Relativistic jets are frequently involved in high-energy astrophysics phenomena, including pulsar wind nebulae, gamma-ray bursts, and radio-loud active galactic nuclei. We have recently developed a new three-dimensional, high-order, shock-capturing, relativistic hydrodynamics (RHD) code, which can simulate ultra-relativistic flows; it is equipped with the weighted essentially non-oscillatory (WENO) scheme, the strong-stability preserving Runge-Kutta time-stepping method, and a realistic equation of state. We have applied the code for a study of radio jets on kpc scales. Taking advantage of the shock-capturing and high-resolution capabilities, we analyze and quantify in detail the distributions and statistics of shocks, velocity shear, and turbulence in different parts of the jet-induced flows. We find that shocks formed in the jet plasma and backflows are the most effective in dissipating the jet energy, while the shear appears largest across the jet and backflows. We discuss the implication of our work on the acceleration of ultra-high energy cosmic rays.