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مکانیک::
معادله ناویر-استوکس
This is an instance of what is called closure: replacing the infinite hierarchy of moment equations derivable from the Navier-Stokes equations by a finite number of equations for suitable statistical quantities such as two-point corre- lations.
Six years later he discovered a more serious defect: the random coupling model and the DIA fail invariance under random Galilean transformations.10 Ordinary Galilean invariance - for the Navier-Stokes equations - is the obser- vation that if (u(x, t), p(x, t)) are the velocity and pressure fields which solve the Navier-Stokes equations in the absence of boundaries or with periodic boundary conditions, then (u(x - Vt, t) + V, p(x - Vt, t)) are also solutions for an arbitrary choice of the velocity V.
On the one hand this is clearly inconsistent with the Galilean invari- ance of the Navier-Stokes equations.
t* in that fluid element which passes through x at time t, and it satisfies an extended form of the Navier-Stokes equation in the two time variables.
Quite rapidly after this, Kraichnan showed that the DIA equations are actually the exact consequence in a certain limit of a stochastic model, called the random coupling model (RCM), which is obtained by a suitable modifi- cation of the Navier-Stokes equations.
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