Gradient blowup without shock formation in compressible Euler flow

Helge Kristian Jenssen, Alexander Anthony Johnson

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number026125
JournalPhysics of Fluids
Issue number2
StatePublished - Feb 1 2024

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Cite this