If you want to see one of the key differences between Eastern and Western thought, look at the classical art of the two cultures. The West is deeply concerned with static form … the naturalistic reproduction of shape. The Eastern tradition … is like the apotheosis of a sketcher’s technique…. It is, in short, an art that embraces change….
It’s not easy to paint something that is never still. Yet [a] traditional Chinese artist .. capture[s] the fundamental forms of motion. This is nowhere more clear than in the ways in which these two traditions … depict … flowing water….
We like to think that the calculus of Newton and Leibniz gave us a tool to handle the science of change; but for a problem like turbulence, calculus … provides a formalism … we can stare at this equation and realize that we can’t solve it, and in the end we are forced to go back, like … Jean Leray … and gaze instead at the real thing…[the Seine].
Like so many other pattern-forming processes, convection is a non-equilibrium phenomenon…. heat flow need not itself involve motion of the bulk fluid: if the temperature differences are only slight or gradual, heat can be redistributed by conduction….
Convection is … brought about by the fact that a warmer fluid is generally less dense than a cooler one…. One can watch convection currents carry dust aloft above radiators in a heated room—the dust traces out the otherwise invisible motions of the air….
For a heating rate just sufficient to start convection the [Bénard] cells are generally sausage-like [oblong square] rolls…. Neighbouring roll cells circulate in opposite directions…Clearly, the symmetry of the fluid is broken…
As in the case of Turing patterns or viscous fingering, a particular pattern with a particular size has been selected; yet, a moment before its appearance, there was nothing in the system to give any clue of its imminent arrival or its scale.
In 1916 Lord Rayleigh tried to understand what triggered the sudden appearance of this convection pattern. It does not arise as soon as there is a [temperature] gradient…. Rather, a certain threshold in temperature difference has to be reached…and this threshold depends on the composition and the depth of the fluid….
The Rayleigh number is basically a measure of the balance between the forces that promote convection (the buoyancy of the fluid…) and those that oppose it (the frictional forces that arise from the fluid’s viscosity, and the thermal diffusivity…). … Only when the driving force (the temperature gradient) becomes big enough to overcoe …. resistance do the convection cells appear. … one can map out the generic behaviour of convecting fluids as a function of Rayleigh number, without having to worry about whether the fluid is water, oil or glycerine.. For what it is worth, the critical Rayleigh number for the start of convection is 1708.
Philip Ball, The Self-Made Tapestry: Pattern Formation in Nature