Abstract
The viscoelastic analogue to the Newtonian Orr amplification mechanism is examined using linear theory. A weak, twodimensional Gaussian vortex is superposed onto a uniform viscoelastic shear flow. Whilst in the Newtonian solution the spanwise vorticity perturbations are simply advected, the viscoelastic behaviour is markedly different. When the polymer relaxation rate is much slower than the rate of deformation by the shear, the vortex splits into a new pair of corotating but counterpropagating vortices. Furthermore, the disturbance exhibits a significant amplification in its spanwise vorticity as it is tilted forward by the shear. Asymptotic solutions for an OldroydB fluid in the limits of high and low elasticity isolate and explain these two effects. The splitting of the vortex is a manifestation of vorticity wave propagation along the tensioned meanflow streamlines, while the spanwise vorticity growth is driven by the amplification of a polymer torque perturbation. The analysis explicitly demonstrates that the polymer torque amplifies as the disturbance becomes aligned with the shear. This behaviour is opposite to the Orr mechanism for energy amplification in Newtonian flows, and is therefore labelled a ‘reverseOrr’ mechanism. Numerical evaluations of vortex evolutions using the more realistic FENEP model, which takes into account the finite extensibility of the polymer chains, show the same qualitative behaviour. However, a new form of stress perturbation is established in regions where the polymer is significantly stretched, and results in an earlier onset of decay.
Original language  English 

Pages (fromto)  327363 
Number of pages  37 
Journal  Journal of Fluid Mechanics 
Volume  777 
Early online date  20 Jul 2015 
DOIs  
Publication status  Published  25 Aug 2015 
Fingerprint Dive into the research topics of 'The dynamics of spanwise vorticity perturbations in homogeneous viscoelastic shear flow'. Together they form a unique fingerprint.
Profiles

Jacob Page
 School of Mathematics  Lectureship/Readership in Applied and Computational Mathemat
Person: Academic: Research Active (Teaching)