Scalar dissipation rate
= Scalar dissipation rate
{title2=$\epsilon_c=\alpha\langle|\nabla C|^2\rangle$}
With this half-variance convention, the unforced scalar equation gives $d\langle C^2/2\rangle/dt=-\epsilon_c$ in a homogeneous incompressible flow. Authors defining dissipation of the full variance instead use $2\alpha\langle|\nabla C|^2\rangle$. Stating the convention is necessary when relating the dissipation rate to a <scalar structure function>.