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Earth, Planets and Space
Fig. 1 | Earth, Planets and Space

Fig. 1

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. 1

Thermal state in the fluid layer of different model geometries estimated for various values of \(r_k\) in the range of \(1\le {r_k}\le 100\). a Plots against height from the bottom surface of the reference temperature \(\overline{T}\). Also shown by thin dashed lines for comparison are the plots of several adiabats against height. b Plots against height of the magnitude of the gradient of temperature \(|{\text{d}}\overline{T}/{\text{d}}r|\) (or \(|{\text{d}}\overline{T}/{\text{d}}z|\)) in the radial (vertical) directions. c Plots against height of the potential temperature \(\overline{T}_\text {pot}\). Also shown by thick gray lines are the ranges of depths where the thermal stratification given by \(\overline{T}\) is stable owing to the increase in \(\overline{T}_\text {pot}\) with height

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