Experimental study of the convection in a rotating tangent cylinder

Abstract

This paper experimentally investigates the convection in a fast rotating Tangent Cylinder (TC), for Ekman numbers down to $E=3.36\times10^{-6}$, in a configuration relevant to the liquid core of the Earth. In the apparatus, the TC results from the Proudman-Taylor constraint incurred by rotating 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 $Ra_c\sim E^{4/3}$ and $a_c\sim E^{1/3}$ with the Ekman number $E$. Though exhibiting the same exponents as for plane rotating convection, these laws are indicative of much larger convective plumes at onset. The structure and dynamics of these 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 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 latitudes (close to the heater), depending on the criticality and the Ekman number. Nevertheless the intensity of the thermal wind measured by the Rossby number scales as $Ro\sim 0.85(Ra_q^*)^{0.41}$ with the Rayleigh number based on the heat flux $Ra_q^*$. This scaling suggests that the convection in the TC is driven by quasi-geostrophic dynamics, a finding supported by the scaling for the rotation-normalised Nusselt number $Nu^{*} \sim (Ra_{q}^{*})^{5/9}$.