Three-dimensional localized Rayleigh–Bénard convection in temperature-dependent viscosity fluids

The stability range of localized three-dimensional convective cells in Rayleigh–Bénard convection is determined across a broad range of viscosity contrasts between the boundaries of the fluid layer, for both free-slip and no-slip boundary conditions. The localized convective cell is generated by a finite-amplitude initial perturbation at subcritical Rayleigh numbers. It appears as a radially symmetric upwelling surrounded by nearly stagnant fluid, which can be characterized as an extremely weak plume. The parameter range in which three-dimensional localized upwellings are stable is slightly larger than that found for two-dimensional rolls. With free-slip boundaries, the lowest viscosity contrast at which the three-dimensional system can exhibit localization is approximately 35, about four times lower than for two-dimensional rolls. The wide range of conditions under which localization occurs in three-dimensional systems due to temperature-dependent viscosity further emphasizes its importance for the understanding of processes within the interiors of planetary bodies and for industrial applications.