# Langevin equation

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where <math> dW(t) </math> is a Wiener process. | where <math> dW(t) </math> is a Wiener process. | ||

- | <math> u' </math> is the turbulence intensity and math> \tau </math> | + | <math> u' </math> is the turbulence intensity and <math> \tau </math> a Lagrangian time-scale. |

Th finite difference approximation of the above equation is | Th finite difference approximation of the above equation is | ||

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The Wiener process can be understood as Gaussian random variable with 0 mean | The Wiener process can be understood as Gaussian random variable with 0 mean | ||

and variance <math> dt</math> | and variance <math> dt</math> | ||

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+ | {{Stub}} |

## Latest revision as of 14:30, 15 June 2007

The stochastic differential equation (SDE) for velocity component , the Langevin equation is

where is a Wiener process. is the turbulence intensity and a Lagrangian time-scale.

Th finite difference approximation of the above equation is

where is a standardized Gaussian random variable with 0 mean an unity variance which is independent of on all other time steps (Pope 1994). The Wiener process can be understood as Gaussian random variable with 0 mean and variance