The effect of rotation on radial horizontal convection and Nusselt number scaling in a cylindrical container

The effect of rotation on horizontal convection flow in a free-surface cylindrical enclosure driven by a radially increasing temperature profile along the base is investigated numerically and theoretically. The governing equations of mass, momentum and energy subject to Boussinesq approximation applied to gravity term, have been discretised using a spectral-element method for velocity and temperature fields. Results of a scaling analysis are compared with numerical simulations at a fixed Prandtl number Pr=6.14Pr=6.14, Reynolds numbers up to 3200, and Rayleigh number up to 3.2×10113.2×1011 in an enclosure with height-to-radius ratio H/R=0.4H/R=0.4. The results show that heat transfer in rotating horizontal convection is significantly affected by rotation, and where rotation effects are significant, Nusselt number scalings adapted from Park and Whitehead and Stern describe the behaviour at moderate and high rotation rates, respectively. A scaling analysis is conducted to describe the suppression of convective flow at high rotation rates. Flows are characterised in terms of a rotation parameter and are divided into three regimes: a diffusive regime with Nusselt number independent of thermal forcing and rotation, a rotation-affected convective regime, and a convective regime unaffected by rotation at sufficiently high Rayleigh number.