  The nature of turbulence in molecular clouds is one of the key parameters
that control star formation efficiency: compressive motions, as opposed to
solenoidal motions, can trigger the collapse of cores, or mark the expansion of
Hii regions. We try to observationally derive the fractions of momentum density
($\rho v$) contained in the solenoidal and compressive modes of turbulence in
the Orion B molecular cloud and relate these fractions to the star formation
efficiency in the cloud. The implementation of a statistical method developed
by Brunt & Federrath (2014), applied to a $^{13}$CO(J=1-0) datacube obtained
with the IRAM-30m telescope, allows us to retrieve 3-dimensional quantities
from the projected quantities provided by the observations, yielding an
estimate of the compressive versus solenoidal ratio in various regions of the
cloud. Despite the Orion B molecular cloud being highly supersonic (mean Mach
number $\sim$ 6), the fractions of motion in each mode diverge significantly
from equipartition. The cloud's motions are on average mostly solenoidal
(excess > 8 % with respect to equipartition), which is consistent with its low
star formation rate. On the other hand, the motions around the main
star-forming regions (NGC 2023 and NGC 2024) prove to be strongly compressive.
We have successfully applied to observational data a method that was so far
only tested on simulations, and have shown that there can be a strong
intra-cloud variability of the compressive and solenoidal fractions, these
fractions being in turn related to the star formation efficiency. This opens a
new possibility for star-formation diagnostics in galactic molecular clouds.
