Multiscale Structure of Turbulent Channel Flow and

Polymer Dynamics in Viscoelastic Turbulence

My PhD thesis was undertaken at the Institute for Mathematical Sciences of Imperial College London between October 2006 and February 2010 [link] [pdf]


This thesis focuses on two important issues in turbulence theory of wall-bounded flows. One is the recent debate on the form of the mean velocity profile (is it a log-law or a power-law with very weak power exponent?) and on its scalings with Reynolds number. In particular, this study relates the mean flow profile of the turbulent channel flow with the underlying topological structure of the fluctuating velocity field through the concept of critical points, a dynamical systems concept that is a natural way to quantify the multiscale structure of turbulence. This connection gives a new phenomenological picture of wall-bounded turbulence in terms of the topology of the flow. This theory validated against existing data, indicates that the issue on the form of the mean velocity profile at the asymptotic limit of infinite Reynolds number could be resolved by understanding the scaling of turbulent kinetic energy with Reynolds number.

The other major issue addressed here is on the fundamental mechanism(s) of viscoelastic turbulence that lead to the polymer-induced turbulent drag reduction phenomenon and its dynamical aspects. A great challenge in this problem is the computation of viscoelastic turbulent flows, since the understanding of polymer physics is restricted to mechanical models. An effective numerical method to solve the governing equation for polymers modeled as nonlinear springs, without using any artificial assumptions as usual, was implemented here for the first time on a three-dimensional channel flow geometry. The superiority of this algorithm is depicted on the results, which are much closer to experimental observations. This allowed a more detailed study of the polymer-turbulence dynamical interactions, which yields a clearer picture on a mechanism that is governed by the polymer-turbulence energy transfers.