evidence for a stationary shock in the vicinity of B. Comparison of the present VLBI observations with those made 8.43 years ago suggests a significant northward motion for A2 with an apparent transverse velocity $\beta_{app}=3.7\pm0.4\, c$. The apparent superluminal motion suggests that the relativistic jet plasma moves at a velocity of $\gtrsim0.96\,
    c$ if the jet is viewed at an inclination angle less than $20\degr$. A simple precessing jet model and a hydrodynamical isothermal jet model with helical-mode Kelvin-Helmholtz instabilities are used to fit the oscillatory jet trajectory of 3C 48 defined by the bright knots.
author:
- |
    T. An$^{1}$[^1], X.Y. Hong$^{1}$, M.J. Hardcastle$^{2,3}$, D.M. Worrall$^{3}$, T. Venturi$^{4}$, T.J. Pearson$^{5}$, Z.-Q. Shen$^{1}$, W. Zhao$^{1}$ and W.X. Feng$^{6}$\
    $^{1}$ Shanghai Astronomical Observatory, Chinese Academy of Sciences, 200030, Shanghai, China\
    $^{2}$ School of Physics, Astronomy and Mathematics, University of Hertfordshire, College Lane, Hatfield AL10 9AB\
    $^{3}$ Department of Physics, University of Bristol, Tyndall Avenue, Bristol BS8 1TL\
    $^{4}$ INAF – Istituto di Radioastronomia, I-40129, Bologna, Italy\
    $^{5}$ California Institute of Technology, Mail Stop 105-24, Pasadena, CA 91125, USA\
    $^{6}$ Liaocheng University, 252059, Liaocheng, China
title: 'Kinematics of the parsec-scale radio jet in 3C 48'
---

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galaxies: active, galaxies: kinematics, galaxies: 