Abstract
In this paper, we find a new large scale instability which appears in obliquely rotating flow with the small scale turbulence, generated by external force with small Reynolds number. The external force has no helicity. The theory is based on the rigorous method of multi-scale asymptotic expansion. Nonlinear equations for instability are obtained in the third order of the perturbation theory. In this article, we explain in detail the nonlinear stage of the instability and we find the nonlinear periodic vortices and the vortex kinks of Beltrami type.
Highlights
It is well known that the rotating effects play an important role in many theoretical and practical applications for fluid mechanics [1] and are especially important for geophysics and astrophysics [2]-[4] when one has to deal with rotating objects such as the Earth, Jupiter, the Sun, etc
In this work we found new large scale instability in rotating fluid
It is supposed that the small scale vortex external force in rotating coordinates system acts on fluid which maintains the small velocity field fluctuations
Summary
It is well known that the rotating effects play an important role in many theoretical and practical applications for fluid mechanics [1] and are especially important for geophysics and astrophysics [2]-[4] when one has to deal with rotating objects such as the Earth, Jupiter, the Sun, etc. The nonlinear large scale helical vortex structures such as Beltrami vortices or localized kinks appear as a result of the development of this instability in rotating fluid. This supposes that the external mall-scale force substitutes the action of small-scale turbulence. From this point of view, in this study we found a new example of the α-effect The theory of this instability is based on a rigorous method of multi-scale development, which was proposed by Frisch, She and Sulem for the theory of the AKA effect [14].
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