Transitions and scaling in horizontal convection driven by different temperature profiles

Horizontal convection has been used as an idealised model of the ocean overturning circulation, where some non-uniform buoyancy forcing profile is imposed along a horizontal boundary. Several different driving temperature profiles have been chosen for past numerical and laboratory studies, likely for convenience, yet the effect of the shape of the chosen profile on the resulting horizontal convection flow remains unexplored. Here high order numerical simulation is used to investigate this problem. Time independent, periodic and chaotic regimes are identified as functions of Rayleigh number (Ra) and profile shape, with a step temperature profile being found to be more unstable than a linear temperature profile. Using a nonlinear Stuart–Landau analysis, the primary instability is consistently found to occur through a supercritical (non-hysteretic) bifurcation. This research highlights the importance of the horizontal buoyancy forcing profile in determining the thermal forcing required to produce instability in horizontal convection. In addition, Nusselt number scales to Ra^1/5 in the fully convective regime, with scaling exponents elevating beyond Ra≈10¹⁰. This elevated scaling was more pronounced for the linear thermal boundary profile than for the step profile over the computed Rayleigh numbers range.