Regimes of rotating convection in an experimental model of the Earth’s tangent cylinder

Summary The flow in the liquid core of the Earth is controlled by the interplay between buoyancy and the Coriolis force due to planetary rotation. Fast rotation imposes the Taylor-Proudman Constraint (TPC) that opposes fluid motion across an imaginary cylindrical surface called the Tangent Cylinder (TC) obtained by extruding the equatorial perimeter of the solid inner core along the rotation direction, and up to the core-mantle boundary (CMB). Because this boundary is imaginary, however, mass and heat transfer through the TC, as well as the regimes of convection within the TC may differ from those inside a solid cylinder with well-defined boundary conditions. How to best model this peculiar boundary is to date unclear, and so is how its influence on the flow inside and outside the TC differs from that of canonical boundary conditions. This impedes our understanding of the flow in the polar regions of the core. To clarify this question, we mimic the TC geometry experimentally in the Little Earth Experiment 2 (LEE2), where the CMB is modelled as a cold, cylindrical vessel filled with water, with a hot cylinder inside it acting as the inner solid core. The vessel is filled with water so as to optically map the velocity field in regimes of supercriticality and rotational constraint consistent with those of the Earth (Rayleigh number up to R\!a=191 times critical and ratio of inertial to Coriolis forces in the range 10−3 to 10−1). We find that although the regimes of convection within the TC broadly resemble those within a cylinder with solid impermeable insulating walls (CSIIW), the TC boundary introduces differences of particular significance in the context of the Earth’s core. The main new mechanism arises out of the baroclinicity near the cold lateral boundary of the vessel, which drives inertia at the outer boundary of the TC, as convection in the equatorial regions of the Earth’s core does. The baroclinicity just outside the TC suppresses the classical wall modes found in CSIIW and the inertia there causes an early breakdown of the TPC at the TC boundary. The breakdown appears locally at low supercriticality R\!a 3 and then over the entire TC surface at R\!a 36. The flow remains dominated by the Coriolis force even up to R\!a=191, but inertia near the TC boundary drives a transition to geostrophic turbulence around R\!a 36. It also promotes the emergence of a few large structures, of similar topology to the flux patches observed in geomagnetic data. The heat flux escapes increasingly through the TC boundary as the TPC there becomes weaker. It eventually bypasses the axial heat flux and homogenises temperature laterally. This translates into a diffusivity-free scaling expressed in terms of the diffusivity-free counterparts of the Nusselt and flux-based Rayleigh numbers as N\!u^*~ (R\!aq^*)1/3, that is independent of rotation. Hence inertia driven by baroclinicity outside the TC provides a convenient route to geostrophic turbulence, which is otherwise difficult to reach in experiments. These results also highlight a process whereby the convection outside the TC may control turbulence inside it and bypass the axial heat transfer. We finally discuss how Earth’s conditions, especially its magnetic field may change how this process acts within the Earth’s core.