| This dissertation focuses on the fluid dynamics of dilute polymer solutions. At low Reynolds number, viscoelastic stagnation-point flow is studied, where various instabilities have been reported experimentally. We computationally demonstrate the existence of a supercritical oscillatory instability of low-Reynolds number viscoelastic flow in a two-dimensional cross-slot geometry. A mechanism of this instability is presented, which arises from the coupling of flow with extensional stresses and their steep gradients in the stagnation point region.;In turbulent flows, polymer additives are known to reduce turbulent friction drag significantly at very low concentrations. By applying the minimal flow unit (MFU) method to viscoelastic turbulent flows at a Reynolds number close to the laminar-turbulence transition, the essential self-sustaining turbulent motions are isolated. These MFU solutions contain a series of qualitatively different stages, including one asymptotic limit showing the characteristic of maximum drag reduction (MDR): i.e. the mean flow is universal with respect to changing polymer-related parameters. Before this asymptotic limit, distinctions between a low- (LDR) and high-degree (HDR) of drag reduction are noticed, including an abrupt increase in the minimal box size of sustaining turbulence as well as transitions in many flow statistics quantities. Spatiotemporal flow structures, as well as the fact this transition is observed at less than 15% drag reduction, show that LDR--HDR transition is caused by a qualitative change in the dynamics of the self-sustaining process. These solutions recover all key transitions commonly observed and studied at much higher Reynolds numbers. In all stages of transition, even in the Newtonian limit, we find intervals of "hibernating" turbulence that display many features of the experimental MDR: weak streamwise vortices, nearly nonexistent streamwise variations and a mean velocity gradient that quantitatively matches experiments. As viscoelasticity increases, the frequency of these intervals also increases, while the intervals themselves are unchanged, leading to flows that increasingly resemble MDR. This observation points out a new direction of understanding the unsolved mechanism of MDR. |
