具有剪切和旋转的流体动力学turbulence的雷诺应力
Reynolds stresses from hydrodynamic turbulence with shear and rotation
摘要：
研究大尺度剪切和旋转作用下湍流动量输运的雷诺应力。采用三维数值模拟方法研究了均匀各向同性强迫湍流中大尺度剪切和旋转影响下的湍流输运。我们研究了三种情况：一个只有剪切，和其他两个地方，除了剪切，旋转。这些情况的不同之处在于旋转矢量相对于z方向的角度（0或90 \degr）。在旋转或剪切保持恒定的情况下，使用两个θ值执行两个运行子集。当只存在剪切时，非对角应力可以用湍流粘度来描述，而如果系统也旋转，则会出现对应力的非扩散贡献（Λ效应）。直接模拟的分析结果从一个简单的封闭模型进行了比较。我们发现，湍流粘度的顺序的一阶平滑的结果，在研究的参数制度和足够大的雷诺数的Strouhal数，描述的相关性周转时间的比率，大约是1.5。这与基于最小τ近似的闭合模型是一致的，该模型对类似Strouhal数的模拟数据产生了合理的拟合。在存在旋转的情况下，分离应力的扩散和非扩散分量是具有挑战性的，但从表面上看，我们可以获得约为湍流粘度0.1倍的非扩散贡献。我们还发现，简单的封闭模型是能够再现的数值结果的定性特征，提供的Strouhal数是为了统一。
英文摘要：
To study the Reynolds stresses which describe turbulent momentum transport from turbulence affected by large-scale shear and rotation. Three-dimensional numerical simulations are used to study turbulent transport under the influences of large-scale shear and rotation in homogeneous, isotropically forced turbulence. We study three cases: one with only shear, and two others where in addition to shear, rotation is present. These cases differ by the angle (0 or 90\degr) the rotation vector makes with respect to the z-direction. Two subsets of runs are performed with both values of θwhere either rotation or shear is kept constant. When only shear is present, the off-diagonal stress can be described by turbulent viscosity whereas if the system also rotates, nondiffusive contributions (Λ-effect) to the stress can arise. Comparison of the direct simulations are made with analytical results from a simple closure model. We find that the turbulent viscosity is of the order of the first order smoothing result in the parameter regime studied and that for sufficiently large Reynolds numbers the Strouhal number, describing the ratio of correlation to turnover times, is roughly 1.5. This is consistent with the closure model based on the minimal tau-approximation which produces a reasonable fit to the simulation data for similar Strouhal numbers. In the cases where rotation is present, separating the diffusive and nondiffusive components of the stress turns out to be challenging but taking the results at face value, we can obtain nondiffusive contributions of the order of 0.1 times the turbulent viscosity. We also find that the simple closure model is able to reproduce most of the qualitative features of the numerical results provided that the Strouhal number is of the order of unity.
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