  The transition from the diffuse warm neutral medium (WNM) to the dense cold
neutral medium (CNM) is what set the initial conditions to the formation of
molecular clouds. The properties of the turbulent cascade in the WNM, essential
to describe this radiative condensation process, have remained elusive in part
due to the difficulty to map out the structure and kinematics of each H I
thermal phases. Here we present an analysis of a 21 cm hyper-spectral data cube
from the GHIGLS HI survey where the contribution of the WNM is extracted using
ROHSA, a Gaussian decomposition tool that includes spatial regularization. The
distance and volume of the WNM emission is estimated using 3D dust extinction
map information. The thermal and turbulent contributions to the Doppler line
width of the WNM were disentangled using two techniques, one based on the
statistical properties of the column density and centroid velocity fields, and
another on the relative motions of CNM structures as a probe of turbulent
motions. We found that the volume of WNM sampled here, located at the outer
edge of the Local Bubble, shows thermal properties in accordance with expected
values for heating and cooling processes typical of the Solar neighbourhood.
The WNM has the properties of sub/trans-sonic turbulence, with a turbulent Mach
number at the largest scale probed here (l = 130 pc) of Ms = 0.87 +- 0.15, a
density contrast of 0.6 +- 0.2, and velocity and density power spectra
compatible with k-11/3. The low Mach number of the WNM provides dynamical
conditions that allows the condensation mode of thermal instability (TI) to
grow freely and form CNM structures, as predicted by theory.
