Impact of meridional flow variations on solar cycle asymmetry. Panel (a): Results when the meridional flow varies randomly with a coherence time of one month. The black curve (right y-axis) shows the magnetic energy density evolution, while the blue curve (left y-axis) shows the amplitude variation of the meridional flow. Panels (b)–(e): Asymmetry measures derived from the same simulation. These four panels represent the same quantities as in Fig. 3. We have also included an additional 50% stochastic fluctuation in the poloidal field generation mechanism.