  We propose several new observables/correlators, based on correlations between
two or more subevents separated in pseudorapidity $\eta$, to study the
longitudinal flow fluctuations. We show that these observables are sensitive to
the event-by-event fluctuations, as a function of $\eta$, of the initial
condition as well as the non-linear mode-mixing effects. Experimental
measurement of these observables shall provide important new constraints on the
boost-variant event-by-event initial conditions required by all 3+1-dimensional
viscous hydrodynamics models.
