Rapidly rotating Rayleigh-Bénard convection in liquid metals
Geophysics
Final Report Abstract
In this project turbulent rotating Rayleigh-Bénard convection was investigated, with the focus on liquid metal as working fluid. Comprehensive direct numerical simulations (DNS) have been performed, and a close collaboration with laboratory experiments conducted at the SpinLab at UCLA has been established. The obtained results are relevant for several areas of planetary physics, atmospheric sciences and geophysics. We were particularly interested in applying our findings to planetary core convection and tornado-like vortices. The code goldfish has been advanced to incorporate centrifugal buoyancy effects as well as magnetic fields to simulate these systems. Combined laboratory-numerical simulations in non-rotating liquid gallium convection in an aspect ratio two cylinder have revealed that the large-scale circulation (LSC) can perform a fully 3D motion resembling a twirling jump rope. At this aspect ratio the LSC has the greatest freedom to move, and thus, this study provides an essential link between studies in confined geometries used in experiments and simulations and the effectively unconfined fluid layers in natural settings, such as the Sun or planetary atmospheres and cores, where an agglomeration of LSCs forms larger patterns. The discovery of the jump rope LSC mode implies that the currently accepted paradigm of a quasi-planar oscillating LSC needs to be augmented. When rotation is added to the system of Rayleigh-Bénard convection, the flow becomes strongly multimodal in a low-Prandtl fluid. Flow fields obtained by DNS were analysed using the sparsity-promoting variant of the dynamic mode decomposition (DMD). Utilising this technique, the coherent structures governing the dynamics of the flow were extracted, as well as their associated frequencies. DMD revealed that there are high-frequency modes that are a superposition of oscillatory columns and cylinder-scale inertial waves. We found coexisting prograde and retrograde modes, as well as quasi-axisymmetric torsional modes. For higher supercriticalities, the flow also becomes unstable to wall modes. These low-frequency modes can both coexist with the oscillatory modes and even couple to them. We further showed, that the characteristic feature of moderate-Prandtl number fluids, the quasi-steady Taylor columns, is entirely absent in low-Prandtl number flows. Coriolis-centrifugal convection has been investigated to study more realistic flows. Typically, centrifugal buoyancy is wholly neglected in numerical simulations and attempted to be kept small in laboratory experiments. However, especially in the modern state-of-the-art large-scale rotating convection devices, this is experimentally challenging. It had hitherto been unknown, how centrifugation affects the turbulent regime of rotating convection. We have shown that somewhat counter-intuitively, centrifugal effects set in earlier at smaller aspect ratios. Further, we showed analytically that the direct effect of centrifugal buoyancy yields a reduction of the heat transport, but indirectly, it can cause a simultaneous increase of the viscous dissipation and thereby the heat transport through a change of the flow morphology. These direct and indirect effects yield a net heat transport suppression in the regime where Coriolis and centrifugal force are of equal importance and a net heat transport enhancement in the quasi-cyclostrophic regime. In addition, we demonstrated that Coriolis-centrifugal convection can provide a simplified, yet self-consistent, model system for tornadoes, hurricanes, and typhoons. Thus, it turned out, that centrifugal buoyancy is, in fact, of greater importance than previously thought.
Publications
- 2017. Prograde, retrograde and oscillatory modes in rotating Rayleigh–Bénard convection. J. Fluid Mech. 831, 182–211
Horn, S. & Schmid, P. J.
(See online at https://doi.org/10.1017/jfm.2017.631) - 2018. Jump Rope Vortex in Liquid Metal Convection. Proc. Natl. Acad. Sci. 115, 12674–12679
Vogt, T., Horn, S., Grannan, A. M. & Aurnou, J. M.
(See online at https://doi.org/10.1073/pnas.1812260115) - 2018. Regimes of Coriolis-Centrifugal Convection. Phys. Rev. Lett. 120, 204502
Horn, S. & Aurnou, J. M.
(See online at https://doi.org/10.1103/PhysRevLett.120.204502) - 2019. Rotating convection with centrifugal buoyancy: Numerical predictions for laboratory experiments. Phys. Rev. Fluids 4 (7), 073501
Horn, S. & Aurnou, J. M.
(See online at https://doi.org/10.1103/PhysRevFluids.4.073501)
