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.
7 More- Received 16 June 2018
DOI:https://doi.org/10.1103/PhysRevFluids.3.110503
©2018 American Physical Society
Physics Subject Headings (PhySH)
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.