Session H13: Geophysical Fluid Dynamics: Rotating Flows (5:45pm - 6:30pm CST)

Rapidly rotating Rayleigh-Benard convection under the influence of external magnetic field

Motivated by the small-scale dynamics of the Earth's core, we study numerically rapidly rotating Rayleigh-B\'{e}nard magnetoconvection with a horizontal field and tilted rotation. We consider small-scales, low Ekman numbers $10^{-5}\div10^{-7}$ and in the regime where magnetic diffusivity much larger than thermal diffusivity $q = \kappa/\nu\sim10^{-4}$. The parameters are chosen to investigate the nature of small scale instabilities in the Earth's core which are driven by rotation of the planet and magnetic field generated by the geodynamo. Our local simulation focused on formation and time evolution of parasitic modes on elevator modes, which are driven by inertia. Along with 3D numerical studies which were carried out in open source spectral solver DEDALUS, we provide qualitative analysis of nonlinear solutions, and analyse the turbulent transport relevant for the evolution of larger scales.   

A Statistical Closure for Turbulent Zonal Jets based on the Generalized Quasilinear Approximation

The generalized quasilinear (GQL) approximation was applied recently to the simulation of zonal jets on the spherical surface and on the beta plane. GQL allows for a systematic improvement over quasilinear equations by generalizing the conventional Reynolds decomposition: rather than decomposing fields into a mean and fluctuation, GQL projects them into large- and small-scale zonal modes. In this framework, considerable accuracy can be achieved in regimes with strong driving even when few large-scale zonal modes are retained. In the present work, we derive a statistical closure based on cumulant expansions starting from the GQL approximation. The resulting generalised cumulant expansion (GCE2) equations allow for direct statistical simulation of the first and second cumulants. Thus, GCE2 retains the generalisation embodied in GQL and also precludes the need for Direct Numerical Simulation in order to collect statistics. We use GCE2 to simulate a deterministically-forced barotropic jet on the spherical surface and on the beta plane, and evaluate its performance in comparison to GQL. Plausible applications of GCE2 to other astro/geophysical problems are discussed.   

Convection in the Full Sphere: Predicting the Rossby Number of Mean & Fluctuating Flows

We use Dedalus to study numerical simulations of rotating, Boussinesq convection in a full-sphere geometry which fully resolves the singularity at the origin. In order to understand the behavior of convection in the fully-molten cores of young terrestrial planets and the cores of massive stars, it is crucial to understand the behavior of convection in this full-sphere geometry. In this work, we study a large suite of simulations in which the strength of convective driving and planetary rotation (quantified by the Rayleigh and Ekman numbers) vary by many orders of magnitude. We explore the structure and magnitude of mean flows, such as differential rotation, as well as the fluctuations away from these mean flows. We show how to \emph{a priori} predict the importance of rotation (quantified by the Rossby number) on these flows, and we ground these predictions in a fundamental understanding of the forces balances which appear in the simulations.   

Tornado Formation by Rotating Plumes

Through laboratory experiments, numerical simulations and theory, we examine the evolution of plumes as they are influenced by background rotation in a uniform-density ambient fluid. In all cases the source Rossby number is sufficiently large that rotation does not directly affect the plume itself at early times. However, on a time scale on the order of half a rotation period, the plume deflects from the vertical axis. In some experiments and simulations, the deflection persists and the flow precesses about the vertical axis. In other cases, shortly after being deflected, the build up of swirling motion around the plume causes it to laminarize near the source to form a vortex that then extends vertically away from the source to form a columnar vortex, which we refer to as a tornado. For this phenomenon to occur, the plume at the source must be ``lazy''. The dynamics governing plume deflection and possible laminarization are revealed through analysis of three-dimensional simulations.   

On the asymmetry of cyclones and anticyclones in the cellular regime of rotating Rayleigh-Benard convection

In rotating Rayleigh-Benard convection, rotation breaks the symmetry on its rotating axis, making the cyclones and anticyclones unequal in size and magnitude. A theory of such vorticity asymmetry is proposed specifically for the rotation-dominated (called cellular or geostrophic) regime. The property that columnar updraft and downdraft plumes are densely packed is shown to make the vertical vorticity profile at the vortex center approximately linear with height via thermal wind relation. This simplification of morphology enables a linkage between the vorticity strength of a plume which is quantified by vorticity Rossby number Ro$_{\mathrm{V}}$, and the vorticity magnitude difference between the plumes' cyclonic and anticyclonic ends which is quantified with a nondimensional asymmetry factor $\delta $. The relationship between $\delta $ and Ro$_{\mathrm{V}}$ is found to be constrained by vertical vorticity equation alone. An analytical solution is found using asymptotic expansion, which shows that the asymmetry is generated mainly by the vertical advection and stretching of vertical vorticity in fluid interior, and is modified by the Ekman layer dynamics.   

Not Participating

Granular agglomerates held together by self-gravity are called rubble-piles. Several of them are believed to have a solid core. In this work we explore the surface mechanics of rotating top-shaped asteroids like Ryugu and Bennu using a shallow granular flow theory derived from mass and momentum balance laws. Additionally, occurrence of surface phenomena is likely to change their spin rate. We model this by conserving the angular momentum of the system. After a preliminary investigation of the dynamics of a single grain on a gravitating double-cone top, we study the effect of different landsliding events on it's spin rate. The travelling of dunes and the effect of the Coriolis force on mass shedding are also looked into. We find that pole-ward and equator-ward motion of surface regolith increase and decrease the spin rate respectively. Dunes move towards equilibriation points defined by the location where effective tangential gravity is zero. The Coriolis force abates mass shedding when the regolith motion is retrograde i.e. azimuthal velocity is in a direction opposite to the asteroid's rotation.