Nonlinear Dynamics of Turbulent and Stokes Flows

Dr. Jae Sung Park is a postdoctoral associate in the Department of Chemical and Biological Engineering at the University of Wisconsin-Madison. Dr. Park received his B.S. in Mechanical Engineering in 2006 at Hanyang University, Seoul, Republic of Korea. He received his M.S. and Ph.D. in Mechanical Engineering from the University of Illinois at Urbana-Champaign in 2008 and 2012, respectively. His research interests encompass a wide range of fluid mechanics, covering from low Reynolds number flows (Stokes flow) to high Reynolds number flows (turbulent flow). He studies various problems numerically using advanced computational algorithms.

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The theoretical and numerical analysis of fluid flows is of paramount importance for understanding basic nonlinear phenomena in science and engineering. In this talk, I will discuss two problems of interest at very different Reynolds numbers. The modeling, analysis and computation for both problems will be presented in detail with their engineering applications.

The first part is dedicated to high Reynolds number flows (turbulent flow). In recent years, the discovery of nonlinear traveling wave solutions to the Navier-Stokes equations, or exact coherent states, has greatly advanced the understanding of the nature of turbulent flows. These solutions are unstable saddle points in state space, while the time evolution of a turbulent flow is a dynamical trajectory wandering around them. Several new classes of exact coherent states are computed for Newtonian channel flow. In particular, one solution family shows very intriguing behavior in terms of mean profiles: its upper and lower branches appear to approach the classical Newtonian profiles and an asymptotic profile found in viscoelastic turbulence, respectively. This asymptotic profile is the so-called maximum drag reduction, which has been heavily studied in a rheological drag reduction phenomenon. In this regard, our traveling wave solutions may play a role as promising targets for turbulence control strategies for drag reduction.

The second part of the talk will be dedicated to low Reynolds number flows (Stokes flow). The ability to manipulate small particles at the micro- and nanoscale plays a central role in a wide range of technological applications. To this end, electric fields offer a low-cost and efficient method of controlling particle motions. In this study, I investigate suspension dynamics that result from two nonlinear electrokinetic effects: dielectrophoresis and induced-charge electrophoresis. Both effects are shown to cause significant particle-particle interactions and the formation of complex patterns, which are analyzed in detail using large-scale numerical simulations. I then conclude by discussing applications of this study to the assembly of colloidal structures by electrophoretic deposition.