Impact of meridional flow variations on solar cycle asymmetry. Panel (a): Simulation results where the meridional flow is modulated by the active region eruption belt using the term δvsin²(2θ_max), with θ_max denoting the latitude of peak toroidal field strength. A random component with a coherence time of three months is superimposed on this modulation to account for convective turbulence, resulting in a hybrid meridional flow profile. The black curve (right y-axis) shows the evolution of magnetic energy density, while the blue curve (left y-axis) shows the variation in the amplitude of the meridional flow. Panels (b)–(e): Asymmetry measures from the same simulation, showing the same quantities as in Fig. 3, with an added 50% stochastic fluctuation in the poloidal field source.