Rotating annulus experiments to study the beta-effect in atmospheric dynamics

在旋转环空实验中，我们利用锥底研究了地形的β效应，发现当锥底的斜率为0.4时，波数2的气流按照准地转位涡方程传播到层化层中，并且漂移速度比平底低。在这项研究中，我们试图在波数为1和轴对称的流动中获得更明显的β效应，因为理论上已知垂直波的传播随着波数的降低而更强。由于波数为1的流动很难产生，所以我们研究了轴对称流动。为了测量纬向速度的垂直相关性，这里发现了一个非常有用的方法：在环空的中间半径垂直投射绿色激光光片，并从侧面拍摄垂直光片的视频图像。因此，我们可以得到比波数2流动更昂贵的贝塔效应。为了直观地观察垂直流动，进一步向水中注入几滴尿氨酸溶液，并将卤素光片垂直和经向投射，我们可以得到代表流动拉格朗日轨迹的尿氨酸曲线的图片。从观察线的形状可以看出，子午线的向上垂直分量在锥形底部明显强于平坦底部。为了进行这项研究，我们访问了埃因霍温理工大学等几个研究所，向他们介绍了我们的实验，并参观了他们的实验。在那里我们可以得到有用的信息，特别是在技术点，激光光片可用于拍摄PIV分析的视频照片：墨水等染料非常有助于可视化非常缓慢的流动，在理论点上，它们支持我们的观点，即使在斜压层中，锥形底部也会引起地形β效应。

In the rotating annulus experiments, we have studied the topographic beta-effect with the use of a conical bottom and found so far that when the slope of the conical bottom is set 0.4, the wavenumber-2 flow propagates into the stratified layer according to the quasi-geostrophic potential vorticity equation and has a lower drift velocity than in the case of the flat bottom. In this research, we pursued to get more evident beta-effect in the wavenumber-1 and axisymmetric flows because the vertical wave propagations are theoretically known to be stronger as wavenumber is lower. Because it was found very difficult to produce the wavenumber-1 flow, we studied the axisymmetric flow. To measure the vertical dependence of the zonal velocities, here was found a very useful method: a green laser light sheet is projected vertically at the mid-radius of the annulus and video pictures of the vertical sheet are taken from the side. Thus, we could get a dearer beta-effect than in the wavenumber-2 flows. To see directly the vertical flow, furthermore, injecting several drops of uranine solution into the water and projected the halogen light-sheet vertically and meridionally, we could obtain pictures of curved lines of uranine to represent the Lagrangian trajectories of the flow. From the shapes of the observed lines, we could understand that the upward vertical component of the meridional flow is clearly stronger in the conical bottom than in the flat one.To proceed this study, we visited several institutes such as University of Technology at Eindhoven to give them a talk of our experiments and see their experiments. There we could get useful information, especially that in the technical points, a laser light sheet is available for taking the video pictures of PIV analysis: dye such as ink is very helpful to visualize very slow flows and in the theoretical points, they supported our idea that even in the baroclinic layer the conical bottom would cause the topographic beta-effect.