Horizontal convection: Effect of aspect ratio on Rayleigh number scaling and stability

Horizontal convection in a rectangular enclosure driven by a linear temperature profile along the bottom boundary is investigated numerically using a spectral-element discretization for velocity and temperature fields. A Boussinesq approximation is employed to model buoyancy. The emphasis of this study is on the scaling of mean Nusselt number and boundary layer quantities with aspect ratio and Rayleigh number.At low Rayleigh number, Nusselt number and boundary layer thickness are found to be independent of Rayleigh number but dependent on aspect ratio. At higher Rayleigh numbers, convective flow dominates, and Nusselt number, boundary layer thickness and peak boundary layer velocity become independent of aspect ratio. In this regime, the Rayleigh number scaling of these quantities agrees well with exponents predicted by theory, with respective values of 1/5, −1/5 and 2/5. Unsteady flow develops at a critical Rayleigh number independent of aspect ratio, and the development of unsteady flow is found to lead to an increase in the Nusselt number scaling exponent from 0.2 to approximately 0.3, which is closer to the theoretical upper bound than has yet been reported in the study of horizontal convection flows.