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Gradshteyn, I.S. and Ryzhik, I.M. (1974) Tables of Integrals, Sums, Series and Products. Academic Press, San Diego, San Francisco, New York, Boston, London, Sydney, Tokyo.

has been cited by the following article:

• TITLE: Nonlinear Vortex Structures in Obliquely Rotating Fluid

  AUTHORS: Michael Kopp, Anatoly Tur, Vladimir Yanovsky

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

  JOURNAL NAME: Open Journal of Fluid Dynamics, Vol.5 No.4, December 18, 2015

  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.