Non-local vorticity generation by surface roughness in viscoelastic shear flows

Abstract eng:
The vorticity response to small-amplitude surface undulations in a viscoelastic Couette flow is examined. An integral measure is defined to quantify the depth of vorticity penetration into the bulk flow. Three regimes of penetration are identified, and each occupies a sector of a phase diagram parameterized by the ratios of the channel depth and of the critical-layer (CL) height to the lengthscale of the surface roughness. The CL emerges due to the propagation of vorticity waves along the tensioned mean-flow streamlines. The most intriguing behavior, the trans-critical regime, occurs when the CL lies within one wavelength from the wall. In trans-critical flows a kinematic mechanism associated with the relative realignment of the polymer by the mean shear amplifies the vorticity in ‘sheets’ around the CL. The effect is dominant at this location since the vorticity waves appear steady to an observer advecting with the mean flow.

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