Abstract

First, the motivation for and the history behind Karhunen-Loeve (KL) Analysis (also called Karhunen-Loeve decomposition, proper orthogonal decomposition, empirical eigenfunction decomposition, etc.) is presented in the context of drag reduction dynamics and turbulence modeling. Then, the theory and numerical methods of KL decomposition is discussed in detail, with the intent of summarizing the current body of literature presented on the topic of the numerical methods, as well as providing a reasonably self-contained introduction to the numerical methods needed to undertake this thesis. The theory is also extended slightly to clarify the concept of degeneracy when exploring the dynamics of the temporal eigenfunctions and their relation to the fluctuating kinetic energy of the flow.

After that, the actual implementation of the theory is presented. A new method, related to the Direct Method of generating spatial eigenfunctions, is discussed, along with its implementation. Spatial eigenfunctions and eigenvalues obtained by this new method were exactly the same as those spatial eigenfunctions and eigenvalues obtained by Handler, who used the Method of Snapshots in a 2006 publication. (Abstract shortened by UMI.)