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

使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综合作用。首先，我们研究了旋转和稳定分层的混合作用如何影响垂直涡旋及其不对称的产生和发展机理。我们研究了两种流场，即稳定分层的旋转湍流和热风。结论如下：稳定分层的旋转湍流。（1）检查了雷诺应力和printTl数量对垂直涡旋的不对称性的影响。垂直涡旋的不对称性与涡旋拉伸有关。与其他涡流与∂u_3/∂x_3<0相比，与∂u_3/∂x_3> 0 $相关的垂直涡流。在两个组件和低printtl数字案例中。反气旋与拉伸项∂u_3/∂x_3> 0相关。另一方面，在一个组件和高printtl数字案例中，…更多的旋风与之相关。 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 Printtl 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 （1）稳定分层的强度影响湍流统计和涡流结构。当稳定分层较弱时，垂直速度会增加，流场是一个占地的。但是，随着雷诺数的增加，流场倾向于成为各向同性。另一方面，当稳定分层强烈时，垂直速度分量被抑制，流场往往是两国式化的。然后，生成煎饼形涡旋斑块的结构。（2）当稳定分层较弱并且流场变得不稳定时，非线性涡流拉伸项会超过雷诺数的增加。然后，旋风的优势消失了，旋风和反气旋均增强。当稳定分层很紧张时。然而，在相对较高的雷诺数数量仍然观察到旋风的优势。（3）垂直涡旋是由于第一阶段的平均剪切而通过涡旋倾斜而产生的，然后它们是由于科里奥利力引起的线性涡流拉伸而产生的。另外，当添加非线性涡旋拉伸的效果时，旋风将占主导地位。隔离，使用DNS和快速失真理论（RDT）详细研究了旋转，不稳定分层和非线性项的综合作用。结论如下：（1）在旋转的不稳定分层的流动中，伸长的涡流柱以平行于旋转轴平行的方向生成。这些涡旋列是通过与外部施加的旋转ω和应变速率∂u_3/∂x_3相关的线性涡旋拉伸的影响而产生的。线性涡旋拉伸与从斜力涡度到正压涡度的能量转化过程密切相关。 RDT无法生成涡流列，因为需要非线性项来抑制振荡并增强应变速率的幅度∂u_3/∂x_3。（2）涡流列的时间演变由代表旋转频率的Brunt-Vaisala频率的参数确定。当速度和温度波动变为二维时，涡流柱开始出现，它们的互相关系数几乎变成统一。垂直涡流的水平长度比变形的内部rossby半径大。这，尽管浮力应确定其垂直结构，但科里奥利力直接影响涡流的水平结构。较少的