The Large Scale Instability in Rotating Fluid with Small Scale Force

Michael  Kopp; Vladimir  Yanovsky; Anatoly  Tur

doi:10.4236/ojfd.2015.52015

Michael Kopp¹, Anatoly Tur², Vladimir Yanovsky¹

Abstract: In this paper, we find a new large scale instability in rotating flow forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain the nonlinear stage of the instability and the generation vortex kinks.

Keywords: Large Scale Vortex Instability, Coriolis Force, Multi-Scale Development, Small Scale Turbulence, Vortex Kinks

Cite this paper: Kopp, M. , Tur, A. and Yanovsky, V. (2015) The Large Scale Instability in Rotating Fluid with Small Scale Force. Open Journal of Fluid Dynamics, 5, 128-138. doi: 10.4236/ojfd.2015.52015.

References

[1] Grinspen, H.P. (1990) The Theory of Rotating Fluids. Breukelen Press, Brookline.

[2] Roberts, P.H. and Soward, A.M. (1978) Rotating Fluids in Geophysics. Academic Press, London.

[3] Clarke, C. and Carswell, B. (2007) Principles of Astrophysical Fluid Dynamics. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511813450

[4] Vallis, G.K. (2010) Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, Cambridge.

[5] Abramowicz, M.A., Lanza, A., Spigel, E.A. and Szuszkiewicz, E. (1992) Vortices on Accretion Disks. Nature, 356, 41-43.
http://dx.doi.org/10.1038/356041a0

[6] Brandt, P.N., Scharmer, G.B., Ferguson, S., Shine, R.A., Tarbell, T.D. and Title, A.M. (1988) Vortex Flow in the Solar Photosphere. Nature, 335, 238.
http://dx.doi.org/10.1038/335238a0

[7] Dritschel, G. and Legras, B. (1993) Modeling Oceanic and Atmospheric Vortices. Physics Today, 46, 44.
http://dx.doi.org/10.1063/1.881375

[8] Moiseev, S.S., Sagdeev, R.Z., Tur, A.V., Khomenko, G.A. and Yanovsky, V.V. (1983) A Theory of Large-Scale Structure Origination in Hydrodynamic Turbulence. Soviet Physics—JETP, 58, 1149.

[9] Moiseev, S.S., Rutkevich, P.B., Tur, A.V. and Yanovsky, V.V. (1988) Vortex Dynamos in a Helical Turbulent Convection. Soviet Physics—JETP, 67, 294.

[10] Lupyan, E.A., Mazurov, A.A., Rutkevich, P.B. and Tur, A.V. (1992) Generation of Large-Scale Vortices through the Action of Spiral Turbulence of a Convective Nature. Soviet Physics—JETP, 75, 833.

[11] Khomenko, G.A., Moiseev, S.S. and Tur, A.V. (1991) The Hydrodynamic Alpha-Effect in a Compressible Fluid. Journal of Fluid Mechanics, 225, 355.
http://dx.doi.org/10.1017/S0022112091002082

[12] Levina, G.V., Moiseev, S.S. and Rutkevich, P.B. (2000) Hydrodynamic Alpha-Effect in a Convective System. Advances in Fluid Mechanics, 25, 111.

[13] Frisch, U., She, Z.S. and Sulem, P.L. (1987) Large-Scale Flow Driven by the Anisotropic Kinetic Alpha Effect. Physica D, 28, 382.
http://dx.doi.org/10.1016/0167-2789(87)90026-1

[14] Tur, A.V. and Yanovsky, V.V. (2013) Non Linear Vortex Structures in Stratified Fluid Driven by Small-Scale Helical Force. Open Journal of Fluid Dynamics, 3, 64.
http://dx.doi.org/10.4236/ojfd.2013.32009

[15] Kitchatinov, L.L., Rudiger, G. and Khomenko, G. (1994) Large-Scale Vortices in Rotating Stratified Disks. Astronomy & Astrophysics, 287, 320.

[16] Moffat, H.K. (1978) Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press, Cambridge.

[17] Gradshteyn, I.S. and Ryzhik, I.M. (2000) Table of Integrals, Series, and Prodacts. Academic Press, London.