  Coherent flows of self-propelled particles are characterized by vortices and
jets that sustain chaotic flows, referred to as active turbulence. Here, we
reveal a crossover between defect-free active turbulence and active turbulence
laden with topological defects. Interestingly, we show that concurrent to the
crossover from defect-free to defect-laden active turbulence is the restoration
of the previously broken $\SO(2)$-symmetry signaled by the fast decay of the
two-point correlations. By stability analyses of the topological charge density
field, we provide theoretical insights on the criterion for the crossover to
the defect-laden active turbulent state. Despite the distinct symmetry features
between these two active turbulence regimes, the flow fluctuations exhibit
universal statistical scaling behaviors at large scales, while the spectrum of
polarity fluctuations decays exponentially at small length scales compared to
the active energy injection length. These findings reveal a new dynamical
crossover between distinct spatiotemporal organization patterns in polar active
mater.
