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Direct numerical simulation and modelling of transport phenomena in rotating turbulent flow under density stratification affecting environmental variation

影响环境变化的密度分层下旋转湍流输运现象的直接数值模拟和建模

基本信息

批准号：
10450085
负责人：
NAGANO Yasutaka
金额：
$ 5.95万
依托单位：
Nagoya Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-10450085/
关键词：
Turbulent flow Rotational flow Density stratification Direct numerical simulation Turbulence model

项目摘要

The combined effects of buoyancy and Coriolis forces were investigated using direct numerical simulation (DNS) of homogeneous turbulence. First, we investigated how the mixed effects of rotation and stable stratification affect the generation and development mechanism of the vertical vortices and their asymmetry. We studied two kinds of flow fields, i.e., stably stratified rotating turbulence and thermal wind. The conclusions are as follows :Stably stratified rotating turbulence.(1) The effects of the anisotropy of Reynolds stresses and Prandtl number on the asymmetry of the vertical vortices were examined. The asymmetry of the vertical vortices is associated with vortex stretching. Vertical vortices associated with ∂u_3/∂x_3>0$ are enhanced in comparison with the other vortices with ∂u_3/∂x_3<0. In two-component and low Prandtl number cases. the anticyclones are well correlated with the stretching term ∂u_3/∂x_3>0. On the other hand, in one-component and high Prandtl number cases, the … More cyclones are correlated with it. When the vertical vortices are correlated with the positive strain rate ∂u_3/∂x_3>0, their horizontal scale becomes smaller than the internal Rossby radius of deformation.(2) At low Prandtl numbers, turbulence is two-dimensionalized and the merging of the cyclonie vortices results in the elongated Taylor columns observed in the numerical simulation with the quasi-geostrophic approximation.Thermal wind.(1) The intensity of the stable stratification affects turbulence statistics and vortical structures. When the stable stratification is weak, the vertical velocity increases and the flow field is one-componentalized. However, the flow field tends to become isotropic with an increase in the Reynolds number. On the other hand, the vertical velocity component is suppressed and the flow field tends to be two-componentalized when the stable stratification is intense. Then, the structures of the pancake-shaped vortex patches are generated.(2) When the stable stratification is weak and the flow field becomes unstable, the nonlinear vortex stretching term surpasses the incrcase in the Reynolds number. Then, the dominance of the cyclones disappears and both the cyclones and anticyclones are enhanced. When the stable stratification is intense. however, the dominance of the cyclones is still observed at relatively high Reynolds numbers.(3) The vertical vortices are generated by vortex tilting due to the mean shear in the first period, and then they are developed by the linear vortex stretching due to the Coriolis force. In addition, when the effect of the nonlinear vortex stretching is added, the cyclones become dominant.Next, the combined effects of rotation, unstable stratification and nonlinear term were studied in detail using both DNS and rapid distortion theory (RDT). The conclusions are as follows :(1) In the unstably stratified flow with rotation, the elongated vortex columns are generated in the direction parallel to the axis of rotation. These vortex columns are generated by the effect of linear vortex stretching associated with the externally imposed rotation Ω and strain rate ∂u_3/∂x_3. The linear vortex stretching is closely associated with the process of energy conversion from baroclinic vorticity to barotropic vorticity. RDT cannot generate the vortex columns, because the nonlinear term is required to suppress the oscillation and enhance the magnitude of the strain rate ∂u_3/∂x_3.(2) The time evolution of vortex columns is determined by the parameter representing the ratio of the Brunt-Vaisala frequency to the angular frequency of rotation. The vortex columns begin to emerge when both velocity and temperature fluctuations become two-dimensional, and their cross-correlation coeflicient becomes almost unity. The horizontal length scale of the vertical vortex becomes larger than the internal Rossby radius of deformation. Thus, the Coriolis force directly affects the horizontal structures of the vortex, although the buoyancy force should determine their vertical structure. Less

采用均匀湍流的直接数值模拟（DNS）研究了浮力和科里奥利力的联合效应。首先，研究了旋转和稳定分层的混合效应如何影响垂直涡的产生和发展机制及其不对称性。研究了稳定分层旋转湍流和热风两种流场。结论如下：稳定分层旋转湍流。(1)考察了雷诺应力各向异性和普朗特数对垂直涡旋不对称性的影响。垂直涡旋的不对称性与涡旋拉伸有关。与∂u_3/∂x_3> $相关的垂直涡相比，与∂u_3/∂x_3<0相关的垂直涡增强。在双组分和低普朗特数情况下。反气旋与拉伸项∂u_3/∂x_3>有很好的相关性。另一方面，在单分量和高普朗特数情况下，更多的气旋与之相关。当垂直涡旋与正应变速率∂u_3/∂x_3>相关时，其水平尺度小于内部变形的罗斯比半径。(2)在低普朗特数时，湍流是二维的，气旋涡旋的合并导致了准地转近似数值模拟中观察到的细长的泰勒柱。风热。(1)稳定分层的强度影响湍流统计和涡旋结构。当稳定分层较弱时，垂直速度增大，流场呈单分量化。随着雷诺数的增加，流场趋于各向同性。另一方面，当稳定分层强烈时，垂直速度分量受到抑制，流场趋于双分量化。然后，生成了饼状涡斑的结构。(2)当稳定分层较弱，流场变得不稳定时，非线性涡旋拉伸项超过雷诺数的增量。然后，气旋的优势消失，气旋和反气旋都增强。当稳定分层强烈时。然而，在相对较高的雷诺数下，仍然观察到气旋的优势。(3)垂直涡旋是由第一阶段平均剪切作用下的涡旋倾斜产生的，然后由科里奥利力作用下的线性涡旋拉伸发展而来。此外，当加入非线性涡旋拉伸的影响时，气旋成为主导。其次，利用DNS和快速畸变理论（RDT）详细研究了旋转、不稳定分层和非线性项的联合效应。结果表明：(1)在旋转不稳定分层流动中，沿平行于旋转轴方向产生了细长涡柱。这些漩涡柱是由与外部施加的旋转Ω和应变速率∂u_3/∂x_3相关的线性漩涡拉伸效应产生的。涡旋的线性伸展与斜压涡向正压涡的能量转换过程密切相关。RDT不能生成涡列，因为需要非线性项来抑制振荡并增强应变速率∂u_3/∂x_3的幅度。(2)旋涡柱的时间演化由表示Brunt-Vaisala频率与旋转角频率之比的参数决定。当速度波动和温度波动都变为二维时，涡柱开始出现，它们的互相关系数趋于一致。垂直涡的水平长度尺度大于内部的罗斯比变形半径。因此，科里奥利力直接影响涡旋的水平结构，尽管浮力应该决定它们的垂直结构。少