Title:

Nonlinear exact coherent structures in high Reynolds number shear flows

Recently a dynamical systems approach to the process of transition to turbulence has arisen in which so called exact coherent structures play a key role. Such structures are equilibrium states which are exact solutions of the NavierStokes equations. Given the nature of the governing equations such states can be difficult to find due to the size of the state space and nonlinear effects. Techniques such as homotopy and artificial forcing have been used to overcome these issues. However, here we will focus on finding such states at large Reynolds numbers where an asymptotically large parameter allows the identification of the leading order effects, from which the structure of the states can be described. The states described in this thesis will be split into two general types. The first are of vortexTollmienSchlichtingwave type and these states arise via the viscous instability mechanism. The flows studied here (plane Poiseuille flow and the asymptotic suction boundary layer) both exhibit a linear instability and hence we can find nonlinear travelling wave equilibrium states which bifurcate directly from the basic state. Importantly the class of states studied here have a large spanwise wavelength. We will find and investigate these states, finding that they appear to terminate in a singularity caused by the lack of spanwise diffusion at leading order. The second type are characterised by the presence of structures both in the freestream and close to the wall, and were first found by Deguchi & Hall (J. Fluid Mech, vol. 752, 2014, pp. 602625). We will consider two variations of these states. The first is the effect of wall curvature which leads to the imperfect bifurcation of Görtler vortices from the basic state. The second is the spontaneous generation of near wall structures when freestream structures are assumed to appear impulsively at some downstream location.
