 Monochromatic small-Reynolds-number mean electromotive force

Suppose a steady solenoidal velocity satisfies $\Delta \mathbf{u}=-\mathbf{u}$, and spatial averaging permits integration by parts without boundary terms. For a uniform test magnetic field $\mathbf{B}$, the small-magnetic Reynolds number expansion gives ${\mathbf{b}}_1=(\mathbf{B}\cdot \nabla )\mathbf{u}$ and $\Delta {\mathbf{b}}_2=-\nabla \times (\mathbf{u}\times {\mathbf{b}}_1)$. Using the self-adjointness of the Laplacian inside the average,The second equality concerns the averaged mean-field electromotive force; it does not assert that the quadratic forcing itself is monochromatic.

// Target: fluid-mechanics.bigb