Closure and Order-Reduction of Turbulent Dynamical Systems

Turbulent dynamical systems are characterized by both a large dimensional phase space and a large dimension of persistent or intermittent instabilities (i.e., a large number of positive Lyapunov exponents on the attractor). They are ubiquitous in many complex systems with fluid flow such as, engineering turbulence at high Reynolds numbers, confined plasmas, as well as atmospheric and oceanic turbulence.

The scope of this work is (1) to design effective turbulent closure schemes that respect the synergistic activity between unstable linear dynamics, nonlinear energy transfers, and stable dynamics, which is apparent in turbulent systems, and (2) to develop order-reduction techniques that take into account the nonlinear energy transfers associated with the omitted modes.