Finite amplitude thermal convection with variable gravity (Q5932785)

The authors study the finite amplitude thermal convection in a horizontal layer of infinite Prandtl number fluid with variable gravity. Gravity is restricted to vary quadratically with respect to the vertical variable. A perturbation technique based on a small parameter (the ratio of the vertical to horizontal dimensions of convective cells) is applied to examine the convective modes whose amplitudes can be either small or of order unity. Stability of these solutions is investigated with respect to three-dimensional disturbances. The variable gravity function introduces two new non-dimensional parameters. For certain range of these parameters, the authors show that double or triple cellular structures can be realized in the vertical direction. Hexagonal patterns are preferred for sufficiently small convective amplitude, while square patterns can become dominant for larger values of convective amplitude. Variable gravity can also affect significantly the wavelength of cellular patterns and the onset of convective motion.