Final equilibrium state of a two-dimensional shear layer
Final equilibrium state of a two-dimensional shear layer
复制标题
二维剪切层的最终平衡状态
DOI：
10.1017/s0022112091000642
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发表时间：
1991
影响因子：
3.7
通讯作者：
R. Robert
中科院分区：
文献类型：
--
作者：
J. Sommeria;C. Staquet;R. Robert
我们用伪谱方法，通过直接数值模拟N-S方程，检验了二维湍流中有序结构的新统计理论。我们将该理论应用于由均匀涡度带演化而来的剪切层的最终平衡态：通过在运动常数的约束下最大化一个熵来预测涡度与流函数之间的关系。然后得到了流函数的偏微分方程式。在初始涡度带非常薄的特殊情况下，斯图尔特涡旋似乎是该方程的一族解。在更一般的情况下，我们不求解方程，但我们通过检查流函数和涡量在数值计算的最终平衡状态下的关系来检验该理论。在涡度混合度较强的地区得到了很好的一致性。然而，在整个流体区发生完全混合之前，必须先达到局部平衡。
We test a new statistical theory of organized structures in two-dimensional turbulence by direct numerical stimulations of the Navier–Stokes equations, using a pseudo-spectral method. We apply the theory to the final equilibrium state of a shear layer evolving from a band of uniform vorticity: a relationship between vorticity and stream function is predicted by maximizing an entropy with the constraints due the constants of the motion. A partial differential equation for the stream function is then obtained. In the particular case of a very thin initial vorticity band, the Stuart's vortices appear to be a family of solutions for this equation. In more general cases we do not solve the equation, but we test the theory by inspecting the relationship between stream function and vorticity in the final equilibrium state of the numerical computation. An excellent agreement is obtained in regions with strong vorticity mixing. However, local equilibrium is obtained before a complete mixing can occur in the whole fluid domain.