Wall-bounded turbulent flows such as plane Couette flow, channel, pipe flows and boundary layer flows are fundamental problem of interest that we often meet in many scientific and engineering situations. The goal of the present thesis is to investigate the origin of large-scale streaky motions observed in the wall-bounded turbulent flows. Under a hypothesis that the large-scale streaky motions sustain with a process similar to the well-known near-wall self-sustaining cycle, the present thesis have pursued on four separate subjects: (i) non-modal amplification of streaks, (ii) the secondary instability of the finite amplitude streaks, (iii) existence of a self-sustaining process at large scale and (iv) turbulent skin friction reduction by forcing streaks. First, using a linear model with turbulent mean flow and the related eddy viscosity, it is shown that the streaks are largely amplified by harmonic and stochastic forcing. The largely amplified streaks undergo the secondary instability and it has been associated with the formation of the large-scale motions (bulge). The existence of a self-sustaining process involving the amplification and instability of streaks at large scale is proved by quenching the smaller-scale energy carrying eddies in the near-wall and logarithmic regions. Finally, it is shown that artificially forcing of large-scale streaks reduce the turbulent skin friction up to 10\% by attenuating the near-wall streamwise vortices.

Recently, a new kind of turbulence has been discovered in the flow of concentrated polymer melts and solutions. These flows, known as purely elastic flows, become unstable when the elastic forces are stronger than the viscous forces. This contrasts with Newtonian turbulence, a more familiar regime where the fluid inertia dominates. While there is little understanding of purely elastic turbulence, there is a well-established dynamical systems approach to the transition from laminar flow to Newtonian turbulence. In this project, I apply this approach to purely elastic flows. Laminar flows are characterised by ordered, locally-parallel streamlines of fluid, with only diffusive mixing perpendicular to the flow direction. In contrast, turbulent flows are in a state of continuous instability: tiny differences in the location of fluid elements upstream make a large difference to their later locations downstream. The emerging understanding of the transition from a laminar to turbulent flow is in terms of exact coherent structures (ECS) — patterns of the flow that occur near to the transition to turbulence. The problem I address in this thesis is how to predict when a purely elastic flow will become unstable and when it will transition to turbulence. I consider a variety of flows and examine the purely elastic instabilities that arise. This prepares the ground for the identification of a three-dimensional steady state solution to the equations, corresponding to an exact coherent structure. I have organised my research primarily around obtaining a purely elastic exact coherent structure, however, solving this problem requires a very accurate prediction of the exact solution to the equations of motion. In Chapter 2 I start from a Newtonian ECS (travelling wave solutions in two-dimensional flow) and attempt to connect it to the purely elastic regime. Although I found no such connection, the results corroborate other evidence on the effect of elasticity on travelling waves in Poiseuille flow. The Newtonian plane Couette ECS is sustained by the Kelvin-Helmholtz instability. I discover a purely elastic counterpart of this mechanism in Chapter 3, and explore the non-linear evolution of this instability in Chapter 4. In Chapter 5 I turn to a slightly different problem, a (previously unexplained) instability in a purely elastic oscillatory shear flow. My numerical analysis supports the experimental evidence for instability of this flow, and relates it to the instability described in Chapter 3. In Chapter 6 I discover a self-sustaining flow, and discuss how it may lead to a purely elastic 3D exact coherent structure.