Existence of Steady Subsonic Euler Flows through Infinitely Long Periodic Nozzles

TL;DR

This paper proves the existence and uniqueness of steady subsonic Euler flows in infinitely long, periodic nozzles under certain conditions, including small Bernoulli variation and specific mass flux regimes, also addressing subsonic-sonic flows at critical values.

Contribution

It establishes the global existence and uniqueness of steady subsonic Euler flows in periodic nozzles, including the case of subsonic-sonic flows at critical mass flux values.

Findings

Existence of unique steady subsonic flows under small Bernoulli variation.

Periodic flows with the same period as the nozzle.

Existence of subsonic-sonic flows at critical mass flux when Bernoulli is constant.

Abstract

In this paper, we study the global existence of steady subsonic Euler flows through infinitely long nozzles which are periodic in $x_1$ direction with the period $L$. It is shown that when the variation of Bernoulli function at some given section is small and mass flux is in a suitable regime, there exists a unique global subsonic flow in the nozzle. Furthermore, the flow is also periodic in $x_1$ direction with the period $L$. If, in particular, the Bernoulli function is a constant, we also get the existence of subsonic-sonic flows when the mass flux takes the critical value.