Shadowgraph Measurements of Rotating Convective Planetary Core-Style Flows

The local scale of rotating convection, & ell;, is a fundamental parameter in many turbulent geophysical and astrophysical fluid systems, yet it is often poorly constrained. Here we conduct rotating convection laboratory experiments analogous to convecting flows in planetary cores and subsurface oceans to obtain measurements of the local scales of motion. Utilizing silicone oil as the working fluid, we employ shadowgraph imagery to visualize the flow, from which we extract values of the characteristic cross-axial scale of convective columns and plumes. These measurements are compared to the theoretical values of the critical onset length scale, & ell;crit, and the turbulent length scale, & ell;turb. Our experimentally obtained length scale measurements simultaneously agree with both the onset and turbulent scale predictions across three orders of magnitude in convective supercriticality (102 less than or similar to Ra similar to less than or similar to 105) $(1{0}<^>{2}\lesssim \tilde{Ra}\lesssim 1{0}<^>{5})$, a correlation that is consistent with inferences made in prior studies. We further explore the nature of this correlation and its implications for geophysical and astrophysical systems. Turbulent convection occurs within the liquid metal, water, and gaseous fluid layers of planetary interiors such as Earth's molten iron outer core, the subsurface oceans of icy moons, and the deep atmospheres of gas planets, respectively. The flow in each of these systems is strongly affected by the rotation of the planetary body. This rotation organizes the convecting flow into columnar structures elongated in the direction of the rotation axis. The horizontal width of the columnar flows is known as the local length scale of rotating convection, and is crucially the scale at which important planetary phenomena are driven, such as the induction of Earth's magnetic field. However, this quantity is not well known for geophysical systems. Here we conduct rotating convection laboratory experiments analogous to the convecting flows in planetary interiors, in which the local length scale is measured using a visualization technique called shadowgraph imaging. We compare our measurements to theoretical scaling arguments for laminar and turbulent rotating flows, and find a simultaneous agreement with both. This heretofore unappreciated correlation with both theoretical scales presents difficulties when interpreting laboratory and numerical experimental results in the context of more extreme geophysical flows, a challenge we address in the discussion. Laboratory convection experiments simulate turbulent flows within the polar regions of planetary cores and subsurface oceans The convective flow scale, measured via shadowgraph imaging, agrees with both the critical and turbulent scale predictions This agreement cannot be explained without advancement in convection theory, and implies mean field dynamo action occurs in Earth's core