Resonant Kelvin-Helmholtz modes in sheared relativistic flows

TL;DR

This paper investigates the stability of sheared relativistic jets using analytical linear analysis combined with high-resolution simulations, revealing resonant modes that influence jet stability and could impact understanding of extragalactic jets.

Contribution

It introduces the first combined analytical and numerical study of resonant Kelvin-Helmholtz modes in relativistic jets, highlighting their role in jet stability.

Findings

Resonant modes are identified in the linear regime.

Simulations confirm the linear analysis results.

High-order reflection modes affect long-term jet stability.

Abstract

Qualitatively new aspects of the (linear and non-linear) stability of sheared relativistic (slab) jets are analyzed. The linear problem has been solved for a wide range of jet models well inside the ultrarelativistic domain (flow Lorentz factors up to 20; specific internal energies $\approx 60c^2$). As a distinct feature of our work, we have combined the analytical linear approach with high-resolution relativistic hydrodynamical simulations, which has allowed us i) to identify, in the linear regime, resonant modes specific to the relativistic shear layer ii) to confirm the result of the linear analysis with numerical simulations and, iii) more interestingly, to follow the instability development through the non-linear regime. We find that very high-order reflection modes with dominant growth rates can modify the global, long-term stability of the relativistic flow. We discuss the dependence of these resonant modes on the jet flow Lorentz factor and specific internal energy, and on the shear layer thickness. The results could have potential applications in the field of extragalactic relativistic jets.