  We study the stability of a non-rotating single-component jet using
two-dimensional special relativistic hydrodynamic simulations. By assuming
translational invariance along the jet axis, we exclude the destabilization
effect by Kelvin-Helmholtz mode. The nonlinear evolution of the transverse
structure of the jet with a normal jet velocity is highlighted. An intriguing
finding in our study is that Rayleigh-Taylor and Richtmeier-Meshkov type
instabilities can destroy cylindrical jet configuration as a result of
spontaneously induced radial oscillating motion. This is powered by in-situ
energy conversion between the thermal and bulk kinetic energies. The effective
inertia ratio of the jet to the surrounding medium $\eta$ determines a
threshold for the onset of instabilities. The condition $\eta < 1$ should be
satisfied for the transverse structure of the jet being persisted.
