Linear theory of the Rayleigh-Taylor instability at a discontinuous surface of a relativistic flow
Linear theory of the Rayleigh-Taylor instability at a discontinuous surface of a relativistic flow
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相对论流不连续表面的瑞利-泰勒不稳定性的线性理论
DOI：
10.1093/mnras/stx2012
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发表时间：
2017
影响因子：
4.8
通讯作者：
Manel Perucho
中科院分区：
文献类型：
--
作者：
Jin Matsumoto;Miguel A. Aloy;Manel Perucho
我们在喷流传播时径向振荡的背景下，讨论相对论流不连续表面的线性稳定性。振荡的恢复力预计将在喷流与其蚕茧之间的界面上驱动瑞利-泰勒不稳定(RTI)。我们进行了线性分析和数值模拟，研究了横向平面内RTI对均匀加速射流的增长。在该系统中，由匀速加速度产生的惯性力作为振动的恢复力。我们发现，不仅被界面分离的两种流体之间的惯性差，而且由于横跨射流不连续表面的洛伦兹因子的差异，界面处的压力也有助于驱动RTI。色散关系表明，当射流的洛伦兹因子远大于蚕茧的洛伦兹因子，且射流界面的压力为相对论时，各模的线性增长率最大。通过比较解析模型和数值模拟中RTI的线性增长率，证实了解析推导的相对论RTI色散关系的正确性。
We address the linear stability of a discontinuous surface of a relativistic flow in the context of a jet that oscillates radially as it propagates. The restoring force of the oscillation is expected to drive a Rayleigh–Taylor instability (RTI) at the interface between the jet and its cocoon. We perform a linear analysis and numerical simulations of the growth of the RTI in the transverse plane to the jet flow with a uniform acceleration. In this system, an inertia force due to the uniform acceleration acts as the restoring force for the oscillation. We find that not only the difference in the inertia between the two fluids separated by the interface but also the pressure at the interface helps to drive the RTI because of a difference in the Lorenz factor across the discontinuous surface of the jet. The dispersion relation indicates that the linear growth rate of each mode becomes maximum when the Lorentz factor of the jet is much larger than that of the cocoon and the pressure at the jet interface is relativistic. By comparing the linear growth rates of the RTI in the analytical model and the numerical simulations, the validity of our analytically derived dispersion relation for the relativistic RTI is confirmed.