Average contributions to the induction equation from advection (solid black), field-line stretching (solid red), flow divergence (solid blue), and a residual term (solid green) to the vertical field component at the sinks of the NEF (left) and at the sinks of the CEF (right). The averages have been focused on localized regions that have fairly strong fields (Bz < −2 kG for the sinks of the NEF and Bz > 2 kG for the sinks of the CEF) and supersonic downflows at the local log(τ) = 0 level. The residual term represents the numerical magnetic diffusivity as an approximated magnitude that is calculated by the negative sum of the advective, stretching, and divergent terms; but it also contains potential contributions from time variation. The dashed and dotted lines represent approximated terms that provide a major contribution to the advective term (black) and to the stretching term (red), whose general expressions are indicated in the lower labels. The dash-dotted blue line represents the contribution to the divergence term due to flows perpendicular to the vertical field component, i.e., radial and azimuthal flow components.
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