Structure-function spectral filter
= Structure-function spectral filter
{title2=$H(x)=1+3\cos x/x^2-3\sin x/x^3$}
In isotropic incompressible three-dimensional <turbulence>, $3S_2(r)/4=\int E(k)H(kr)\,dk$, 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.