Self-organisation in complex fluids

 I am at the beach this week and so a lot of time is spent staring at waves, clouds, sunsets, and patterns in the sand. There is a lot of beauty and a lot of beautiful science, most of which I know only a little about. For example, what is the essential physics and simplest theory that can explain the patterns below?


To start understanding the beautiful patterns seen in natural systems I have found helpful the two-page Quick Study in Physics Today

The universe in a cup of coffee by John Wettlaufer
Your morning java or tea is a rotating, cooling laboratory that reflects the physics of such large-scale phenomena as stellar dynamics and energy transport in Earth’s atmosphere and oceans. 
A nice demonstration is to put the hot liquid in a glass jar and then just add a few drops of cold milk and see the beautiful patterns that emerge.

The key idea is there is a balance between thermal bouyancy (hot air rises) and viscous stresses. This balance can lead to symmetry breaking and self-organisation. In planetary systems rotation can play a significant role, particularly when there is a balance of viscous forces and the coriolis force. This can lead to the formation of vortices. The Quick Study includes snapshops from a video that is worth watching,  supplementary material from this PRL.

The article also discusses the importance of Rayleigh-Benard convection in many geophysical phenomena. Something interesting I learnt is that this is actually a misnomer, as is often the case in science. According to Wikipedia, 
This pattern of convection, whose effects are due solely to a temperature gradient, was first successfully analyzed in 1916 by Lord Rayleigh (1842–1919).[16] Rayleigh assumed boundary conditions in which the vertical velocity component and temperature disturbance vanish at the top and bottom boundaries (perfect thermal conduction). Those assumptions resulted in the analysis losing any connection with Henri Bénard's experiment. This resulted in discrepancies between theoretical and experimental results until 1958, when John Pearson (1930– ) reworked the problem based on surface tension.[9] This is what was originally observed by Bénard.

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