New Relativistic Effects in the Dynamics of Nonlinear Hydrodynamical Waves

TL;DR

This paper investigates new relativistic effects in the dynamics of nonlinear hydrodynamical waves, revealing how tangential velocities influence wave-pattern transitions uniquely in special relativity.

Contribution

It demonstrates that varying initial tangential velocities causes smooth transitions between wave-patterns in relativistic hydrodynamics, a phenomenon absent in Newtonian physics.

Findings

Tangential velocities induce wave-pattern transitions in relativistic fluids.

Relativistic effects are driven by Lorentz factor coupling, with no Newtonian equivalent.

Smooth wave-pattern changes can be achieved by adjusting initial tangential velocities.

Abstract

In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity. When the fluid is allowed to relax, one of three possible wave-patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a special relativistic Riemann problem when velocities tangential to the initial discontinuity surface are present. We show that a smooth transition from one wave-pattern to another can be produced by varying the initial tangential velocities while otherwise maintaining the initial states unmodified. These special relativistic effects are produced by the coupling through the relativistic Lorentz factors and do not have a Newtonian counterpart.