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SPECTRAL ELEMENT METHOD (Onsager, Batchelor, ...):

* For the PASSIVE SCALAR problem:

Scalar variance spectrum= G(k) =

Constancy of scalar flux along the cascade:

* In the inertial regime of Kolmogorov

3d turbulence:

* In the Batchelor regime

(i.e. n‡D and k†(e/nD2)1/4

(Obukhov-Corrsin)

(Batchelor)

Stretching rate

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