The joint cascade of energy and helicity in three-dimensional turbulence
The joint cascade of energy and helicity in three-dimensional turbulence
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DOI：
10.1063/1.1533070
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发表时间：
2003-02-01
影响因子：
4.6
通讯作者：
Eyink, GL
中科院分区：
文献类型：
--
作者：
Chen, QN;Chen, SY;Eyink, GL
三维 (3D) 湍流具有能量和螺旋度作为无粘性运动常数。与二维 (2D) 湍流相反，在二维 (2D) 湍流中，第二个无粘性不变量（熵）将能量级联阻挡到小尺度，而在 3D 湍流中，能量和螺旋度同时出现到小尺度的联合级联。人们早就认识到，2D 和 3D 之间的关键区别在于，熵是一个非负量，而螺旋度可以有任一符号。通过将速度螺旋分解为正极化波和负极化波，阐明了允许能量和螺旋度联合级联的基本抵消机制。这种分解在本研究中不仅在理论上得到应用，而且还被用于均匀和各向同性 3D 湍流的数值模拟中。结果表明，能量向小尺度的转移会在高波数下的+和-螺旋模式中分别产生螺旋度的巨大增长，在无限雷诺数的极限内发散。然而，由于在小尺度上恢复反射不变性的趋势，两种模式的净螺旋度在该极限内仍然是有限的。由于能量和螺旋度在 + 和 - 模式中不是单独守恒的，因此两个不变量有四个“类通量”量，它们对应于从大尺度转移到小尺度以及到 + 螺旋模式或到 - 螺旋模式的转移。在单独的 + 和 - 通道中，大尺度的螺旋通量在达到 Kolmogorov 耗散波数 k(E) 的波数上不是恒定的，而仅达到较小的波数 k(H)，最近由 Ditlevsen 和 Giuliani [Phys.流体 13, 3508 (2001);物理。资源。 E 63, 036304 (2001)]。然而，与他们的论点相反，净螺旋通量在直到柯尔莫哥洛夫波数的过程中都是恒定的：螺旋级联的惯性范围并不比能量级联更短。 + 和 - 模式之间的能量和螺旋度的传递（允许联合级联）被证明是由于两个不同的物理过程，即平流和涡旋拉伸。 (C) 2003 年美国物理研究所。
Three-dimensional (3D) turbulence has both energy and helicity as inviscid constants of motion. In contrast to two-dimensional (2D) turbulence, where a second inviscid invariant-the enstrophy-blocks the energy cascade to small scales, in 3D there is a joint cascade of both energy and helicity simultaneously to small scales. It has long been recognized that the crucial difference between 2D and 3D is that enstrophy is a nonnegative quantity whereas the helicity can have either sign. The basic cancellation mechanism which permits a joint cascade of energy and helicity is illuminated by means of the helical decomposition of the velocity into positively and negatively polarized waves. This decomposition is employed in the present study both theoretically and also in a numerical simulation of homogeneous and isotropic 3D turbulence. It is shown that the transfer of energy to small scales produces a tremendous growth of helicity separately in the + and - helical modes at high wave numbers, diverging in the limit of infinite Reynolds number. However, because of a tendency to restore reflection invariance at small scales, the net helicity from both modes remains finite in that limit. Since energy and helicity are not separately conserved in the + and - modes, there are four "fluxlike" quantities for both invariants, which correspond to transfer either out of large scales or into small scales and either to + helical or to - helical modes. The helicity fluxes out of large scales in the separate + and - channels are not constant in wave number up to the Kolmogorov dissipation wave number k(E) but only up to a smaller wave number k(H), recently identified by Ditlevsen and Giuliani [Phys. Fluids 13, 3508 (2001); Phys. Res. E 63, 036304 (2001)]. However, contrary to their argument, the net helicity flux is shown to be constant all the way up to the Kolmogorov wave number: there is no shorter inertial range for helicity cascade than for energy cascade. The transfer of energy and helicity between + and - modes, which permits the joint cascade, is shown to be due to two distinct physical processes, advection and vortex stretching. (C) 2003 American Institute of Physics.