The successive formation and disappearance of density structures in simple expanding systems

TL;DR

This paper derives exact solutions for one-dimensional compressible fluid flows, revealing transient phenomena like density collapse and wavelet dissolution, influenced by initial conditions and force types, with implications for plasma and astrophysical systems.

Contribution

It provides the first exact nonlinear solutions showing successive formation and disappearance of density structures in expanding fluid systems.

Findings

Density collapse occurs in finite space-time.

Wavelet structures can successively dissolve during expansion.

Plasma oscillations weaken nonlinear effects in electron fluids.

Abstract

The Lagrangian fluid description is employed to solve the initial value problem for one-dimensional, compressible fluid flows represented by the Euler-Poisson system. Exact nonlinear and time-dependent solutions are obtained, which exhibit a variety of transient phenomena such as a density collapse in finite space-time or the appearance and, for the first time, a successive dissolution of wavelet structures during the same event. The latter are superimposed on the gross density pattern in the course of the uni-directional expansion of an initially localized density hump. Whereas self-gravitating fluids will always experience collapse, neutral fluids and fluids with repulsive forces, such as a non-neutral, pure electron fluid, can exhibit an evolution of the second type, being determined by the initial conditions. For an electron fluid, being embedded in a neutralizing ion background, these nonlinearities are, however, strongly diminished due to the omnipresent plasma oscillations, which weaken and alternatively change the sign of the collective force.