  Using data obtained by the high resolution CRisp Imaging SpectroPolarimeter
instrument on the Swedish 1-m Solar Telescope, we investigate the dynamics and
stability of quiet-Sun chromospheric jets observed at disk center. Small-scale
features, such as Rapid Redshifted and Blueshifted Excursions, appearing as
high speed jets in the wings of the H$\alpha$ line, are characterized by short
lifetimes and rapid fading without any descending behavior. To study the
theoretical aspects of their stability without considering their formation
mechanism, we model chromospheric jets as twisted magnetic flux tubes moving
along their axis, and use the ideal linear incompressible magnetohydrodynamic
approximation to derive the governing dispersion equation. Analytical solutions
of the dispersion equation indicate that this type of jet is unstable to
Kelvin-Helmholtz instability (KHI), with a very short (few seconds) instability
growth time at high upflow speeds. The generated vortices and unresolved
turbulent flows associated with the KHI could be observed as broadening of
chromospheric spectral lines. Analysis of the H$\alpha$ line profiles shows
that the detected structures have enhanced line widths with respect to the
background. We also investigate the stability of a larger scale H$\alpha$ jet
that was ejected along the line-of-sight. Vortex-like features, rapidly
developing around the jet's boundary, are considered as evidence of the KHI.
The analysis of the energy equation in the partially ionized plasma shows that
the ion-neutral collisions may lead to the fast heating of the KH vortices over
timescales comparable to the lifetime of chromospheric jets.
