The Rayleigh problem for a wavy wall (impulsive motion generation of viscous fluid flow)

Shankar, PN and Sinha, UN (1976) The Rayleigh problem for a wavy wall (impulsive motion generation of viscous fluid flow). Journal of Fluid Mechanics, 77 . pp. 243-256. ISSN 0022-1120

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    The problem of the flow generated in a viscous fluid by the impulsive motion of a wavy wall is treated as a perturbation about the known solution for a straight wall. It is shown that, while a unified treatment for high and low Reynolds numbers is possible in principle, the two limiting cases have to be treated separately in order to get results in closed form. It is also shown that a straightforward perturbation expansion in Reynolds number is not possible because the known solution is of exponential order in that parameter. At low Reynolds numbers the waviness of the wall quickly ceases to be of importance as the liquid is dragged along by the wall. At high Reynolds numbers on the other hand, the effects of viscosity are shown to be confined to a narrow layer close to the wall and the known potential solution emerges in time. The latter solution is a good illustration of the interaction between a viscous fluid field and its related inviscid field.

    Item Type: Journal Article
    Additional Information: copyright for this article belongs to Cambridge University Press
    Uncontrolled Keywords: Boundary layer flow;Incompressible fluids;Reynolds number;Viscous flow;Vorticity;Wall flow;Flow distribution;Inviscid flow
    Subjects: ENGINEERING > Fluid Mechanics and Thermodynamics
    Division/Department: Aerodynamics, Aerodynamics
    Depositing User: Ms. Alphones Mary
    Date Deposited: 24 Apr 2006
    Last Modified: 24 May 2010 09:40

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