Experimental study of the convection in a rotating tangent cylinder

Abstract

This paper experimentally investigates the convection in a rapidly rotating Tangent Cylinder (TC), for Ekman numbers down to E = 3.36 × 10 −6 . The apparatus consists of a hemispherical fluid vessel heated in its centre by a protruding heating element of cylindrical shape. The resulting convection that develops above the heater, i.e. within the TC, is shown to set in for critical Rayleigh numbers and wavenumbers respectively scaling as Ra c ∼ E −4/3 and a c ∼ E −1/3 with the Ekman number E. Although exhibiting the same exponents as for plane rotating convection, these laws reflect much larger convective plumes at onset. The structure and dynamics of supercritical plumes are in fact closer to those found in solid rotating cylinders heated from below, suggesting that the confinement within the TC induced by the Taylor-Proudman constraint influences convection in a similar way as solid walls would do. There is a further similarity in that the critical modes in the TC all exhibit a slow retrograde precession at onset. In supercritical regimes, the precession evolves into a thermal wind with a complex structure featuring retrograde rotation at high latitude and either prograde or retrograde rotation at low latitude (close to the heater), depending on the criticality and the Ekman number. The intensity of the thermal wind measured by the Rossby number Ro scales as Ro 5.33(Ra * q ) 0.51 with the Rayleigh number based on the heat flux Ra * q ∈ [10 −9 , 10 −6 ]. This scaling is in agreement with heuristic predictions and previous experiments where the thermal wind is determined by the azimuthal curl of the balance between the Coriolis force and buoyancy.Within the range Ra ∈ [2 × 10 7 , 10 9 ] which we explored, we also observe a transition in the heat transfer through the TC from a diffusivity-free regime where N u 0.38E 2 Ra 1.58 to a rotation-independent regime where N u 0.2Ra 0.33 .

Oscillatory thermal–inertial flows in liquid metal rotating convection

“…Livermore, Hollerbach & Finlay 2017; Aujogue et al. 2018; Favier & Knobloch 2020). The thermo-mechanical boundary conditions, though, differ significantly between our laboratory and DNS cylinders and the tangent cylinder free shear layer in the core.…”

“…However, in a recent experimental study it has been argued that slowly oscillatory, wall-mode-like flows form at the virtual boundary of the tangent cylinder, which is the virtual cylinder circumscribing Earth's solid inner core and aligned with the axis of rotation (Aujogue et al. 2018).…”

“…2010; Aujogue et al. 2018). Studying convection in fluids is attractive from a numerical point of view because the numerical costs are much lower than for high and low fluids (Shishkina et al.…”

Rotating thermal convection in liquid gallium: multi-modal flow, absent steady columns

“…With gravity parallel to both the rotation axis and the axis of the cylindrical container, the experimental set-up employed here, in particular, simulates convective processes occurring at high latitudes within a planetary core's tangent cylinder volume (Aurnou et al 2003;Aujogue et al 2018). In rapidly rotating spherical shells that approximate a planet's outer core geometry, thermal convection onsets outside the tangent cylinder (Busse 1970) or via equatorially trapped thermal inertial waves (Zhang & Schubert 2000).…”

Mean flow anisotropy without waves in rotating turbulence

“…x [25], where δz is the separation between two points along the z−axis. In practice, neither C ux (δz) nor C u ′ x (δz) fully decorrelate over h p ≤ z ≤ H. Hence, following [14], l z and l ′ z are defined at an arbitrary value β = 0.5 of the correlations, rather than 0.…”