Coherent structures and transient amplification mechanisms in transitional and turbulent flows

Abstract

In this thesis, a generic explanation for coherent structures based on the filtering properties of the linearised Navier-Stokes equations is first investigated. By computing the componentwise optimal perturbations in homogeneous shear flow, it has been found the optimal perturbations can capture the linear evolution of a small-amplitude perturbation. This capability of optimal perturbations is further examined in fully developed turbulent channel flow with non-linearity taken into account. The spanwise length scale of streamwise and spanwise velocity structures can be predicted by the generalised optimal perturbations. However, this is not always the case given the selectivity of the linearised Navier-Stokes operator not always strong enough to outweigh the nonlinear effect. Then, the precise role of the spanwise velocity perturbations in transition of plane Couette flow is studied by considering a set of initial conditions combining the optimal perturbation for spanwise velocity with the one for all the velocity components. By varying their amplitudes, two representative transition scenarios are found: oblique and streak transitions. In the former, the spanwise velocity perturbation amplified with the Orr mechanism initiates both streak amplification and breakdown, whereas, in the latter, its role is limited only to the streak breakdown at the late stage of transition. Eventually, the effect of adverse pressure gradient (APG) on near-wall turbulence is studied, with a particular attention to the turbulence production mechanism. The generation of near-wall streaks is suppressed due to the significant reduction of the mean shear in the region near the lower wall. The near-wall self-sustaining process is significantly weakened or destroyed as APG increases, while the turbulent fluctuations become more isotropic and localised. Using a conditional averaging analysis, a new near-wall turbulence production mechanism initiated by the wall-normal nonlinear transport of an outer wall-normal velocity fluctuation towards the wall amplified via the Orr mechanism is uncovered.