Stochastic Approaches to Transitions in Fluid Flows
September 12-14, Ithaca, NY, USA
Transition phenomena in flows of liquids and gases are of great fundamental interest from those occurring in microfluid flows to those in the large-scale atmospheric and oceanic circulation. Transitions in industrial and environmental flows are also of great practical interest. Dynamical systems approaches, such as bifurcation theory, have provided cornerstone analyses methods to study linear instabilities and subsequent nonlinear behavior. In the fluid dynamics community, these methods are considered to be useful either for low-dimensional models of the transition phenomena or for simple transitions (symmetry breaking, oscillatory instabilities) in high-dimensional deterministic models. A prominent classical example, which has been extensively studied, is the flow between rotating cylinders (Taylor-Couette flow), which undergoes successive transitions when the rotation rate of the inner cylinder is increased.
Over the past decade, many new techniques have been developed to deal with complex transition phenomena in high-dimensional stochastic models. These range from novel numerical methods, such as dynamical orthogonal field methods, to techniques from ergodic theory, such as transfer and Koopman operator estimation. These techniques enable the study of the mechanisms of much more complicated transition phenomena, such as the so-called wind-reversals in turbulent Rayleigh-Benard convection. In these flows, at least two different large-scale statistical equilibrium flow states occur in what is called the `ultimate turbulence' regime. The boundaries in parameter space where such states occur are not bounded by simple bifurcations but more generally are characterized as attractor `crises'.
It is timely to bring the different groups, working on method development as
well as applications, together. These groups are spread over (applied)
mathematics departments, engineering and physics departments. During the
workshop we aim to discuss the mathematical and numerical way forward, to
exchange experience with current applications of these new methods and to
explore new ones.
RF Smith School of Chemical and Biomolecular Engineering, Cornell University
CRITICS, H2020 ITN
Center for Applied Mathematics, Cornell University
National Science Foundation (NSF)