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In fluid thermodynamics, Rayleigh–Bénard convection is a type of natural convection, occurring in a planar horizontal layer of fluid heated from below, in which the fluid develops a regular pattern of convection cells known as Bénard cells.
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In this model the red fluid – initially on top, and afterwards below – represents a more dense fluid and the blue fluid represents one which is less dense. The Rayleigh–Taylor instability is another application of hydrodynamic stability and also occurs between two fluids but this time the densities of the fluids are different. [6]
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.
Hydrodynamics simulation of a single "finger" of the Rayleigh–Taylor instability. [1] Note the formation of Kelvin–Helmholtz instabilities, in the second and later snapshots shown (starting initially around the level =), as well as the formation of a "mushroom cap" at a later stage in the third and fourth frame in the sequence.
In fluid mechanics, the Rayleigh number (Ra, after Lord Rayleigh [1]) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. [ 2 ] [ 3 ] [ 4 ] It characterises the fluid's flow regime: [ 5 ] a value in a certain lower range denotes laminar flow ; a value in a higher range ...
Rayleigh–Bénard convection; Rayleigh–Plesset equation; Reynolds-averaged Navier–Stokes (RANS) equations; Reynolds transport theorem; Riemann problem; Taylor–von Neumann–Sedov blast wave; Turbulence modeling. Turbulence kinetic energy (TKE) K-epsilon turbulence model; k–omega turbulence model; Spalart–Allmaras turbulence model ...
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...