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 -