• Invited

Role of singularities in hydrodynamics

J. Eggers
Phys. Rev. Fluids 3, 110503 – Published 21 November 2018
An article within the collection: 2018 Invited Papers

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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  • Received 16 June 2018

DOI:https://doi.org/10.1103/PhysRevFluids.3.110503

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Collections

This article appears in the following collection:

2018 Invited Papers

Physical Review Fluids publishes a collection of papers associated with the invited talks presented at the 70th Annual Meeting of the APS Division of Fluid Dynamics.

Authors & Affiliations

J. Eggers

  • School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom

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Issue

Vol. 3, Iss. 11 — November 2018

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