  Using nonlinear, fully relativistic, simulations we investigate the dynamics
and gravitational-wave signature associated with instabilities in neutron star
postmerger remnants. For simplified models of the remnant we establish the
presence of an instability in stars with moderate $T/|W|$, the ratio between
the kinetic and the gravitational potential energies. Detailed analysis of the
density oscillation pattern reveals a \emph{local} instability in the inner
region of the more realistic differential rotation profile. We apply Rayleigh's
inflection theorem and Fj{\o}rtoft's theorem to analyze the stability criteria
concluding that this \emph{inner local} instability originates from a shear
instability close to the peak of the angular velocity profile, and that it
later evolves into a fast-rotating m=2 oscillation pattern. We discuss the
importance of the presence of a corotation point in the fluid, its connection
with the shear instability, and comparisons to the Rossby wave and Papaloizou
Pringle instabilities considered in the wider literature.
