Nonlinear Vortex Structures Driven by Small-Scale Non-helical Forces in Obliquely Rotating Stratified Fluids

Authors

  • M.I. Kopp Institute for Single Crystals, Nat. Acad. of Sci. of Ukraine
  • A.V. Tur Universit´e de Toulouse [UPS], CNRS, Institut de Recherche en Astrophysique et Plan´etologie
  • V.V. Yanovsky Institute for Single Crystals, Nat. Acad. of Sci. of Ukraine, V.N. Karazin Kharkiv National University

DOI:

https://doi.org/10.15407/ujpe66.6.478

Keywords:

equations of hydrodynamics in the Boussinesq approximation, Coriolis force, multiscale asymptotic expansions, small-scale nonhelical turbulence, a-effect

Abstract

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.

References

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].

https://doi.org/10.1007/978-3-319-52733-8

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).

https://doi.org/10.1016/S0079-1946(97)81158-5

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).

https://doi.org/10.4236/ojfd.2013.32009

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

Downloads

Published

2021-07-06

How to Cite

Kopp, M., Tur, A., & Yanovsky, V. (2021). Nonlinear Vortex Structures Driven by Small-Scale Non-helical Forces in Obliquely Rotating Stratified Fluids. Ukrainian Journal of Physics, 66(6), 478. https://doi.org/10.15407/ujpe66.6.478

Issue

Section

General physics