Gradient blowup without shock formation in compressible Euler flow

The well-known Guderley similarity solution provides a fundamental example of how a spherically converging shock wave can generate amplitude blowup in compressible Euler flow. Recent work has shown that the same phenomenon can occur in continuous flow. In this work, we analyze a different type of continuous similarity flows in which density, velocity, and sound speed all suffer gradient blowup at collapse, while remaining locally bounded. We give examples where, notwithstanding the presence of gradient singularities, no shock wave appears at collapse and the flow is globally continuous.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in [Gradient blowup without shock formation in compressible Euler flow. Physics of Fluids 36, 2 (2024)] and may be found at https://doi.org/10.1063/5.0185592.

Files

Metadata

Work Title Gradient blowup without shock formation in compressible Euler flow
Access
Open Access
Creators
  1. Helge Kristian Jenssen
  2. Alexander Anthony Johnson
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Physics of Fluids
Publication Date February 27, 2024
Publisher Identifier (DOI)
  1. https://doi.org/10.1063/5.0185592
Deposited January 29, 2025

Versions

Analytics

Collections

This resource is currently not in any collection.

Work History

Version 1
published

  • Created
  • Added Published_version-1.pdf
  • Added Creator Helge Kristian Jenssen
  • Added Creator Alexander Anthony Johnson
  • Published
  • Updated