).
A. Tur, V. Yanovsky. Coherent Vortex Structures in Fluids and Plasmas (Springer, 2017) [ISBN: 978-3-319-52733-8].
A.M. Freedman, A.V. Khoperskov. Physics of Galactic Disks (FIZMATLIT, 2011) (in Russian).
S.S. Moiseev, P.B. Rutkevitch, A.V. Tur, V.V. Yanovsky. Vortex dynamos in a helical turbulent convection. Sov. Phys. JETP 67, 294 (1988).
E.A. Lypyan, A.A. Mazurov, P.B. Rutkevitch, A.V. Tur. Generation of large-scale vortices through the action of spiral turbulence of a convective nature. Sov. Phys.JETP 75, 838 (1992).
S.S. Moiseev, K.R. Oganjan, P.B. Rutkevich, A.V. Tur, G.A. Khomenko, V.V. Yanovsky. Vortex dynamo in helical turbulence. In: Integrability and Kinetic Equations for Solitons (Naukova Dumka, 1990) (in Russian).
G.V. Levina, S.E. Startsev, V.D. Zimin, S.S. Moiseev. About another physical mechanism of large-scale structures generation at turbulent convection in the horizontal fluid layer. Phys. Chem. of the Earth Parts 21, 563 (1996).
G.V. Levina, S.S. Moiseev, P.B. Rutkevich. Hydrodynamic alpha-eff ect in a convective system. Advances in Fluid Mechanics 25, 111 (2000).
A.V. Tur, V.V. Yanovsky. Large-scale instability in hydrodynamics with stable temperature stratifi cation driven by small-scale helical force. arXiv:1204.5024 v.1[physics. Fludyn.] (2012).
A.V. Tur, V.V. Yanovsky. Non linear vortex structure in stratifi ed driven by small-scale helical forse. Open Journal of Fluid Dynamics 3, 64 (2013).
E.A. Novikov. Functionals and the random force method in turbulence theory. Sov. Phys. JETP 47 (11), 1919 (1964).
V.I. Klyatskin. Stochastic Equations and Waves in Randomly Inhomogeneous Media (Nauka, 1980) (in Russian).
U. Frisch, Z.S. She, P.L. Sulem. Large-scale fl ow driven by the anisotropic kinetic alpha eff ect. Physica D 28, 382 (1987). https://doi.org/10.1016/0167-2789(87)90026-1
G. R¨udiger. On the a-effect for slow and fast rotation. Astron. Nachr. 299, 217 (1978). https://doi.org/10.1002/asna.19782990408
G. Moff at. Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University Press, 1978).
M.I. Kopp, A.V. Tur, V.V. Yanovsky. Nonlinear vortex structures in rotating fl uid obliquely. Open Journal of Fluid Dynamics 5, 311 (2015). https://doi.org/10.4236/ojfd.2015.54032
How to Cite
License to Publish the Paper
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.