Estimating the propagation of a uniformly accelerated jet

TL;DR

This paper investigates the dynamics of a uniformly accelerating Herbig-Haro jet through analytic models and numerical simulations, revealing conditions under which these models accurately predict jet propagation.

Contribution

It provides analytic solutions for jet motion with accelerating ejection velocity and compares them with numerical simulations, highlighting conditions for model accuracy.

Findings

Analytic models match simulations for over-dense, over-pressured jets.

Flow initially follows center of mass solution, then approaches ram-pressure balance.

Good agreement between models and simulations under specific density and pressure conditions.

Abstract

We study the problem of a Herbig-Haro jet with a uniformly accelerating ejection velocity, travelling into a uniform environment. For the ejection density we consider two cases: a time-independent density, and a time-independent mass loss rate. For these two cases, we obtain analytic solutions for the motion of the jet head using a ram-pressure balance and a center of mass equation of motion. We also compute axisymmetric numerical simulations of the same flow, and compare the time-dependent positions of the leading working surface shocks with the predictions of the two analytic models. We find that if the jet is over-dense and over-pressured (with respect to the environment) during its evolution, a good agreement is obtained with the analytic models, with the flow initially following the center of mass analytic solution, and (for the constant ejection density case) at later times approaching the ram-pressure balance solution.