Turbulent energy spectrum
= Turbulent energy spectrum
{title2=$E(k)$}
The <turbulent energy spectrum> $E(k)$ distributes <kinetic energy> over wavenumber shells, normalized by $\int_0^\infty E(k)\,dk=\langle|\mathbf u|^2\rangle/2$. For isotropic <incompressible flow> its tensor form is $\Phi_{ij}=E(k)(\delta_{ij}-k_ik_j/k^2)/(4\pi k^2)$. Its low-wavenumber behavior records large-eddy <momentum> statistics.