Editing Convection (section)

==Pattern formation==
[[Image:Convection1.png|thumb|right|A fluid under [[Rayleigh–Bénard convection]]: the left picture represents the thermal field and the right picture its two-dimensional [[Fourier transform]].]]

Convection, especially [[Rayleigh–Bénard convection]], where the convecting fluid is contained by two rigid horizontal plates, is a convenient example of a [[Pattern formation|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 theory|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 approximation (buoyancy)|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 [[spiral]]s, may begin to appear.