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 Richtmyer-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 η determines a threshold for the onset of instabilities. The condition η < 1 should be satisfied for the transverse structure of the jet being persisted.
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