Generalized helical Beltrami flows in hydrodynamics and magnetohydrodynamics
Generalized helical Beltrami flows in hydrodynamics and magnetohydrodynamics
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流体动力学和磁流体动力学中的广义螺旋贝尔特拉米流
DOI：
10.1017/s0022112091001209
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发表时间：
1991
影响因子：
3.7
通讯作者：
D. Dritschel
中科院分区：
文献类型：
--
作者：
D. Dritschel
当流动具有螺旋对称性时，当流动由一个刚性旋转的基本部分加上一个贝尔特拉米扰动部分（涡量与速度成正比或略加推广）组成时，非线性三维欧拉方程可以简化为一个简单的线性方程。这个线性方程的解表示稳定旋转的任意振幅的非轴对称波。在圆形截面的直管中流动的情况下，可以构造精确解。不可压缩的，非耗散的磁流体动力学方程得到类似的结果。除了一个刚性旋转的基流外，还可能存在一个随半径线性变化的环形磁场。
The nonlinear, three-dimensional Euler equations can be reduced to a simple linear equation when the flow has helical symmetry and when the flow consists of a rigidly rotating basic part plus a Beltrami disturbance part (with vorticity proportional to velocity or a slight generalization of this). Solutions to this linear equation represent steadily rotating, non-axisymmetric waves of arbitrary amplitude. Exact solutions can be constructed in the case of flow in a straight pipe of circular cross-section. Analogous results are obtained for the incompressible, non-dissipative equations of magnetohydrodynamics. In addition to a rigidly rotating basic flow, there may exist a toroidal magnetic field varying linearly with radius.