  Nonhelical turbulence within a linear shear flow has demonstrated efficient
amplification of large-scale magnetic fields, as evidenced in numerical
simulations. Despite this, the precise mechanism underlying such shear dynamos
remains elusive. The incoherent $\alpha$ model emerges as a potential dynamo
driver, wherein shear flow collaborates with a zero-mean fluctuating transport
coefficient, $\alpha$, commonly linked to the kinetic helicity of the flow, to
drive large-scale magnetic fields. Previous renovating-flow models have
proposed that the correlation time of helicity fluctuations must be
sufficiently extended to overcome turbulent magnetic diffusivity and instigate
dynamo action, yet only empirical validation of this concept remains
outstanding. In this study, we conduct direct numerical simulations of
nonhelically forced hydrodynamic turbulence. We scrutinize the correlation
times of velocity and kinetic helicity fluctuations in distinct flow
configurations, including rotation, shearing, and Keplerian flows.
Additionally, for shearing cases, we explore their burgulence counterparts. Our
findings indicate that rotation contributes to a prolonged correlation time of
helicity compared to velocity. This is particularly notable in
auto-correlations of both volume-averaged quantities and individual Fourier
modes, attributed to the formation of vortices at larger scales. In contrast,
moderate shear strength does not exhibit significant scale separation, with
shear flows elongating vortices in the direction of shear. Shearing burgulence,
characterized by shorter helicity correlation times, appears less conducive to
hosting the incoherent $\alpha$ effect. Notably, at modest shear rates, only
Keplerian flows exhibit sufficiently coherent helicity fluctuations, in
contrast to purely shearing flows, implying potentially distinct dynamo
mechanisms in these two cases.
