CAREER: Innovation in Turbulence Research and the Scientific Computing Curriculum

University Of New Hampshire, Durham NH

Investigators

Abstract

PI: Gibson, John F. Proposal Number: 1554149 The proposed research is focused on the computational and theoretical investigation of the fundamental turbulent flow phenomena that lead to the generation and sustainment of turbulence. The proposed approach to this problem is a rigorous mathematical treatment for laminar-to-turbulence transition and then an extension of these concepts to fully turbulent flows. The results of this research could have an impact on engineering and technology applications where turbulence is important, and this means most of the flows that surround us and most of the flows in the process industry. Recent research has shown that exact coherent structures in the form of unstable equilibria, traveling waves, and periodic orbits can be computed precisely for moderately turbulent shear flows, by treating well-resolved numerical simulations of the Navier-Stokes equations as very high-dimensional dynamical systems. These invariant solutions capture the form and behavior of coherent structures observed in experiment and simulation since the 1950s, and they suggest an approach for leveraging ideas from dynamical systems theory to exploit the inherent low-dimensionality of self-organized structures in turbulent shear flows. The goals of the proposed research are to develop these ideas into a rigorous understanding of the structure and dynamics of turbulence at moderate Reynolds numbers, and to extend successes of this approach to high Reynolds numbers. Specific objectives of the proposed research are: (1) to develop a comprehensive database of exact coherent structures for pressure-driven channel flow, from moderate to high Reynolds numbers, and (2) to rigorously derive quantitatively accurate and predictive reduced-order models of turbulent shear flow based on the dynamics of these structures. Successful achievement of these objectives will form the basis for a precise spatiotemporal understanding of momentum and vorticity transport and turbulent energy production in wall-bounded shear flows, and will demonstrate the utility of exact coherent structures and high-dimensional dynamical systems theory in analyzing turbulence. There are also plans to modernize the computational mathematics curriculum in New Hampshire and bring the teaching of Julia (the hybrid computing language to be used in the proposed research) into the classroom.