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The motion of a thin liquid layer on the outer surface of a rotating cylinder

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Abstract.

We derive the shallow water equations describing the motion of a thin liquid film on the outer surface of a rotating cylinder. These equations are an analogue of the modified Boussinesq equations describing shallow water flows with constant vorticity. The standard multi-scale methods are employed to construct asymptotic equations in the long-wave approximation. These asymptotic equations are analyzed using the hodograph method. It is found that for the particular case of a dispersionless irrotational flow, the equations describing flows on the outer surface of a cylinder reduce to elliptic equations. Numerical evaluation of the exact solutions obtained shows that the asymptotic equations possess a rich variety of solutions representing various wave patterns.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Menoufiya University, 32511, Menoufiya, Egypt

    A. M. Morad

  2. Southern Federal University, Rostov-on-Don, Russia

    M. Yu. Zhukov

Authors
  1. A. M. Morad
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  2. M. Yu. Zhukov
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Correspondence to A. M. Morad.

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Morad, A.M., Zhukov, M.Y. The motion of a thin liquid layer on the outer surface of a rotating cylinder. Eur. Phys. J. Plus 130, 8 (2015). https://doi.org/10.1140/epjp/i2015-15008-6

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  • DOI: https://doi.org/10.1140/epjp/i2015-15008-6

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