{"id":5519,"date":"2020-12-18T05:59:57","date_gmt":"2020-12-18T10:59:57","guid":{"rendered":"https:\/\/blogs.sw.siemens.com\/simulating-the-real-world\/?p=5519"},"modified":"2026-03-27T09:00:31","modified_gmt":"2026-03-27T13:00:31","slug":"chaotic-fluid-dynamics-part-3-wheels","status":"publish","type":"post","link":"https:\/\/blogs.sw.siemens.com\/simulating-the-real-world\/2020\/12\/18\/chaotic-fluid-dynamics-part-3-wheels\/","title":{"rendered":"Chaotic Fluid Dynamics Part 3 \u2013 Wheels"},"content":{"rendered":"\n

Rayleigh\u2013B\u00e9nard convection involves the transport of heat from a hot bottom surface to a cold top surface. If the temperature difference between top and bottom is big enough, fluid rolls up into counter-rotating convection cells that transport the heat. Under certain conditions these convection cells flip-flop chaotically between rotating in a clockwise and counter-clockwise directions. Ed Lorenz’s famous ‘strange attractor’ is a graphical description of this behaviour:<\/p>\n\n\n

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Lorenz Attractor. Convection intensity vs Temperature variation vs Temperature difference for Rayleigh\u2013B\u00e9nard convection when Prandtl number = 10, Rayleigh number is 28 times greater than the critical value and aspect ratio of model is 2:1.<\/figcaption><\/figure><\/div>\n\n\n

A Pedagogic Example<\/h2>\n\n\n\n

The Malkus waterwheel<\/a> is a fluid-mechanical model that intends to capture the same physical mechanisms as Rayleigh\u2013B\u00e9nard convection. A tap\/faucet supplies water at the top of the wheel, filling freely swinging cups positioned on the wheel periphery. Each cup has a hole in the bottom allow the liquid to slowly leak out:<\/p>\n\n\n\n