Turbulence is of tremendous importance in a wide range of astrophysical and geophysical flows. Unfortunately, the equations of motion are notoriously difficult to solve. I will introduce an approach to low-dimensional modeling of turbulent flows that focuses on the the large, coherent flow structures which often occur, such as convection rolls in the atmosphere or ocean currents. These structures and their dynamics can be described with relatively few variables using a model consisting of stochastic ordinary differential equations. As a model system to test this approach, we use Rayleigh-Benard convection experiments, in which a container is filled with water and heated from below. Buoyancy drives a flow which organizes into a roll-shaped circulation. This convection roll exhibits a wide range of dynamics including erratic meandering, spontaneous flow reversals, and several oscillation modes, all of which are reminiscent of phenomena observed in astro/geophysical flows. A simple model of stochastic motion in a potential quantitatively reproduces all of these observed flow dynamics. The potential term is a direct function of boundary geometry (i.e. topography), and is found to accurately predict the different flow dynamics observed in experiments with different boundary geometries. This approach may lead to more general and relatively easy to solve models for turbulent flows with potential applications to climate, weather, and even the turbulent dynamo that generates Earth’s magnetic field.
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Institute for Planets and Exoplanets
