  We show that spherical infall models (SIMs) can better describe some galaxy
clusters in redshift slice space than in traditional axially-convolved
projection space. This is because in SIM, the presence of transverse motion
between cluster and observer, and/or shear flow about the cluster (such as
rotation), causes the infall artifact to tilt, obscuring the characteristic
two-trumpet profile; and some clusters resemble such tilted artifacts.
  We illustrate the disadvantages of applying SIM to convolved data and, as an
alternative, introduce a method fitting a tilted 2D envelope to determine a 3D
envelope. We also introduce a fitting algorithm and test it on toy SIM
simulations as well as three clusters (Virgo, A1459, and A1066). We derive
relations useful for using the tilt and width-to-length ratio of the fitted
envelopes to analyze peculiar velocities. We apply them to our three clusters
as a demonstration. We find that transverse motion between cluster and observer
can be ruled out as sole cause of the observed tilts, and that a multi-cluster
study could be a feasible way to find our infall toward Virgo cluster.
