In channel flows of viscoelastic fluids at high Deborah numbers, the dynamics are dominated by the constitutive relation, leading to the formation of plug-like velocity profiles. In this study, systematic numerical simulations were performed using the Upper-Convected Maxwell (UCM) model combined with an artificial compressibility method. Under conditions of both high Reynolds and Deborah numbers, a supercritical region appears at the channel center, where the elastic wave propagation speed exceeds the flow velocity, resulting in a flattened velocity distribution. In contrast, in the subcritical region near the wall, elastic forces arising from normal stresses act against the pressure gradient, reversing the sign of the shear stress gradient. This mechanism produces an anomalous stress distribution and distinctive velocity profiles.
Kawaguchi et al. (Wed,) studied this question.