Fig. 5

An overall structure of the stagnant-lid convection of \({\text{Ra}}=10^9\), \(r_k\equiv {k_\text {bot}/k_\text {top}}=30\) and \(r_\eta \equiv \eta _\text {top}/\eta _\text {bot}=10^7\) obtained in the numerical experiments of Kameyama and Yamamoto (2018). a The distributions of temperature T. The contour interval is 0.05. The color scale is indicated at the bottom of the figure. b Plots against dimensionless height z of the horizontally averaged temperature \(\langle {T}\rangle \) (thick red line) at the height of z. Also shown for comparison by thin black lines are the plots of several adiabats against z, while by dotted black lines are the vertical profiles of temperature \(\overline{T}\) given by steady one-dimensional heat conduction in the vertical direction. c Plots against z of the magnitude of vertical gradient of \(\langle {T}\rangle \) (red solid line) at the height of z. Also shown for comparison by blue dashed line is the magnitude of adiabatic temperature gradients given by \(\langle {T}\rangle \) at z. d The distributions of potential temperature \(T_\text {pot}\). The color scale is indicated at the bottom of the figure. The contour lines for \(T_\text {pot}\) are shown at the interval of 0.005 only in the range of \(T_\text {pot}\ge 0.49\). e Plots against z of the horizontally averaged potential temperature \(\langle {T_\text {pot}}\rangle \) at the height of z. f Plots against z of the root-mean-squares of the magnitude of the velocity vector \(\sqrt{\langle {v^2}\rangle }\) (red solid line) and the vertical velocity \(\sqrt{\langle {v_z^2}\rangle }\) (blue dashed line) at the height of z