New conservation laws of helically symmetric, plane and rotationally symmetric viscous and inviscid flows
New conservation laws of helically symmetric, plane and rotationally symmetric viscous and inviscid flows
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螺旋对称、平面和旋转对称粘性和无粘流的新守恒定律
DOI：
10.1017/jfm.2013.72
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发表时间：
2013
影响因子：
3.7
通讯作者：
M. Oberlack
中科院分区：
文献类型：
--
作者：
Olga Kelbin;A. Cheviakov;M. Oberlack
摘要螺旋不变的减少，由于一组减少的独立变量$（t，r，\xi）$与$\xi = az+ B\varphi $出现从一个圆柱坐标系的粘性和非粘性的时间相关的流体流动方程，与所有三个速度分量一般非零，被认为是在原始变量和涡量制定。导出了完整的方程组。本文用直接构造法系统地研究了螺旋不变系统的局部守恒律。各种新的一套守恒定律的无粘和粘性流，包括家庭，涉及任意函数，推导出来。对于欧拉和Navier-Stokes流，推导出了无穷多组与涡量有关的守恒律。特别是，对于欧拉流，我们得到了一个家庭的保守量，推广螺旋。另外，还考虑了在不变方向上速度分量为零的二元流的特殊情况，并计算了适用于这种流的特殊守恒量。特别是，它表明，著名的无限集的广义拟能守恒定律，平面流也持有一般的两个组件的螺旋不变流和轴对称的两个组件流。
Abstract Helically invariant reductions due to a reduced set of independent variables $(t, r, \xi )$ with $\xi = az+ b\varphi $ emerging from a cylindrical coordinate system of viscous and inviscid time-dependent fluid flow equations, with all three velocity components generally non-zero, are considered in primitive variables and in the vorticity formulation. Full sets of equations are derived. Local conservation laws of helically invariant systems are systematically sought through the direct construction method. Various new sets of conservation laws for both inviscid and viscous flows, including families that involve arbitrary functions, are derived. For both Euler and Navier–Stokes flows, infinite sets of vorticity-related conservation laws are derived. In particular, for Euler flows, we obtain a family of conserved quantities that generalize helicity. The special case of two-component flows, with zero velocity component in the invariant direction, is additionally considered, and special conserved quantities that hold for such flows are computed. In particular, it is shown that the well-known infinite set of generalized enstrophy conservation laws that holds for plane flows also holds for the general two-component helically invariant flows and for axisymmetric two-component flows.