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 | ||
Revision as of 17:30, 2 November 2005
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 
