Fig. 3: Thermal structures of tidally-locked mantle.
From: Convective dynamics in mantle of tidally-locked exoplanets
Mean temperature distributions for (a) Θ = 0.33, (b) Θ = 1.00, and (c) Θ = 3.33. Colorbars intricate the boundary conditions for each condition. d Horizontally averaged temperature profiles using the whole domain, corresponding to (a, b, and c). e Horizontally averaged temperature profiles using the dayside only. f The Nusselt numbers Nu versus the hybrid Rayleigh numbers Ra. Colors correspond to Θ as indicated by the colormap, and symbols represent Pr. Conditions highlighted with orange circles are those shown as (a, b, and c). Solid lines are the best power-law fittings for the data with Θ ≤ 1 (Nu ∝ Ra0.11), Θ ≈ 3 (Nu ∝ Ra0.21), and Θ = 10 (Nu ∝ Ra0.21), obtained with the least-squares fitting. g The local Nusselt numbers \({{{{\rm{Nu}}}}}_{{{{\rm{top}}}}}^{{{{\rm{D}}}}}\) and \({{{{\rm{Nu}}}}}_{{{{\rm{bot}}}}}^{{{{\rm{D}}}}}\) (or \({{{{\rm{Nu}}}}}_{{{{\rm{bot}}}}}^{{{{\rm{N}}}}}\) and \({{{{\rm{Nu}}}}}_{{{{\rm{top}}}}}^{{{{\rm{N}}}}}\)) versus the hybrid Rayleigh numbers Ra. Upward triangles are \({{{{\rm{Nu}}}}}_{{{{\rm{top}}}}}^{{{{\rm{D}}}}}(={{{{\rm{Nu}}}}}_{{{{\rm{bot}}}}}^{{{{\rm{N}}}}})\) and downward triangles are \({{{{\rm{Nu}}}}}_{{{{\rm{bot}}}}}^{{{{\rm{D}}}}}(={{{{\rm{Nu}}}}}_{{{{\rm{top}}}}}^{{{{\rm{N}}}}})\). The latter is a positive definite, whereas the former can be negative to compensate for the massive horizontal heat transport at large Θ.
