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مدل کوپلینگ تصادفی
10.2 Closures: realizability, Galilean invariance and the random coupling models; MHD turbulence
However, after a few months, Kraichnan found that the DIA equa- tions are actually the exact consequences of a certain random coupling model obtained from the hydrodynamical equations (Navier-Stokes or MHD) by a suitable modification of the nonlinear interactions (see Section 10.2.2).
The random coupling model has many properties in common with the origi- nal hydrodynamical equations, such as symmetries, energy conservation, etc.
But Kraichnan noted that, when various correlation functions are expanded in terms of Feynman diagrams, the random coupling model retains only a sub- class of all diagrams; in particular it misses the so-called vertex corrections which contribute (in field-theoretic language) to the renormalization of the nonlinear interaction.9
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.
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