Abstract / Description of output
A smallamplitude sinusoidal surface undulation on the lower wall of Couette flow induces a vorticity perturbation. Using linear analysis, this vorticity field is examined when the fluid is viscoelastic and contrasted to the Newtonian configuration. For strongly elastic OldroydB fluids, the penetration of induced vorticity into the bulk can be classified using two dimensionless quantities: the ratios of (i) the channel depth and of (ii) the shearwaves’ critical layer depth to the wavelength of the surface roughness. In the shallowelastic regime, where the roughness wavelength is larger than the channel depth and the critical layer is outside of the domain, the bulk flow response is a distortion of the tensioned streamlines to match the surface topography, and a constant perturbation vorticity fills the channel. This vorticity is significantly amplified in a thin solvent boundary layer at the upper wall. In the deepelastic case, the critical layer is far from the wall and the perturbation vorticity decays exponentially with height. In the third, transcritical regime, the critical layer height is within a wavelength of the lower wall and a kinematic amplification mechanism generates vorticity in its vicinity. The analysis is extended to localized, Gaussian wall bumps using Fourier synthesis. The Newtonian flow response consists of a single vortex above the bump. In the shallowelastic flow, a second vortex with opposite circulation is established upstream of the surface protrusion and is induced by the vorticity layer on the upper wall. In the deep transcritical case, the perturbation field consists of a pair of counterrotating vortices centred on the large vorticity around the critical layer. The more realistic FENEP model, which accounts for the finite extensibility of the polymer chains, shows the same qualitative behaviour.
Original language  English 

Pages (fromto)  392429 
Number of pages  38 
Journal  Journal of Fluid Mechanics 
Volume  801 
Early online date  25 Jul 2016 
DOIs  
Publication status  Published  25 Aug 2016 
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Jacob Page
 School of Mathematics  Lectureship/Readership in Applied and Computational Mathemat
Person: Academic: Research Active (Teaching)