Instabilities and emergence of coherent structures in the turbulent channel flow

Turbulent flows are characterised by a marvellous phenomenology combining chaos and order, fluctuations on multiple scales and recurrent patterns named coherent structures. This thesis aims to elucidate certain physical processes involving coherent structures in the turbulent channel flow. Different numerical techniques are implemented towards this aim, with a common ground: investigate how coherent structures become unstable and, eventually, generate new coherent structures on different scales. This investigation is divided into three parts. In the first part, the generation of extreme dissipation events is considered. Nonlinear optimal perturbations are computed with respect to a fully turbulent snapshot, and the dynamics induced by these perturbations are analysed and compared to the dynamics of naturally occurring extreme events, establishing a connection between the two. Interestingly, the nonlinear optimal perturbation works towards a destabilisation of near-wall streaks, suggesting that an instability of streaks is a possible cause of extreme events. In the second part, the instability of streaks is addressed more directly but in a different direction. A linear stability analysis is performed on an array of periodic streaks to show that these structures undergo sub-harmonic or detuned instabilities with unstable modes characterised by large wavelengths (several times larger than the streak’s wavelength). These instabilities are related to the large-scale motions (LSMs) observed in experiments and direct numerical simulations of high-Reynolds number flows. In the third part, the large-scale linear instability of streaks is revisited at low Reynolds number in order to capture the wavelengths and the critical Reynolds number of the instability leading to laminar-turbulent patterns. The thesis concludes with the development of a nonlinear model for laminar-turbulent pattern formation. Ideas, limitations and possible directions to improve this model are tested and discussed.