Eur. Phys. J. Plus (2015) 130: 8
https://doi.org/10.1140/epjp/i2015-15008-6

Regular Article

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

¹ Department of Mathematics, Faculty of Science, Menoufiya University, 32511, Menoufiya, Egypt
² Southern Federal University, Rostov-on-Don, Russia

^* e-mail: am.morad@menofia.edu.eg

Received: 9 October 2014
Revised: 16 December 2014
Accepted: 18 December 2014
Published online: 16 January 2015

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.