Advances and Applications in Fluid Mechanics © 2013 Pushpa Publishing House, Allahabad, India Published Online: January 2014 Available online at http://pphmj.com/journals/aafm.htm Volume 14, Number 2, 2013, Pages 243-254 Received: June 18, 2013; Accepted: July 5, 2013 2010 Mathematics Subject Classification: 76-XX. Keywords and phrases: Stokes second problem, harmonic oscillatory motion, phase difference, Lagrangian formalism. ON A SPECIAL CASE OF RAYLEIGH-STOKES OSCILLATING FLOW J. Venetis School of Civil Engineering NTU Athens 5 Heroes of Polytechnion Avenue GR 15773 Athens Greece e-mail: john24@otenet.gr; john.venetis@yahoo.com Abstract In this paper, the author investigates a specific subcase of Rayleigh- Stokes oscillating flow, which is also known as Stokes second problem. In particular, the author focuses on an oscillating flux field that takes place between two semi-infinite plates which are located vertically, without intersecting each other. Evidently, the two ideal lines along which these plates are directed join one another vertically. The flow field is created by a simple harmonic oscillatory motion which is carried out by these plates, as they move backwards and forwards with respect to their constant equilibrium points. Another essential feature of these two oscillatory motions is that they have a constant phase difference throughout. Introduction The first exact solution to first and second Stokes problem was obtained