  Recent experimental observations by Bouillant \textit{et al. }(\textit{Nat.
Phys.}) revealed that below a certain radius, a Leidenfrost water drop starts
to self-rotate and propel. To better describe this internal mode transition, we
study experimentally and numerically the global stability of a water drop in a
Leidenfrost regime. In the experiment, the surface temperature and the internal
flow fields of a drop with initial radius $R\approx3.7$~mm are measured using
infrared camera and particle induced velocimetry, respectively, and show the
existence of critical radii on successive azimuthal mode (of wavenumber $m$)
transitions. Numerically, the steady base flow is computed assuming a
non-deformable interface while the heat exchange on the boundary is modeled by
an empirical correlation law. In absence of precise knowledge of the surface
contamination properties, the surface tension gradient appears as the only
tunable parameter to match experimental observations. The stability analysis of
nominally axisymmetric base flow shows dominant unstable azimuthal mode
transitions at radii close to the experimental observations. The unstable
eigenvectors for the azimuthal wavenumber $m=3$ and $m=2$ are reminiscent to
the experimental observations while the rolling mode is best described by the
$m=1$ eigenvector.
