The role of singularities in hydrodynamics

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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.
Original languageEnglish
Article number110503
JournalPhysical Review Fluids
Publication statusPublished - 21 Nov 2018


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