On the smooth transition to convection

It is shown that small imperfections or impurities always present in experiments may account for the smooth transitions from conduction to convection observed at a critical Rayleigh number in viscous fluid heating. The imperfections embrace several types of thermal noise in the applied temperature, including those due to irregularities in the fluid container, or imperfect insulation of the container walls. When a small parameter characterizing the amplitude of this noise is introduced into the classical Boussinesq theory of thermal convection, the smooth transitions may be explained.