#### Presentation Title

Determining Lyapunov Exponents for Turbulent Rayleigh-Benard Convection

#### Faculty Mentor

Dr. Janet Scheel

#### Start Date

18-11-2017 12:30 PM

#### End Date

18-11-2017 1:30 PM

#### Location

BSC-Ursa Minor 129

#### Session

Poster 2

#### Type of Presentation

Poster

#### Subject Area

physical_mathematical_sciences

#### Abstract

Rayleigh-Benard Convection (RBC) is a controlled model for studying nonequilibrium fluid dynamics. The apparatus for studying the dynamics of RBC consists of a closed, rigid, upright container holding a fluid that is heated uniformly and consistently across the bottom cross section. The parallel top plate of the container is held at a uniformly colder temperature than the bottom plate. The temperature difference between the parallel plates drives heat flow through the fluid from the bottom to the top, initially via conduction, then via both conduction and convection as this temperature difference increases. In nonlinear dynamical systems such as turbulent RBC, Lyapunov exponents measure the exponential sensitivity to initial conditions, while the Nusselt number measures the heat flux through a cross section of the container. Leading order Lyapunov exponents and Nusselt numbers were tracked over time for cylindrical Rayleigh Benard Convection systems of aspect ratio (ratio of diameter to depth) close to one. Time dependence in the Nusselt number and positive leading order Lyapunov exponents suggest some degree of spatiotemporal chaos in the systems at various Rayleigh numbers. As expected, a higher degree of chaos is exhibited in more turbulent systems, which are at a much higher temperature difference than that required for the onset of convection.

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Determining Lyapunov Exponents for Turbulent Rayleigh-Benard Convection

BSC-Ursa Minor 129

Rayleigh-Benard Convection (RBC) is a controlled model for studying nonequilibrium fluid dynamics. The apparatus for studying the dynamics of RBC consists of a closed, rigid, upright container holding a fluid that is heated uniformly and consistently across the bottom cross section. The parallel top plate of the container is held at a uniformly colder temperature than the bottom plate. The temperature difference between the parallel plates drives heat flow through the fluid from the bottom to the top, initially via conduction, then via both conduction and convection as this temperature difference increases. In nonlinear dynamical systems such as turbulent RBC, Lyapunov exponents measure the exponential sensitivity to initial conditions, while the Nusselt number measures the heat flux through a cross section of the container. Leading order Lyapunov exponents and Nusselt numbers were tracked over time for cylindrical Rayleigh Benard Convection systems of aspect ratio (ratio of diameter to depth) close to one. Time dependence in the Nusselt number and positive leading order Lyapunov exponents suggest some degree of spatiotemporal chaos in the systems at various Rayleigh numbers. As expected, a higher degree of chaos is exhibited in more turbulent systems, which are at a much higher temperature difference than that required for the onset of convection.