Time evolution of various significant variables in the calculation for the first harmonic illustrated in Fig. 4. Left panel: maximum of the field. Middle panel: location of the singularities, with the upper curve corresponding to L(t), and the lower one to L_cs(t). Right panel: flux integral in the central lobe of the solution. In each panel, the result of the Bifrost calculation is shown as a black solid line and the power laws derived from Eqs. (13)–(15) as red dashed lines.