LAMINAR TURBULENT TRANSITION - SPECTRAL ANALYSIS AND COHERENT STRUCTURES OF DNS WAVEPACKETS

Abstract

This thesis concerns a direct numerical simulation (DNS) of wavepackets undergoing laminar turbulent transition in a Blasius boundary layer. A fully crossed factorial simulation design is used, in which 18 different wavepackets are analyzed to determine the combined effects of frequency, bandwidth and amplitude on the transition process. Fast Fourier transforms (FFT) are then performed to extract the one, two and three-dimensional (3D) spatio-temporal spectra of the flow. In particular, the three-dimensional spectrum yields new information about modes that overlap ambiguously in lower dimensions. Subsequently, inverse Fourier transforms of subsets of the 3D spectrum result in coherent structures of the flow. These are compared with the results of proper orthogonal decomposition (POD). A hybrid POD-FFT approach is also pioneered to synergize the strengths of both methods, taking advantage of the optimal basis constructed by POD, and connecting it with classical theories of Craik and Herbert via FFT.