  We investigate the initiation and subsequent evolution of Crow instability in
an inhomogeneous unitary Fermi gas using zero-temperature Galilei-invariant
non-linear Schr\"odinger equation. Considering a cigar-shaped unitary Fermi
gas, we generate the vortex-antivortex pair either by phase-imprinting or by
moving a Gaussian obstacle potential. We observe that the Crow instability in a
unitary Fermi gas leads to the decay of the vortex-antivortex pair into
multiple vortex rings and ultimately into sound waves.
