  The rapidity dependence of two-particle momentum correlations can be used to
probe the viscosity of the liquid produced in heavy nuclei collisions at RHIC.
We reexamine this probe in light of the recent experimental analyses of the
azimuthal-angle dependence of number correlations, which demonstrate the
importance of initial state fluctuations propagated by hydrodynamic flow in
these correlations. The NEXSPHERIO model combines fluctuating initial
conditions with viscosity-free hydrodynamic evolution and, indeed, has been
shown to describe azimuthal correlations. We use this model to compute the
number density correlation $R_{2}$ and the momentum current correlation
function {\it C}, at low transverse momentum in Au+Au collisions at
$\sqrt{s_{NN}} = $~200 GeV. {\it C} is sensitive to details of the collision
dynamics. Its longitudinal width is expected to broaden under the influence of
viscous effects and narrow in the presence of sizable radial flow. While
NEXSPHERIO model qualitatively describes the emergence of a near-side
ridge-like structure for both the $R_2$ and {\it C} observables, we find that
it predicts a longitudinal narrowing of the near side peak of these correlation
functions for increasing number of participants in contrast with recent
observations by the STAR Collaboration of a significant broadening in most
central collisions relative to peripheral collisions.
