Solenoidal isotropic spectral tensor (source code)

= Solenoidal isotropic spectral tensor
{title2=$\widehat C_{ij}=H(k)(\delta_{ij}-k_i k_j/k^2)$}

For a statistically homogeneous, isotropic, reflection-symmetric <solenoidal> vector <random field> in three dimensions, the nonzero-wavevector <spectral tensor> is a scalar multiple of the <transverse projector of a vector field>. Isotropy gives $A(k)\delta_{ij}+D(k)k_i k_j$, while zero <divergence> gives $A+Dk^2=0$. Its <trace> is $2A$, giving the displayed normalization. Without reflection symmetry an additional antisymmetric, helical term can occur.