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