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

  • A. M. MoradEmail author
  • M. Yu. Zhukov
Regular Article


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.


Soliton Free Boundary Shallow Water Equation Boussinesq Equation Asymptotic Equation 
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Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceMenoufiya UniversityMenoufiyaEgypt
  2. 2.Southern Federal UniversityRostov-on-DonRussia

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