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We address the linear stability of a discontinuous surface of a relativisticflow in the context of a jet that oscillates radially as it propagates. Therestoring force of the oscillation is expected to drive a Rayleigh-Taylorinstability (RTI) at the interface between the jet and its cocoon. We perform alinear analysis and numerical simulations of the growth of the RTI in thetransverse plane to the jet flow with a uniform acceleration. In this system,an inertia force due to the uniform acceleration acts as the restoring forcefor the oscillation. We find that not only the difference in the inertiabetween the two fluids separated by the interface but also the pressure at theinterface helps to drive the RTI because of a difference in the Lorenz factoracross the discontinuous surface of the jet. The dispersion relation indicatesthat the linear growth rate of each mode becomes maximum when the Lorentzfactor of the jet is much larger than that of the cocoon and the pressure atthe jet interface is relativistic. By comparing the linear growth rates of theRTI in the analytical model and the numerical simulations, the validity of ouranalytically derived dispersion relation for the relativistic RTI is confirmed.

Linear Theory of the Rayleigh-Taylor Instability at a Discontinuous Surface of a Relativistic Flow