Linearised Navier-Stokes equations and near-wall streaks in turbulent flow subject to drag reduction by wall oscillations

Abstract

Spanwise wall-oscillation is a promising drag reduction technique in turbulent flows. A major factor in drag reduction is the effect of the oscillations on the boundary layer coherent structures, and particularly the weakening of the near-wall streaks. This thesis studies the streaks in various wall oscillations configurations, based on a linear approach to the turbulent flow. The two main aspects are the study of the structures themselves, and an attempt to predict drag. The streak structure is studied mainly in turbulent channel flow subject to harmonic wall forcing, using an optimal perturbation technique. It is shown that the streaks have an angle to the main flow direction, which is almost constant during half an oscillation period and experiences a jump in sign and magnitude twice per period. The linear theory shows that this phenomenon is due to the existence of a structure which is dominant during half a period and has a constant angle. Other features of the linear optimal perturbations are studied, such as their comparison with conditionally averaged turbulent structures. In order to predict drag, the optimal perturbation approach is found to be unsuitable. A more appropriate technique is to use the linearised Navier-Stokes equation subject to random forcing. This was done for a turbulent channel flow subject to travelling wave wall oscillations, thus offering a wide range of comparison with direct numerical simulations, including known regions of drag reduction and drag increase. The main finding is that in the area where drag increase is observed in turbulent flow, the linear operator is unstable. In area where the operator is stable, drag reduction is always predicted. These two topics are the core of this thesis. Other aspects include the derivation and implementation of an optimal perturbation algorithm and a linear solver. Certain theoretical aspects of the optimal perturbation approach were also investigated.