Various integrated quantities as a function of time, for the dipolar simulations with different ν₀ (indicated by line styles). Panel a) shows the open magnetic flux ∫_{r = r1} | B_r | dΩ, panel b) shows ∫_D | j | dV, and panel c) shows H_N (asterisks) and H_S (circles). Panel d) shows the terms in Eq. (18)for the northern hemisphere, with asterisks denoting S₀, circles S₁, squares S_eq, and diamonds S_V.