Skip to main content
Earth, Planets and Space
Fig. 3 | Earth, Planets and Space

Fig. 3

From: Linear analysis on the onset of thermal convection of highly compressible fluids with variable viscosity and thermal conductivity in spherical geometry: implications for the mantle convection of super-Earths

Fig. 3

Schematic illustrations on two-dimensional planes of the structures of incipient flows obtained for the cases with strong temperature-dependent viscosity \(r_\eta =10^8\) and various model geometries together with the values of a \(r_k=1\), b \(r_k=10\) and c \(r_k=100\). Note that for the cases with 3D spherical geometry we showed the flow structures in meridian planes assuming the incipient flows occurring with only zonal components (i.e., the spherical harmonic order \(m=0\)). Shown in color are the distributions of infinitesimal perturbations in temperature \(T'\) normalized by their maxima \(\Theta _\text {max}\). For the color scale for the distribution of \(T/\Theta _\text {max}\), see the scale bar at the bottom of the figure. Shown in solid lines are the contour lines of a “potential” \(\psi \) of the mass flux \(\overline{\rho }\varvec{v}'\). The contour lines are drawn for \(0.1\le |\psi /\psi _\text {max}|\le 0.9\) with the interval of 0.1, where \(\psi _\text {max}\) is the maximum of \(|\psi |\)

Back to article page