Eddy viscosity of three-dimensional flow
Eddy viscosity of three-dimensional flow
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DOI：
10.1017/s0022112095001133
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发表时间：
1995-04
影响因子：
3.7
通讯作者：
A. Wirth;S. Gama;U. Frisch
中科院分区：
文献类型：
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作者：
A. Wirth;S. Gama;U. Frisch
给出了三维受迫空间周期不可压缩流动的涡粘性的详细理论和数值结果。Dubrulle&Frisch(1991)指出，涡粘性通常是一个四阶各向异性张量，它可以用辅助问题的解来表示。这些本质上是三维线性化的Navier-Stokes方程，必须用数值方法求解。波矢k的弱大尺度扰动的动力学是由2乘2矩阵的本征值决定的，这是通过将涡粘张量与两个k矢量压缩并投影到横跨k的平面以确保不可压缩而获得的。因此，三维的涡流粘性可能会变得复杂，但不是二维的。结果表明，对于具有立方对称性的流动，这是不可能的，但其涡粘性可能变为负值。一个实例是等边ABC流(A=B=C=1)。当波矢k在三个坐标平面中的任何一个平面上时，R=1/v>；Rc[bsime]1.92至少有一个涡流粘性为负值。这导致雷诺数的值比具有与基本流动相同的空间周期的不稳定值小约七倍时发生大尺度不稳定。
Detailed theoretical and numerical results are presented for the eddy viscosity of three-dimensional forced spatially periodic incompressible flow. As shown by Dubrulle & Frisch (1991), the eddy viscosity, which is in general a fourth-order anisotropic tensor, is expressible in terms of the solution of auxiliary problems. These are, essentially, three-dimensional linearized Navier–Stokes equations which must be solved numerically. The dynamics of weak large-scale perturbations of wavevector k is determined by the eigenvalues – called here ‘eddy viscosities’ – of a two by two matrix, obtained by contracting the eddy viscosity tensor with two k-vectors and projecting onto the plane transverse to k to ensure incompressibility. As a consequence, eddy viscosities in three dimensions, but not in two, can become complex. It is shown that this is ruled out for flow with cubic symmetry, the eddy viscosities of which may, however, become negative. An instance is the equilateral ABC-flow (A = B = C = 1). When the wavevector k is in any of the three coordinate planes, at least one of the eddy viscosities becomes negative for R = 1/v > Rc [bsime ] 1.92. This leads to a large-scale instability occurring for a value of the Reynolds number about seven times smaller than instabilities having the same spatial periodicity as the basic flow.