Quantifying Chaotic Convection using a Dynamical Systems Approach

Recent advances using a dynamical systems approach to describe chaotic and turbulent fluid motion have generated exciting new insights. In this poster, we describe our efforts to quantify the geometry of chaos for Rayleigh-Bénard convection. Chaotic fluid convection can be described as a trajectory through infinite-dimensional state space. This state space is anticipated to be richly populated with unstable exact solutions which may include equilibria, periodic, and chaotic dynamics. The general picture that has emerged in the literature is that chaotic and turbulent dynamics can be viewed as a trajectory’s meandering through this intricate state space. In addition, the tangent space provides insights into the dynamics of small perturbations to the nonlinear trajectory as it progresses through the state space. Our goal is to use this dynamical systems approach to numerically explore the chaotic dynamics of Rayleigh-Bénard convection. We use a spectral element approach first to determine the approximate minimal size of a shallow periodic box domain that yields chaotic convection. We next describe our approach and progress toward computing the covariant Lyapunov vectors and exact coherent structures for chaotic convection in this minimal domain.

Supported by NSF CBET-2151389