 Structure-function spectral filter

ID: structure-function-spectral-filter

In isotropic incompressible three-dimensional turbulence,

3 S_{2} (r) /4 = \int E (k) H (k r) d k

, with

H (x) = 1 + 3 cos x / x^{2} - 3 sin x / x^{3}

. It is smooth at zero, where

H = x^{2} /10 + O (x^{4})

, and tends to one at large argument. A sharp wavenumber cutoff omits the finite large-scale-gradient contribution.

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