A high-order finite difference investigation of boundary layer perturbations

We present a new numerical treatment of the vorticity-velocity form of the governing equations of fluid motion, based on the application of compact finite differences. The mathematical formulation of these equations is discussed, as are the techniques used to discretise them. The solver thus obtained is validated against analytical solutions to model problems, and against the more physical test case of developing Tollmien-Schlichting waves in a parallelised Blasius boundary layer. We then use this solver to examine a reduced-order model of streaks in a turbulent boundary layer. The properties of the streaks produced by the solver are discussed, with a particular focus on the means of their generation. Following this, we examine the use of spanwise oscillation of the wall, which is known to reduce drag in turbulent boundary layers. The parameters of the oscillation (specifi­ cally its magnitude, its frequency and the phase difference between the wall motion and the streak forcing) are altered and their influence on streak development investigated. It is found that in certain cases, the modification to the basis flow by wall oscillation means that the perturbations can grow exponentially. We also investigate the effects of altering the pattern of oscillation from sinusoidal in time to a smoothed square wave or sawtooth wave. Finally, the results are reviewed and conclusions drawn, and possible extensions to the research presented in the thesis are suggested.