Singularities in fluid mechanics

H. K. Moffatt

Type: Article

Publication Date: 2019-11-18

Citations: 14

DOI: https://doi.org/10.1103/physrevfluids.4.110502

Abstract

A dynamical system is described that captures the near-singular character of vortex reconnection, thus indicating how enstrophy in turbulent flow can become infinite in the zero-viscosity limit. Similarities with the near-singular behavior in the problem of cusp-formation at a free surface are identified.

Locations

Physical Review Fluids - View
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Singularities in Fluid Mechanics	2019	H. K. Moffatt
+	Singularities in Fluid Mechanics	2019	H. K. Moffatt
+	Singularities in fluid dynamics	2008	James Glimm
+	Singularities in Fluid Dynamics and their Resolution	2009	H. K. Moffatt
+	Hydrodynamic Singularities	2001	Jens Eggers
+	Singularities in the transitions to chaos of a convective anisotropic fluid	1986	A. Joets Xiaoqian Yang R. Ribotta
+	Vortex dynamics and singularities in the fluid equations	1986	Alain Pumir
+	Singularities in Three-Dimensional Compressible Euler Flows with Vorticity	1998	J. T. Stuart
+ PDF Chat	Formation of singularities in compressible fluids in two-space dimensions	1989	Mohammad A. Rammaha
+	Finite-time localized singularities as a mechanism for turbulent dissipation	2020	Christophe Josserand Yves Pomeau Sergio Rica
+	Singularities of the equations of fluid motion	1988	Katepalli R. Sreenivasan Charles Meneveau
+	Singularity methods in fluid dynamics	1980	A. I. Vandevooren
+	Cusps in interfacial problems	2009	J. Eggers M. A. Fontelos
+ PDF Chat	The two-fold singularity of nonsmooth flows: Leading order dynamics in -dimensions	2013	Alessandro Colombo Mike R. Jeffrey
+ PDF Chat	Singularities and Similarities in Interface Flows	1994	Andrea L. Bertozzi Michael P. Brenner Todd F. Dupont Leo P. Kadanoff
+	Singular limits in compressible fluid dynamics	1994	H. Beirão da Veiga
+ PDF Chat	Cusp Singularities in Boundary-Driven Diffusive Systems	2013	Guy Bunin Yariv Kafri Daniel K. Podolsky
+	Singularities	1995	T. Dombre Alain Pumir
+ PDF Chat	Singularities in fully developed turbulence	2015	Bhimsen K. Shivamoggi
+	Singularities of solutions to compressible Euler equations with damping	2019	Jianwei Dong Hongxia Xue Guangpu Lou

Works That Cite This (9)

Action	Title	Year	Authors
+ PDF Chat	Intermittency, cascades and thin sets in three-dimensional Navier-Stokes turbulence	2020	John Gibbon
+	Finite-time localized singularities as a mechanism for turbulent dissipation	2020	Christophe Josserand Yves Pomeau Sergio Rica
+ PDF Chat	Singular Solutions to Equations of Fluid Mechanics and Dynamics Near a Hurricane’s Eye	2021	Maximilian F. Hasler
+ PDF Chat	Numerical evidence of anomalous energy dissipation in incompressible Euler flows: towards grid-converged results for the inviscid Taylor–Green problem	2021	Niklas Fehn Martin Kronbichler Peter Münch Wolfgang A. Wall
+ PDF Chat	Polarization singularities and Möbius strips in sound and water-surface waves	2021	Konstantin Y. Bliokh Miguel A. Alonso Danica Sugic M. Perrin Franco Nori Etienne Brasselet
+ PDF Chat	On the Interplay Between Vortices and Harmonic Flows: Hodge Decomposition of Euler’s Equations in 2d	2024	Clodoaldo Grotta Ragazzo Björn Gustafsson Jair Koiller
+ PDF Chat	Moffatt eddies in electrohydrodynamics flows: numerical simulations and analyses	2022	Xuerao He Zhihao Sun Mengqi Zhang
+ PDF Chat	No Existence and Smoothness of Solution of the Navier-Stokes Equation	2022	Hua-Shu Dou
+ PDF Chat	A Method for the Dynamics of Vortices in a Bose-Einstein Condensate: Analytical Equations of the Trajectories of Phase Singularities	2023	Sergi De María-García A. Ferrando J. Alberto Conejero Pedro Fernández de Córdoba Miguel Ángel García-March

Works Cited by This (9)

Action	Title	Year	Authors
+	Geometric constraints on potentially	1996	Charles Fefferman Andrew J. Majda
+ PDF Chat	Remarks on the breakdown of smooth solutions for the 3-D Euler equations	1984	J. Thomas Beale T. Kato Andrew J. Majda
+	Incipient singularities in the Navier-Stokes equations	1985	Eric D. Siggia Alain Pumir
+	On the steady motion of viscous liquid in a corner	1949	W. R. Dean P. E. Montagnon
+ PDF Chat	Enstrophy and circulation scaling for Navier–Stokes reconnection	2018	Robert M. Kerr
+ PDF Chat	Towards a finite-time singularity of the Navier–Stokes equations Part 1. Derivation and analysis of dynamical system	2018	H. K. Moffatt Yoshifumi Kimura
+ PDF Chat	Towards a finite-time singularity of the Navier–Stokes equations. Part 2. Vortex reconnection and singularity evasion	2019	H. K. Moffatt Yoshifumi Kimura
+ PDF Chat	Boundary singularities produced by the motion of soap films	2014	Raymond E. Goldstein J P McTavish H. K. Moffatt Adriana I. Pesci
+	Cascade leading to the emergence of small structures in vortex ring collisions	2018	Ryan McKeown Rodolfo Ostilla–Mónico Alain Pumir Michael P. Brenner Shmuel M. Rubinstein