HYDRODYNAMIC STABILITY ANALYSES OF VISCOELASTIC PARALLEL SHEAR FLOWS

Abstract

The transition to turbulence in a viscoelastic pipe flow has long been believed to be purely a nonlinear phenomenon until the recent discovery of a novel centre-mode linear instability in the flow. This thesis presents a weakly nonlinear stability analysis of the flow based on a cubic Ginzburg-Landau equation governing the disturbance evolution. Results show that the primary flow bifurcation at the linear criticality is subcritical for dilute polymer solutions and changes to be supercritical for relatively more concentrated solutions. This finding theoretically corroborates the coexistence of two different transition routes signified in experimental studies in literature. Further analysis reveals that these two bifurcations also coexist in the viscoelastic channel flow counterpart, suggesting generic instability mechanisms in viscoelastic parallel shear flow systems. In addition, some scaling laws embedded in the weak nonlinearity of the systems have been found in terms of the Landau coefficients at asymptotically high Weissenberg numbers.