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The role of singularities in hydrodynamics

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The role of singularities in hydrodynamics. / Eggers, Jens.

In: Physical Review Fluids, Vol. 3, 110503, 21.11.2018.

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Eggers, Jens. / The role of singularities in hydrodynamics. In: Physical Review Fluids. 2018 ; Vol. 3.

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@article{36cd20648ab8495faf67a63f3454256d,
title = "The role of singularities in hydrodynamics",
abstract = "Some of the most interesting structures observed in hydrodynamicsare 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 potentialflow. These examples show that singularities are characteristic for thetendency 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 morecomplicated flows. The mathematical structure of singularities is self-similar, andtheir characteristics are fixed by universal properties. We review recent developments in this field through the lens of one ofthe great scientific challenges of today: understanding the structure of turbulence.",
author = "Jens Eggers",
year = "2018",
month = "11",
day = "21",
doi = "10.1103/PhysRevFluids.3.110503",
language = "English",
volume = "3",
journal = "Physical Review Fluids",
issn = "2469-990X",
publisher = "American Physical Society (APS)",

}

RIS - suitable for import to EndNote

TY - JOUR

T1 - The role of singularities in hydrodynamics

AU - Eggers, Jens

PY - 2018/11/21

Y1 - 2018/11/21

N2 - Some of the most interesting structures observed in hydrodynamicsare 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 potentialflow. These examples show that singularities are characteristic for thetendency 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 morecomplicated flows. The mathematical structure of singularities is self-similar, andtheir characteristics are fixed by universal properties. We review recent developments in this field through the lens of one ofthe great scientific challenges of today: understanding the structure of turbulence.

AB - Some of the most interesting structures observed in hydrodynamicsare 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 potentialflow. These examples show that singularities are characteristic for thetendency 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 morecomplicated flows. The mathematical structure of singularities is self-similar, andtheir characteristics are fixed by universal properties. We review recent developments in this field through the lens of one ofthe great scientific challenges of today: understanding the structure of turbulence.

U2 - 10.1103/PhysRevFluids.3.110503

DO - 10.1103/PhysRevFluids.3.110503

M3 - Article

VL - 3

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

M1 - 110503

ER -