  The Universe expansion rate is modulated around local inhomogeneities due to
their gravitational potential. Velocity waves are then observed around galaxy
clusters in the Hubble diagram. This paper studies them in a ~738 Mpc wide,
with 2048^3 particles, cosmological simulation of our cosmic environment
(a.k.a. CLONE: Constrained LOcal \& Nesting Environment simulation). For the
first time, the simulation shows that velocity waves that arise in the
lines-of-sight of the most massive dark matter halos agree with those observed
in local galaxy velocity catalogs in the lines-of-sight of Coma and several
other local (Abell) clusters. For the best-constrained clusters such as Virgo
and Centaurus, i.e. those closest to us, secondary waves caused by galaxy
groups, further into the non-linear regime, also stand out. This match is not
utterly expected given that before being evolved into a fully non-linear z=0
state, assuming {\Lambda}CDM, CLONE initial conditions are constrained with
solely linear theory, power spectrum and highly uncertain and sparse local
peculiar velocities. Additionally, Gaussian fits to velocity wave envelopes
show that wave properties are tightly tangled with cluster masses. This link is
complex though and involves the environment and formation history of the
clusters. A proposed metric, measuring the distance between the observed and
several re-centered simulated lines-of-sight, waves included, is shown to be
capable of providing a tight mass range estimate for massive local clusters.
Using machine learning techniques to grasp more thoroughly the complex
wave-mass relation, velocity waves could in the near future be used to provide
additional and independent mass estimates from galaxy dynamics within large
cluster radii.
