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 Rac∼E−^4/3 and ac∼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∈[2×10⁷,10⁹] which we explored, we also observe a transition in the heat transfer through the TC from a diffusivity-free regime where Nu≃0.38E2Ra^1.58 to a rotation-independent regime where Nu≃0.2Ra^0.33.