Zonal Flows in Planetary Fluid Layers

Zonal flows are some of the most ubiquitous and pronounced fluid structures observed in the solar system. They are found in Earth's atmospheres and oceans, likely Earth's liquid outer core, and on the surfaces of the gas giant planets and dwarf stars. They are responsible for mechanisms such as the transfer of heat and momentum in atmospheres, which can lead to complex weather systems on Earth and other planets. Though they are essential to the dynamics of geophysical and astrophysical bodies, their formation, evolution, and breakdown is not well understood. However, it is known that zonal flows in planetary and stellar fluid systems are controlled by the complex interplay of convection, rotation, and magnetic forces. For my dissertation, I have carried out two projects that contribute to our understanding of how zonal flows, and thus geophysical and astrophysical bodies, are influenced by these forces.For the first project, in collaboration with my advisor Jonathan Aurnou and professor Susanne Horn from Coventry University, I developed and used a novel computational code to model the mechanism responsible for the damping of the large-scale, azimuthally directed ``jets'' observed at Jupiter's surface which is not well understood. Electromagnetic forces are thought to play a role as the planet's electrical conductivity increases radially with depth. In order to isolate the jet damping process, we carry out a suite of direct numerical simulations of quasi-two-dimensional, horizontally periodic Rayleigh-B\'{e}nard convection (RBC) with stress-free boundary conditions in the presence of an external, vertical magnetic field. Without a magnetic field, jets, punctuated by intermittent convective bursts, develop at Rayleigh ($Ra$, ratio of buoyancy to diffusion) numbers beyond $10^5$. Five primary flow regimes are found by varying $10^3 \leq Ra \leq 10^{10}$ and the Chandrasekhar number ($Ch$, ratio of Lorentz to viscosity) $0 \leq Ch \leq 10^6$: (i) steady convection rolls, (ii) steady magneto-columns, (iii) unsteady to turbulent magneto-plumes, (iv) horizontally drifting magneto-plumes, and (v) jets with intermittent turbulent convective bursts. We parse the parameter space using transition laws derived from the interaction parameter ($N$, ratio of Lorentz to inertia). The transition to the regime dominated by jets has the most immediate applications to the magnetic damping of Jovian jet flows, where the separation between jets and a magnetically constrained system occurs at a jet-based interaction parameter value of $N_J \approx 1$. We conclude by approximating the value of the Jovian interaction parameter as a function of depth, and find that the jets may brake at approximately $6,000$ km below the surface, which is deeper than recent estimates from NASA's Juno mission. This implies that mechanisms in addition to electromagnetic forces are likely required to fully truncate the jets.For the second project, in collaboration with Jonathan Aurnou and previous UCLA student Taylor Lonner, I developed the theoretical framework for and analyzed the data from a novel experimental device, which was built and run by Taylor. Through this project, we seek to increase our understanding of how turbulent fluid motions in Earth's liquid iron core sustain the geodynamo. The underlying flow, in which zonal jets may also play a key role, is influenced by planetary rotation, buoyancy and magnetic forces, and the geometry of the spherical shell. Recent numerical studies, which aim to characterize the dominant length and velocity scales in spherical rotating convection models, are limited by the long integration times required to access laboratory-scale turbulence. Furthermore, core-style turbulent convection is difficult to simulate with spherical shell experiments due to friction from solid container boundaries, and limitations, to date, on container size.In this project, we take advantage of strong laboratory turbulence by utilizing a cylindrical laboratory device that incorporates both the effects of boundary curvature, quantified by a topographic $\beta$-effect, and a predominantly cylindrically-radial centrifugal forcing, a proxy for gravity, to model low-latitude core convection. The experiment is characterized by a paraboloidal free surface and features a cylindrically-radial temperature gradient to drive convection. This novel set-up approximates the topographic $\beta$ profiles in a sphere, thus providing a meaningful proxy for low-latitude core convection. Three cases of rotating convection at 35, 50, and 60 RPM were run, with UDV velocity profiles, novel surface thermography, and basal thermometry for diagnostics. The combination of the topographic $\beta$-effect and convectively driven turbulence leads to the formation of coherent, alternating prograde-retrograde jets in all three experiments. The analysis in this thesis shows that the width of the jets closely follows a length scale known as the Rhines scale. The Rhines scale is expected when the topographic $\beta$-effect halts the transfer of energy from small to large scales that can occur in turbulent, rapidly rotating systems. Several other interesting flow features are noted here, including topographic and thermal Rossby waves and jet migration that closely match theoretical predictions. This device, with a paraboloidal free surface and laterally driven convection, can provide length and velocity scale estimates for the turbulent dynamics in low-latitude regions of Earth's outer core, and further elucidate the processes responsible for the geomagnetic field