Fig. 6: Dynamics of the simulated MHD wave and its amplitude variations along three selected paths.

a–c Time-distance plots to show the total energy density \(\delta {{{{{{{\mathcal{H}}}}}}}}/{p}_{0}\) along the paths as shown in Fig. 5b, where \(\delta {{{{{{{\mathcal{H}}}}}}}}\) is the difference between total energy density \({{{{{{{\mathcal{H}}}}}}}}\) and the background total energy density \({{{{{{{{\mathcal{H}}}}}}}}}_{0}\). The vertical dotted lines indicate the CH boundaries in the numerical simulation. d The amplitude variation of the wavefront along the selected paths. As the upper/lower paths shown in Fig. 5b are symmetric to each other, the measured values are identical. The values of normalization factors p₀, t₀, and L₀ for the total energy density (\({{{{{{{\mathcal{H}}}}}}}}\)), time (t) and length (x, y, z) are listed in Table 1.