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The role of singularities in hydrodynamics

Research output: Contribution to journalArticle

Original languageEnglish
Article number110503
JournalPhysical Review Fluids
Volume3
DOIs
DateSubmitted - 16 Jun 2018
DateAccepted/In press - 16 Aug 2018
DatePublished (current) - 21 Nov 2018

Abstract

Some of the most interesting structures observed in hydrodynamics
are best understood as singularities of the equations of fluid
mechanics. Examples are drop formation in free-surface flow,
shock waves in compressible gas flow, or vortices in potential
flow. These examples show that singularities are characteristic for the
tendency of the hydrodynamic equations to develop small scale features
spontaneously, starting from smooth initial conditions. As a result,
new structures are created, which form the building blocks of more
complicated flows.
The mathematical structure of singularities is self-similar, and
their characteristics are fixed by universal properties.
We review recent developments in this field through the lens of one of
the great scientific challenges of today: understanding the structure
of turbulence.

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  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the accepted author manuscript (AAM). The final published version (version of record) is available online via APS at https://doi.org/10.1103/PhysRevFluids.3.110503 . Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 3 MB, PDF document

    Licence: Other

  • Full-text PDF (final published version)

    Rights statement: This is the final published version of the article (version of record). It first appeared online via APS at https://doi.org/10.1103/PhysRevFluids.3.110503 . Please refer to any applicable terms of use of the publisher.

    Final published version, 3 MB, PDF document

    Licence: Other

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