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.
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