Comparison of the local quadrupolar eigenfunctions for 𝒟 = −20 (upper panel) and −50 (middle panel) obtained from numerical solution of the local Eqs. (21) and (22) with the approximate eigenfunctions Eqs. (29) and (30): b_ϕ from the numerical solution are shown solid (red) and b_s, dashed (blue); their approximate counterparts are shown with dotted curves of the matching colour. The eigenfunctions are normalised to b_ϕ(0) = 1. Bottom panel: numerical (black, solid) and approximate, Eqs. (31) (red, dashed), solutions for the local growth rate as a function of the local dynamo number.