page_title: Natural convection
section_title: Pattern formation
hierarchical_section_title: Natural convection / Pattern formation
caption_attribution_description: Picture of the thermal field and its two-dimensional Fourier transform of a fluid under Rayleigh-Bénard convection.
context_page_description: Natural convection is a type of flow, of motion of a liquid such as water or a gas such as air, in which the fluid motion is not generated by any external source but by some parts of the fluid being heavier than other parts. The driving force for natural convection is gravity. For example if there is a layer of cold dense air on top of hotter less dense air, gravity pulls more strongly on the denser layer on top, so it falls while the hotter less dense air rises to take its place. This creates circulating flow: convection. As it relies on gravity, there is no convection in free-fall environments, such as that of the orbiting International Space Station. Natural convection can occur when there are hot and cold regions of either air or water, because both water and air become less dense as they are heated. But, for example, in the world's oceans it also occurs due to salt water being heavier than fresh water, so a layer of salt water on top of a layer of fresher water will also cause convection.
  Natural convection has attracted a great deal of attention from researchers because of its presence both in nature and engineering applications.
context_section_description: Convection, especially Rayleigh–Bénard convection, where the convecting fluid is contained by two rigid horizontal plates, is a convenient example of a pattern-forming system.
  When heat is fed into the system from one direction (usually below), at small values it merely diffuses (conducts) from below upward, without causing fluid flow. As the heat flow is increased, above a critical value of the Rayleigh number, the system undergoes a bifurcation from the stable conducting state to the convecting state, where bulk motion of the fluid due to heat begins. If fluid parameters other than density do not depend significantly on temperature, the flow profile is symmetric, with the same volume of fluid rising as falling.  This is known as Boussinesq convection.
  As the temperature difference between the top and bottom of the fluid becomes higher, significant differences in fluid parameters other than density may develop in the fluid due to temperature. An example of such a parameter is viscosity, which may begin to significantly vary horizontally across layers of fluid.  This breaks the symmetry of the system, and generally changes the pattern of up- and down-moving fluid from stripes to hexagons, as seen at right. Such hexagons are one example of a convection cell.
  As the Rayleigh number is increased even further above the value where convection cells first appear, the system may undergo other bifurcations, and other more complex patterns, such as spirals, may begin to appear.
caption: A fluid under Rayleigh–Bénard convection: the left picture represents the thermal field and the right picture its two-dimensional Fourier transform.
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