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When a small thin two-dimensional body enters a viscous wall layer

Part of: Coupling of solid mechanics with other effects Incompressible viscous fluids

Published online by Cambridge University Press:  16 December 2019

R. A. PALMER Open the ORCID record for R. A. PALMER [Opens in a new window]  and
F. T. SMITH
R. A. PALMER
Affiliation:
Department of Mathematics, University College London, LondonWC1E 6BT, UK, emails: ryan.palmer.14@ucl.ac.uk; f.smith@ucl.ac.uk
F. T. SMITH
Affiliation:
Department of Mathematics, University College London, LondonWC1E 6BT, UK, emails: ryan.palmer.14@ucl.ac.uk; f.smith@ucl.ac.uk
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Abstract

If a body enters a viscous-inviscid fluid layer near a wall, then significant effects can be felt from the presence of incident vorticity, viscous forces and nonlinear forces. The focus here is on the response in the outer edge of such a wall layer. Nonlinear two-dimensional unsteady behaviour is examined through modelling, computation and analysis applied for a thin body travelling streamwise upstream or downstream or staying still relative to the wall. The wall layer with its balance between inviscid and viscous effects interacts freely with the body movement, causing relatively high magnitudes of pressure on top of the body and nonlinear responses in the gap between the body and the wall. The study finds explicit solutions for the motion of the body, separation of the flow arising near the wall and possible instabilities occurring over the length scale of any short body.

Keywords

Viscous–inviscid interactionfluid–solid interactionsboundary-layer theory

MSC classification

Primary: 76D09: Viscous-inviscid interaction 74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Secondary: 76D10: Boundary-layer theory, separation and reattachment, higher-order effects
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 6 , December 2020 , pp. 1002 - 1028
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Copyright
© The Authors 2019. Published by Cambridge University Press

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