  We present a scenario in heavy-ion collisions where different modes of
collective motions are noninterdependent, driven by factorized actions in the
created nuclear medium. Such physics mechanisms could each dominate at a
distinct evolution stage, or coexist simultaneously. If the probability of
particle emission is modulated by each nondependent collective motion with a
single-harmonic Fourier expansion, the particle azimuthal distribution should
be the product of all these expansions. Consequently, nonleading cross terms
between collectivity modes appear, and their contributions to experimental
observables could be significant. In particular, we argue that the chiral
magnetic effect (CME) and elliptic flow can develop separately, with their
convolution affecting the observable that is sensitive to the shear-induced
CME. We will use the event-by-event anomalous-viscous fluid dynamics model to
illustrate the effects of this scenario. Besides giving insights into searches
for the CME, we also propose feasible experimental tests based on conventional
flow harmonics, and demonstrate the emergence of nonleading cross terms with a
multiphase transport model.
