Discovery of a coherent, wave-like velocity pattern for the Radcliffe
  Wave
  Recently studies discovered that part of the Gould Belt belongs to a 2.7
kpc-long {coherent, thin} wave consisting of a chain of clouds, where a damped
undulation pattern has been identified from the spatial arrangement of the
clouds. We use the proper motions of Young Stellar Objects (YSOs) anchored
inside the clouds to study the kinematic structure of the Radcliffe Wave in
terms of $v_z$, and identify a damped, wave-like pattern from the $v_z$ space,
which we call "velocity undulation". We propose a new formalism based on the
Ensemble Empirical Mode Decomposition (EEMD) to determine the amplitude,
period, and phase of the undulation pattern, and find that the spatial and the
velocity undulation share an almost identical spatial frequency of about 1.5
kpc, and both are damped when measured from one side to the other. Measured for
the first cycle, they exhibit a phase difference of around $2\pi/3$. The
structure is oscillating around the midplane of the Milky Way disk with an
amplitude of $\sim\,130\,\pm\,20\,\rm pc$. The vertical extent of the Radcliffe
Wave exceeds the thickness of the molecular disk, suggesting that the
undulation of the undulation signature might originate from a perturbation,
e.g. the passage of a dwarf galaxy.
