Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom.
Proc Natl Acad Sci U S A. 2014 Mar 11;111(10):3663-70. doi: 10.1073/pnas.1400277111. Epub 2014 Feb 11.
Helicity is, like energy, a quadratic invariant of the Euler equations of ideal fluid flow, although, unlike energy, it is not sign definite. In physical terms, it represents the degree of linkage of the vortex lines of a flow, conserved when conditions are such that these vortex lines are frozen in the fluid. Some basic properties of helicity are reviewed, with particular reference to (i) its crucial role in the dynamo excitation of magnetic fields in cosmic systems; (ii) its bearing on the existence of Euler flows of arbitrarily complex streamline topology; (iii) the constraining role of the analogous magnetic helicity in the determination of stable knotted minimum-energy magnetostatic structures; and (iv) its role in depleting nonlinearity in the Navier-Stokes equations, with implications for the coherent structures and energy cascade of turbulence. In a final section, some singular phenomena in low Reynolds number flows are briefly described.
螺旋度与能量一样，是理想流体流动的欧拉方程的二次不变量，尽管与能量不同，它不是符号确定的。从物理上讲，它代表了流的涡线的连接程度，当条件使得这些涡线在流体中冻结时，它是守恒的。本文回顾了螺旋度的一些基本性质，特别提到了（i）它在宇宙系统中磁场的发电机激发中的关键作用；（ii）它与任意复杂流线拓扑的欧拉流的存在有关；（iii）在确定稳定的结状最小能量磁静力学结构时，类似的磁螺旋度的约束作用；以及（iv）它在耗散纳维-斯托克斯方程中的非线性方面的作用，对湍流的相干结构和能量级联有影响。在最后一节中，简要描述了低雷诺数流动中的一些奇异现象。
